the mlcopulaselection package -...

The mlCopulaSelection PackageOctober 15, 2006

Type Package

Title Copula selection and fitting using maximum likelihood

Version 1.3

Date 2006-08-12

Author Jesus Garcia and Veronica Gonzalez-Lopez

Maintainer Jesus Garcia <jg@ime.unicamp.br>

Description Use numerical maximum likelihood to choose and fit a bivariate copula model (from alibrary of 40 models) to the data.

License GPL version 2.

R topics documented:clibmodel . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2dcbb1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3dcbb10 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4dcbb2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5dcbb3 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6dcbb4 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7dcbb5 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8dcbb6 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9dcbb7 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10dcbb8 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11dcbb9 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12llbb . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13llbb1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14llbb10 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15llbb1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16llbb1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17llbb1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18llbb5 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19llbb6 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20llbb7 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21llbb8 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22llbb9 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23mlCopulaSelection-package . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24

1

2 clibmodel

mlcbb . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25mlcbbsel . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27

Index 30

clibmodel Auxiliary function used by the function mlcbbsel

Description

Auxiliary function used by the function mlcbbsel

Author(s)

Jesus Garcia, IMECC-UNICAMP and Veronica Gonzalez-Lopez, IMECC-UNICAMP

References

Joe, H., (1997). Multivariate Models and Dependence Concepts. Monogra. Stat. Appl. Probab. 73,London: Chapman and Hall.

Examples

## The function is currently defined asfunction(param,x,y, model = c("CBB1", "CBB2", "CBB3", "CBB4", "CBB5", "CBB6", "CBB7","CBB8", "CBB9", "CBB10","CMM1", "CMM2", "CMM3", "CMM4", "CMM5", "CMM6", "CMM7", "CMM8", "CMM9", "CMM10","CBM1", "CBM2", "CBM3", "CBM4", "CBM5", "CBM6", "CBM7", "CBM8", "CBM9", "CBM10","CMB1", "CMB2", "CMB3", "CMB4", "CMB5", "CMB6", "CMB7", "CMB8", "CMB9", "CMB10")) {model <- match.arg(model)switch(model,

CBB1 = llbb1(param,x,y),CBB2 = llbb2(param,x,y),CBB3 = llbb3(param,x,y),CBB4 = llbb4(param,x,y),CBB5 = llbb5(param,x,y),CBB6 = llbb6(param,x,y),CBB7 = llbb7(param,x,y),CBB8 = llbb8(param,x,y),CBB9 = llbb9(param,x,y),CBB10 = llbb10(param,x,y),CMM1 = llbb1(param,1-x,1-y),CMM2 = llbb2(param,1-x,1-y),CMM3 = llbb3(param,1-x,1-y),CMM4 = llbb4(param,1-x,1-y),CMM5 = llbb5(param,1-x,1-y),CMM6 = llbb6(param,1-x,1-y),CMM7 = llbb7(param,1-x,1-y),CMM8 = llbb8(param,1-x,1-y),CMM9 = llbb9(param,1-x,1-y),CMM10 = llbb10(param,1-x,1-y),CBM1 = llbb1(param,x,1-y),CBM2 = llbb2(param,x,1-y),CBM3 = llbb3(param,x,1-y),CBM4 = llbb4(param,x,1-y),CBM5 = llbb5(param,x,1-y),CBM6 = llbb6(param,x,1-y),CBM7 = llbb7(param,x,1-y),

dcbb1 3

CBM8 = llbb8(param,x,1-y),CBM9 = llbb9(param,x,1-y),CBM10 = llbb10(param,x,1-y),CMB1 = llbb1(param,1-x,y),CMB2 = llbb2(param,1-x,y),CMB3 = llbb3(param,1-x,y),CMB4 = llbb4(param,1-x,y),CMB5 = llbb5(param,1-x,y),CMB6 = llbb6(param,1-x,y),CMB7 = llbb7(param,1-x,y),CMB8 = llbb8(param,1-x,y),CMB9 = llbb9(param,1-x,y),CMB10 = llbb10(param,1-x,y))

}

dcbb1 BB1 copula density function

Description

Calculate the value of the BB1 density.

Usage

dcbb1(theta, delta, u, v)

Arguments

theta Parameter theta of the BB1. (0<theta)

delta Parameter delta of the BB1. (1<delta)

u First coordenate where de density will be evaluated. (0<u<1)

v Second coordenate where de density will be evaluated. (0<v<1)

Value

value of de density BB1 for the parameters theta and delta on ( u , v )

Author(s)

Jesus Garcia, IMECC-UNICAMP and Veronica Gonzalez-Lopez, IMECC-UNICAMP

References

Joe, H., (1997). Multivariate Models and Dependence Concepts. Monogra. Stat. Appl. Probab. 73,London: Chapman and Hall.

4 dcbb10

Examples

res<-dcbb1(0.5,1.5,0.90,0.85)

## The function is currently defined asfunction(theta,delta,u,v){S<-u^(-theta)-1;T<-v^(-theta)-1;-10**(4)W<-S^(delta)+T^(delta);DuS<-(-theta)*u^(-theta-1);DuW<-delta*S^(delta-1)*DuS;DvT<-(-theta)*v^(-theta-1);DvW<-delta*T^(delta-1)*DvT;densi<-(-1/(theta*delta))*(-1/theta-1)*(1+W^(1/delta))^(-1/theta-2)*(1/delta)*W^(1/delta-1)*DvW*W^(1/delta-1)*DuW-(1/(theta*delta))*(1+W^(1/delta))^(-1/theta-1)*(1/delta-1)*W^(1/delta-2)*DvW*DuW}

dcbb10 BB10 copula density function

Description

Calculate the value of the BB10 density.

Usage

dcbb10(theta, delta, u, v)

Arguments

theta Parameter theta of the BB10, (0<theta<1).

delta Parameter delta of the BB10, (0<delta).

u First coordenate where de density will be evaluated. (0<u<1)

v Second coordenate where de density will be evaluated. (0<v<1)

Value

value of de density BB10 for the parameters theta and delta on ( u , v )

Author(s)

Jesus Garcia, IMECC-UNICAMP and Veronica Gonzalez-Lopez, IMECC-UNICAMP

References

Joe, H., (1997). Multivariate Models and Dependence Concepts. Monogra. Stat. Appl. Probab. 73,London: Chapman and Hall.

dcbb2 5

Examples

res<-dcbb10(1.5,1.5,0.75,0.6)

## The function is currently defined asfunction(theta,delta,u,v){S<-1-u^(1/delta);T<-1-v^(1/delta);W<-theta*S*T;C<-u*v*(1-W)^(-delta);DuS<-(-1/delta)*u^(1/delta-1);DuW<-theta*T*DuS;DvT<-(-1/delta)*v^(1/delta-1);DvW<-theta*S*DvT;DvuW<-theta*DuS*DvT;densi<-(1-W)^(-delta)+v*(-delta)*(1-W)^(-delta-1)*(-1)*DvW+u*delta*(1-W)^(-delta-1)*DuW+u*v*delta*(-delta-1)*(1-W)^(-delta-2)*(-1)*DvW*DuW+u*v*delta*(1-W)^(-delta-1)*DvuW}

dcbb2 BB2 copula density function

Description

Calculate the value of the BB2 density.

Usage

dcbb2(theta, delta, u, v)

Arguments

theta Parameter theta of the BB2, (0<theta).

delta Parameter delta of the BB2, (0<delta).

u First coordenate where de density will be evaluated. (0<u<1)

v Second coordenate where de density will be evaluated. (0<v<1)

Value

value of de density BB2 for the parameters theta and delta on ( u , v )

Author(s)

Jesus Garcia, IMECC-UNICAMP and Veronica Gonzalez-Lopez, IMECC-UNICAMP

References

Joe, H., (1997). Multivariate Models and Dependence Concepts. Monogra. Stat. Appl. Probab. 73,London: Chapman and Hall.

6 dcbb3

Examples

res<-dcbb2(0.5,0.5,0.75,0.6)

## The function is currently defined asfunction(theta,delta,u,v){k<-exp(theta*(u^(-delta)-1));t<-exp(theta*(v^(-delta)-1));S<-k+t-1;h<-(1/theta)*log(S);duk<--k*(theta*delta)*u^(-delta-1);dvt<--t*(theta*delta)*v^(-delta-1);duS<-duk;dvS<-dvt;duh<-(1/theta)*duS/S;dvh<-(1/theta)*dvS/S;dvuh<-(-1/theta)*duS*dvS/S^2;densi<-(1/delta)*(1+1/delta)*(1+h)^(-2-1/delta)*dvh*duh-(1/delta)*(1+h)^(-1-1/delta)*dvuh

}

dcbb3 BB3 copula density function

Description

Calculate the value of the BB3 density.

Usage

dcbb3(theta, delta, u, v)

Arguments

theta Parameter theta of the BB3, (0<theta).

delta Parameter delta of the BB3, (1<delta).

u First coordenate where de density will be evaluated. (0<u<1)

v Second coordenate where de density will be evaluated. (0<v<1)

Value

value of de density BB3 for the parameters theta and delta on ( u , v )

Author(s)

Jesus Garcia, IMECC-UNICAMP and Veronica Gonzalez-Lopez, IMECC-UNICAMP

References

Joe, H., (1997). Multivariate Models and Dependence Concepts. Monogra. Stat. Appl. Probab. 73,London: Chapman and Hall.

dcbb4 7

Examples

res<-dcbb3(1.5,1.5,0.75,0.6)

## The function is currently defined asfunction(theta,delta,u,v){W<-exp(theta*(-log(u))^(delta));P<-exp(theta*(-log(v))^(delta));S<-W+P-1;h<-(1/theta)*log(S);F<-exp(-h^(1/delta));duS<-exp((-log(u))^(delta)*theta)*(-theta*delta/u)*(-log(u))^(delta-1);dvS<-exp((-log(v))^(delta)*theta)*(-theta*delta/v)*(-log(v))^(delta-1);dvuh<-(-1/theta)/S^2*duS*dvS;duh<-(1/theta)*duS/S;dvh<-(1/theta)*dvS/S;densi<-F*(1/delta^2)*(h^(1/delta-1))^2*dvh*duh+F*(-1/delta)*(1/delta-1)*(h)^(1/delta-2)*(dvh)*(duh)+F*(-1/delta)*(h)^(1/delta-1)*dvuh}

dcbb4 BB4 copula density function

Description

Calculate the value of the BB4 density.

Usage

dcbb4(theta, delta, u, v)

Arguments

theta Parameter theta of the BB4, (0<theta).

delta Parameter delta of the BB4, (0<delta).

u First coordenate where de density will be evaluated. (0<u<1)

v Second coordenate where de density will be evaluated. (0<v<1)

Value

value of de density BB4 for the parameters theta and delta on ( u , v )

Author(s)

Jesus Garcia, IMECC-UNICAMP and Veronica Gonzalez-Lopez, IMECC-UNICAMP

References

Joe, H., (1997). Multivariate Models and Dependence Concepts. Monogra. Stat. Appl. Probab. 73,London: Chapman and Hall.

8 dcbb5

Examples

res<-dcbb4(1.5,1.5,0.75,0.6)

## The function is currently defined asfunction(theta,delta,u,v){VV<-(u^(-theta)-1)^(-delta);

WW<-(v^(-theta)-1)^(-delta);h<-VV+WW;S<-u^(-theta)+v^(-theta)-1;duh<-delta*theta*u^(-theta-1)*(u^(-theta)-1)^(-delta-1);dvh<-delta*theta*v^(-theta-1)*(v^(-theta)-1)^(-delta-1);duS<-(-theta)*u^(-theta-1);dvS<-(-theta)*v^(-theta-1);densi<-(1/theta)*(1/theta+1)*(S-h^(-1/delta))^(-1/theta-2)*(dvS+1/delta*h^(-1/delta-1)*dvh)*(duS+1/delta*h^(-1/delta-1)*duh)+(-1/theta)*(S-h^(-1/delta))^(-1/theta-1)*((-1/delta)*(1/delta+1)*(h)^(-1/delta-2)*dvh*duh)}

dcbb5 BB5 copula density function

Description

Calculate the value of the BB5 density.

Usage

dcbb5(theta, delta, u, v)

Arguments

theta Parameter theta of the BB5, (1<theta).

delta Parameter delta of the BB5, (0<delta).

u First coordenate where de density will be evaluated. (0<u<1)

v Second coordenate where de density will be evaluated. (0<v<1)

Value

value of de density BB5 for the parameters theta and delta on ( u , v )

Author(s)

Jesus Garcia, IMECC-UNICAMP and Veronica Gonzalez-Lopez, IMECC-UNICAMP

References

Joe, H., (1997). Multivariate Models and Dependence Concepts. Monogra. Stat. Appl. Probab. 73,London: Chapman and Hall.

dcbb6 9

Examples

res<-dcbb5(1.5,1.5,0.75,0.6)

## The function is currently defined asfunction(theta,delta,u,v){t<-(-log(u))^(-theta*delta)+(-log(v))^(-theta*delta);

dut<-(theta*delta/u)*(-log(u))^(-theta*delta-1);dvt<-(theta*delta/v)*(-log(v))^(-theta*delta-1);S<-(-log(u))^(theta)+(-log(v))^(theta);duS<-(-theta/u)*(-log(u))^(theta-1);dvS<-(-theta/v)*(-log(v))^(theta-1);h<-S-t^(-1/delta);duh<-duS+(1/delta)*(t)^(-1/delta-1)*(dut);dvh<-dvS+(1/delta)*(t)^(-1/delta-1)*(dvt);dvuh<--1/delta*(1/delta+1)*t^(-1/delta-2)*dut*dvt;densi<-exp(-h^(1/theta))*(1/theta)^2*(h^(1/theta-1))^2*dvh*duh+exp(-h^(1/theta))*(-1/theta)*(1/theta-1)*h^(1/theta-2)*dvh*duh+exp(-h^(1/theta))*(-1/theta)*h^(1/theta-1)*dvuh}

dcbb6 BB6 copula density function

Description

Calculate the value of the BB6 density.

Usage

dcbb6(t, d, u, v)

Arguments

t Parameter t of the BB6, (1<t).

d Parameter d of the BB6, (1<d).

u First coordenate where de density will be evaluated. (0<u<1)

v Second coordenate where de density will be evaluated. (0<v<1)

Value

value of de density BB6 for the parameters t and d on ( u , v )

Author(s)

Jesus Garcia, IMECC-UNICAMP and Veronica Gonzalez-Lopez, IMECC-UNICAMP

References

Joe, H., (1997). Multivariate Models and Dependence Concepts. Monogra. Stat. Appl. Probab. 73,London: Chapman and Hall.

10 dcbb7

Examples

res<-dcbb6(1.5,1.5,0.75,0.6)

## The function is currently defined asfunction(t,d,u,v){

t19 = (d*t*(-log(-(-u+1.)**t+1.))**(d-1.)*(-log(-(-v+1.)**t+1.))**(d-1.)*exp(-(-log(-(-u+1.)**t+1.))**d-(-log(-(-v+1.)**t+1.))**d)*exp(-(-log(-(-u+1.)**t+1.))**d-(-log(-(-v+1.)**t+1.))**d)**(1./d-1.)*(-u+1.)**(t-1.)*(-v+1.)**(t-1.)*(-exp(-(-log(-(-u+1.)**t+1.))**d-(-log(-(-v+1.)**t+1.))**d)**(1./d)+1.)**(1./t-1.))/(((-u+1.)**t-1.)*((-v+1.)**t-1.))-(t*(-log(-(-u+1.)**t+1.))**(d-1.)*(-log(-(-v+1.)**t+1.))**(d-1.)*exp(-(-log(-(-u+1.)**t+1.))**d-(-log(-(-v+1.)**t+1.))**d)**2*exp(-(-log(-(-u+1.)**t+1.))**d-(-log(-(-v+1.)**t+1.))**d)**(2./d-2.)*(-u+1.)**(t-1.)*(-v+1.)**(t-1.)*(1./t-1.)*(-exp(-(-log(-(-u+1.)**t+1.))**d-(-log(-(-v+1.)**t+1.))**d)**(1./d)+1.)**(1./t-2.))/(((-u+1.)**t-1.)*((-v+1.)**t-1.))+(d*t*(-log(-(-u+1.)**t+1.))**(d-1.)*(-log(-(-v+1.)**t+1.))**(d-1.)*exp(-(-log(-(-u+1.)**t+1.))**d-(-log(-(-v+1.)**t+1.))**d)**2*exp(-(-log(-(-u+1.)**t+1.))**d-(-log(-(-v+1.)**t+1.))**d)**(1./d-2.)*(-u+1.)**(t-1.)*(-v+1.)**(t-1.)*(1./d-1.)*(-exp(-(-log(-(-u+1.)**t+1.))**d-(-log(-(-v+1.)**t+1.))**d)**(1./d)+1.)**(1./t-1.))/(((-u+1.)**t-1.)*((-v+1.)**t-1.))}

dcbb7 BB7 copula density function

Description

Calculate the value of the BB7 density.

Usage

dcbb7(theta, delta, u, v)

Arguments

theta Parameter theta of the BB7, (1<theta).

delta Parameter delta of the BB7, (0<delta).

u First coordenate where de density will be evaluated. (0<u<1)

v Second coordenate where de density will be evaluated. (0<v<1)

Value

value of de density BB7 for the parameters theta and delta on ( u , v )

Author(s)

Jesus Garcia, IMECC-UNICAMP and Veronica Gonzalez-Lopez, IMECC-UNICAMP

References

Joe, H., (1997). Multivariate Models and Dependence Concepts. Monogra. Stat. Appl. Probab. 73,London: Chapman and Hall.

Examples

res<-dcbb7(1.5,1.5,0.75,0.6)

## The function is currently defined asfunction(theta,delta,u,v){WU<-(1-(1-u)^(theta))^(-delta);

WV<-(1-(1-v)^(theta))^(-delta);duWU<-(-delta*theta)*(1-(1-u)^(theta))^(-delta-1)*(1-u)^(theta-1);

dcbb8 11

dvWV<-(-delta*theta)*(1-(1-v)^(theta))^(-delta-1)*(1-v)^(theta-1);K<-WU+WV;duK<-duWU;dvK<-dvWV;S<-K-1;duS<-duK;dvS<-dvK;h<-1-S^(-1/delta);duh<-(1/delta)*S^(-1/delta-1)*duS;dvh<-(1/delta)*S^(-1/delta-1)*dvS;dvuh<-(1/delta)*(-1/delta-1)*(S)^(-1/delta-2)*(dvS)*(duS);densi<-(-1/theta)*(1/theta-1)*h^(1/theta-2)*dvh*duh-(1/theta)*h^(1/theta-1)*dvuh}

dcbb8 BB8 copula density function

Description

Calculate the value of the BB8 density.

Usage

dcbb8(theta, delta, u, v)

Arguments

theta Parameter theta of the BB8, (1<theta).

delta Parameter delta of the BB8, (0<delta<1).

u First coordenate where de density will be evaluated. (0<u<1)

v Second coordenate where de density will be evaluated. (0<v<1)

Value

value of de density BB8 for the parameters theta and delta on ( u , v )

Author(s)

Jesus Garcia, IMECC-UNICAMP and Veronica Gonzalez-Lopez, IMECC-UNICAMP

References

Joe, H., (1997). Multivariate Models and Dependence Concepts. Monogra. Stat. Appl. Probab. 73,London: Chapman and Hall.

12 dcbb9

Examples

res<-dcbb8(1.5,0.5,0.75,0.6)

## The function is currently defined asfunction(theta,delta,u,v){S<-1-(1-delta*u)^(theta);T<-1-(1-delta*v)^(theta);K<-(1-(1-delta)^(theta))^(-1);W<-1-K*S*T;DuS<-theta*delta*(1-delta*u)^(theta-1);DuW<--K*T*DuS;DvT<-theta*delta*(1-delta*v)^(theta-1);DvW<--K*S*DvT;DvuW<--K*DuS*DvT;densi<--delta^(-1)*(1/theta)*(1/theta-1)*W^(1/theta-2)*DvW*DuW-delta^(-1)*(1/theta)*W^(1/theta-1)*DvuW}

dcbb9 BB9 copula density function

Description

Calculate the value of the BB9 density.

Usage

dcbb9(theta, delta, u, v)

Arguments

theta Parameter theta of the BB9, (1<theta).

delta Parameter delta of the BB9, (0<delta).

u First coordenate where de density will be evaluated. (0<u<1)

v Second coordenate where de density will be evaluated. (0<v<1)

Value

value of de density BB9 for the parameters theta and delta on ( u , v )

Author(s)

Jesus Garcia, IMECC-UNICAMP and Veronica Gonzalez-Lopez, IMECC-UNICAMP

References

Joe, H., (1997). Multivariate Models and Dependence Concepts. Monogra. Stat. Appl. Probab. 73,London: Chapman and Hall.

llbb 13

Examples

res<-dcbb9(1.5,1.5,0.75,0.6)

## The function is currently defined asfunction(theta,delta,u,v){S<-delta-log(u);T<-delta-log(v);W<-S^(theta)+T^(theta)-delta^(theta);C<-exp(-W^(1/theta)+delta);DuS<--1/u;DuW<-theta*S^(theta-1)*DuS;DvT<--1/v;DvW<-theta*T^(theta-1)*DvT;densi<-C*(1/theta^2)*(W^(1/theta-1))^2*DvW*DuW+C*(-1/theta)*(1/theta-1)*W^(1/theta-2)*DvW*DuW}

llbb Auxiliary function used by the function mlcbbsel

Description

Auxiliary function used by the function mlcbbsel

Author(s)

Jesus Garcia, IMECC-UNICAMP and Veronica Gonzalez-Lopez, IMECC-UNICAMP

References

Joe, H., (1997). Multivariate Models and Dependence Concepts. Monogra. Stat. Appl. Probab. 73,London: Chapman and Hall.

Examples

## The function is currently defined asfunction(param,u,v, model = c("CBB1", "CBB2", "CBB3", "CBB4", "CBB5", "CBB6", "CBB7","CBB8", "CBB9", "CBB10","CMM1", "CMM2", "CMM3", "CMM4", "CMM5", "CMM6", "CMM7", "CMM8", "CMM9", "CMM10","CBM1", "CBM2", "CBM3", "CBM4", "CBM5", "CBM6", "CBM7", "CBM8", "CBM9", "CBM10","CMB1", "CMB2", "CMB3", "CMB4", "CMB5", "CMB6", "CMB7", "CMB8", "CMB9", "CMB10")){n<-sum(u>=-1)ss<-c(1:n)*0s<-0.for(i in 1:n) { ss[i]<-log(cbbmodel(param[1],param[2],u[i],v[i],model)) }res<-ss}

14 llbb1

llbb1 BB1’s log-likelihood function

Description

Calculate the log-likelihood for the BB1 density.

Usage

llbb1(param, u, v)

Arguments

param bidimensional vector with parameters c(theta,delta) (0<theta and 1<delta)

u vector with the first coordenate of the bivariate data

v vector with the second coordenate of the bivariate data (same size asu)

Details

(u,v) margins must have Uniform(0,1) marginal distribution

Value

BB1’s log-likelihood function for the sample

Author(s)

Jesus Garcia, IMECC-UNICAMP and Veronica Gonzalez-Lopez, IMECC-UNICAMP

References

Joe, H., (1997). Multivariate Models and Dependence Concepts. Monogra. Stat. Appl. Probab. 73,London: Chapman and Hall.

Examples

# The data:u <- c( 0.43, 0.1, 0.2, 0.33, 0.24, 0.29, 0.14, 0.4, 0.39, 0.8, 0.63, 0.16, 0.24, 0.14,0.71, 0.39, 0.48, 0.29, 0.38, 0.37)v <- c(0.01, 0.26, 0.2, 0.36, 0.34, 0.43, 0.27, 0.61, 0.08, 0.25, 0.72, 0.15, 0.14, 0.12, 0.74, 0.18, 0.58, 0.15, 0.34, 0.13)# The log-likelihoodr<-llbb1(c(0.5,1.5),u,v)

## The function is currently defined asfunction(param,u,v){n<-sum(u>=-1)s<-0.for(i in 1:n) { s<-s+log( dcbb1(param[1],param[2],u[i],v[i]) );if(is.nan(s)) {break};}if(is.finite(s)) {res<-s} else {res<- -10**(64)}}

llbb10 15

llbb10 BB10’s log-likelihood function

Description

Calculate the log-likelihood for the BB10 density.

Usage

llbb10(param, u, v)

Arguments

param bidimensional vector with parameters c(theta,delta) (0<theta<1 and 0<delta)

u vector with the first coordenate of the bivariate data

v vector with the second coordenate of the bivariate data (same size asu)

Details

(u,v) margins must have Uniform(0,1) marginal distribution

Value

BB10’s log-likelihood function for the sample

Author(s)

Jesus Garcia, IMECC-UNICAMP and Veronica Gonzalez-Lopez, IMECC-UNICAMP

References

Joe, H., (1997). Multivariate Models and Dependence Concepts. Monogra. Stat. Appl. Probab. 73,London: Chapman and Hall.

Examples

# The data:u <- c( 0.43, 0.1, 0.2, 0.33, 0.24, 0.29, 0.14, 0.4, 0.39, 0.8, 0.63, 0.16, 0.24, 0.14,0.71, 0.39, 0.48, 0.29, 0.38, 0.37)v <- c(0.01, 0.26, 0.2, 0.36, 0.34, 0.43, 0.27, 0.61, 0.08, 0.25, 0.72, 0.15, 0.14, 0.12, 0.74, 0.18, 0.58, 0.15, 0.34, 0.13)# The log-likelihoodr<-llbb10(c(0.5,1.5),u,v)

## The function is currently defined asfunction(param,u,v){n<-sum(u>=-1)s<-0.for(i in 1:n) { s<-s+log(dcbb10(param[1],param[2],u[i],v[i]));if(is.nan(s)) {break}; }if(is.finite(s)) {res<-s} else {res<- -10**(64)}}

16 llbb1

llbb1 BB2’s log-likelihood function

Description

Calculate the log-likelihood for the BB2 density.

Usage

llbb2(param, u, v)

Arguments

param bidimensional vector with parameters c(theta,delta) (0<theta and 0<delta)

u vector with the first coordenate of the bivariate data

v vector with the second coordenate of the bivariate data (same size asu)

Details

(u,v) margins must have Uniform(0,1) marginal distribution

Value

BB2’s log-likelihood function for the sample

Author(s)

Jesus Garcia, IMECC-UNICAMP and Veronica Gonzalez-Lopez, IMECC-UNICAMP

References

Joe, H., (1997). Multivariate Models and Dependence Concepts. Monogra. Stat. Appl. Probab. 73,London: Chapman and Hall.

Examples

# The data:u <- c( 0.43, 0.1, 0.2, 0.33, 0.24, 0.29, 0.14, 0.4, 0.39, 0.8, 0.63, 0.16, 0.24, 0.14,0.71, 0.39, 0.48, 0.29, 0.38, 0.37)v <- c(0.01, 0.26, 0.2, 0.36, 0.34, 0.43, 0.27, 0.61, 0.08, 0.25, 0.72, 0.15, 0.14, 0.12, 0.74, 0.18, 0.58, 0.15, 0.34, 0.13)# The log-likelihoodr<-llbb2(c(0.5,1.5),u,v)

## The function is currently defined asfunction(param,u,v){n<-sum(u>=-1)s<-0.for(i in 1:n) { s<-s+log(dcbb2(param[1],param[2],u[i],v[i]));if(is.nan(s)) {break}; }if(is.finite(s)) {res<-s} else {res<- -10**(64)}}

llbb1 17

llbb1 BB3’s log-likelihood function

Description

Calculate the log-likelihood for the BB3 density.

Usage

llbb3(param, u, v)

Arguments

param bidimensional vector with parameters c(theta,delta) (0<theta and 1<delta)

u vector with the first coordenate of the bivariate data

v vector with the second coordenate of the bivariate data (same size asu)

Details

(u,v) margins must have Uniform(0,1) marginal distribution

Value

BB3’s log-likelihood function for the sample

Author(s)

Jesus Garcia, IMECC-UNICAMP and Veronica Gonzalez-Lopez, IMECC-UNICAMP

References

Joe, H., (1997). Multivariate Models and Dependence Concepts. Monogra. Stat. Appl. Probab. 73,London: Chapman and Hall.

Examples

# The data:u <- c( 0.43, 0.1, 0.2, 0.33, 0.24, 0.29, 0.14, 0.4, 0.39, 0.8, 0.63, 0.16, 0.24, 0.14,0.71, 0.39, 0.48, 0.29, 0.38, 0.37)v <- c(0.01, 0.26, 0.2, 0.36, 0.34, 0.43, 0.27, 0.61, 0.08, 0.25, 0.72, 0.15, 0.14, 0.12, 0.74, 0.18, 0.58, 0.15, 0.34, 0.13)# The log-likelihoodr<-llbb3(c(1.5,1.5),u,v)

## The function is currently defined asfunction(param,u,v){n<-sum(u>=-1)s<-0.for(i in 1:n) { s<-s+log(dcbb3(param[1],param[2],u[i],v[i]));if(is.nan(s)) {break}; }if(is.finite(s)) {res<-s} else {res<- -10**(64)}}

18 llbb1

llbb1 BB4’s log-likelihood function

Description

Calculate the log-likelihood for the BB4 density.

Usage

llbb4(param, u, v)

Arguments

param bidimensional vector with parameters c(theta,delta) (0<theta and 0<delta)

u vector with the first coordenate of the bivariate data

v vector with the second coordenate of the bivariate data (same size asu)

Details

(u,v) margins must have Uniform(0,1) marginal distribution

Value

BB4’s log-likelihood function for the sample

Author(s)

Jesus Garcia, IMECC-UNICAMP and Veronica Gonzalez-Lopez, IMECC-UNICAMP

References

Joe, H., (1997). Multivariate Models and Dependence Concepts. Monogra. Stat. Appl. Probab. 73,London: Chapman and Hall.

Examples

# The data:u <- c( 0.43, 0.1, 0.2, 0.33, 0.24, 0.29, 0.14, 0.4, 0.39, 0.8, 0.63, 0.16, 0.24, 0.14,0.71, 0.39, 0.48, 0.29, 0.38, 0.37)v <- c(0.01, 0.26, 0.2, 0.36, 0.34, 0.43, 0.27, 0.61, 0.08, 0.25, 0.72, 0.15, 0.14, 0.12, 0.74, 0.18, 0.58, 0.15, 0.34, 0.13)# The log-likelihoodr<-llbb4(c(0.5,1.5),u,v)

## The function is currently defined asfunction(param,u,v){n<-sum(u>=-1)s<-0.for(i in 1:n) { s<-s+log(dcbb4(param[1],param[2],u[i],v[i]));if(is.nan(s)) {break}; }if(is.finite(s)) {res<-s} else {res<- -10**(64)}}

llbb5 19

llbb5 BB5’s log-likelihood function

Description

Calculate the log-likelihood for the BB5 density.

Usage

llbb5(param, u, v)

Arguments

param bidimensional vector with parameters c(theta,delta) (1<theta and 0<delta)

u vector with the first coordenate of the bivariate data

v vector with the second coordenate of the bivariate data (same size asu)

Details

(u,v) margins must have Uniform(0,1) marginal distribution

Value

BB5’s log-likelihood function for the sample

Author(s)

Jesus Garcia, IMECC-UNICAMP and Veronica Gonzalez-Lopez, IMECC-UNICAMP

References

Joe, H., (1997). Multivariate Models and Dependence Concepts. Monogra. Stat. Appl. Probab. 73,London: Chapman and Hall.

Examples

# The data:u <- c( 0.43, 0.1, 0.2, 0.33, 0.24, 0.29, 0.14, 0.4, 0.39, 0.8, 0.63, 0.16, 0.24, 0.14,0.71, 0.39, 0.48, 0.29, 0.38, 0.37)v <- c(0.01, 0.26, 0.2, 0.36, 0.34, 0.43, 0.27, 0.61, 0.08, 0.25, 0.72, 0.15, 0.14, 0.12, 0.74, 0.18, 0.58, 0.15, 0.34, 0.13)# The log-likelihoodr<-llbb5(c(1.5,1.5),u,v)

## The function is currently defined asfunction(param,u,v){n<-sum(u>=-1)s<-0.for(i in 1:n) { s<-s+log(dcbb5(param[1],param[2],u[i],v[i]));if(is.nan(s)) {break}; }if(is.finite(s)) {res<-s} else {res<- -10**(64)}}

20 llbb6

llbb6 BB6’s log-likelihood function

Description

Calculate the log-likelihood for the BB6 density.

Usage

llbb6(param, u, v)

Arguments

param bidimensional vector with parameters c(theta,delta) (1<theta and 1<delta)

u vector with the first coordenate of the bivariate data

v vector with the second coordenate of the bivariate data (same size asu)

Details

(u,v) margins must have Uniform(0,1) marginal distribution

Value

BB6’s log-likelihood function for the sample

Author(s)

Jesus Garcia, IMECC-UNICAMP and Veronica Gonzalez-Lopez, IMECC-UNICAMP

References

Joe, H., (1997). Multivariate Models and Dependence Concepts. Monogra. Stat. Appl. Probab. 73,London: Chapman and Hall.

Examples

# The data:u <- c( 0.43, 0.1, 0.2, 0.33, 0.24, 0.29, 0.14, 0.4, 0.39, 0.8, 0.63, 0.16, 0.24, 0.14,0.71, 0.39, 0.48, 0.29, 0.38, 0.37)v <- c(0.01, 0.26, 0.2, 0.36, 0.34, 0.43, 0.27, 0.61, 0.08, 0.25, 0.72, 0.15, 0.14, 0.12, 0.74, 0.18, 0.58, 0.15, 0.34, 0.13)# The log-likelihoodr<-llbb6(c(1.5,1.5),u,v)

## The function is currently defined asfunction(param,u,v){n<-sum(u>=-1)s<-0.for(i in 1:n) { s<-s+log(dcbb6(param[1],param[2],u[i],v[i]));if(is.nan(s)) {break}; }if(is.finite(s)) {res<-s} else {res<- -10**(64)}}

llbb7 21

llbb7 BB7’s log-likelihood function

Description

Calculate the log-likelihood for the BB7 density.

Usage

llbb7(param, u, v)

Arguments

param bidimensional vector with parameters c(theta,delta) (1<theta and 0<delta)

u vector with the first coordenate of the bivariate data

v vector with the second coordenate of the bivariate data (same size asu)

Details

(u,v) margins must have Uniform(0,1) marginal distribution

Value

BB7’s log-likelihood function for the sample

Author(s)

Jesus Garcia, IMECC-UNICAMP and Veronica Gonzalez-Lopez, IMECC-UNICAMP

References

Joe, H., (1997). Multivariate Models and Dependence Concepts. Monogra. Stat. Appl. Probab. 73,London: Chapman and Hall.

Examples

# The data:u <- c( 0.43, 0.1, 0.2, 0.33, 0.24, 0.29, 0.14, 0.4, 0.39, 0.8, 0.63, 0.16, 0.24, 0.14,0.71, 0.39, 0.48, 0.29, 0.38, 0.37)v <- c(0.01, 0.26, 0.2, 0.36, 0.34, 0.43, 0.27, 0.61, 0.08, 0.25, 0.72, 0.15, 0.14, 0.12, 0.74, 0.18, 0.58, 0.15, 0.34, 0.13)# The log-likelihoodr<-llbb7(c(1.5,1.5),u,v)

## The function is currently defined asfunction(param,u,v){n<-sum(u>=-1)s<-0.for(i in 1:n) { s<-s+log(dcbb7(param[1],param[2],u[i],v[i]));if(is.nan(s)) {break}; }if(is.finite(s)) {res<-s} else {res<- -10**(64)}}

22 llbb8

llbb8 BB8’s log-likelihood function

Description

Calculate the log-likelihood for the BB8 density.

Usage

llbb8(param, u, v)

Arguments

param bidimensional vector with parameters c(theta,delta) (1<theta and 0<delta<1)

u vector with the first coordenate of the bivariate data

v vector with the second coordenate of the bivariate data (same size asu)

Details

(u,v) margins must have Uniform(0,1) marginal distribution

Value

BB8’s log-likelihood function for the sample

Author(s)

Jesus Garcia, IMECC-UNICAMP and Veronica Gonzalez-Lopez, IMECC-UNICAMP

References

Joe, H., (1997). Multivariate Models and Dependence Concepts. Monogra. Stat. Appl. Probab. 73,London: Chapman and Hall.

Examples

# The data:u <- c( 0.43, 0.1, 0.2, 0.33, 0.24, 0.29, 0.14, 0.4, 0.39, 0.8, 0.63, 0.16, 0.24, 0.14,0.71, 0.39, 0.48, 0.29, 0.38, 0.37)v <- c(0.01, 0.26, 0.2, 0.36, 0.34, 0.43, 0.27, 0.61, 0.08, 0.25, 0.72, 0.15, 0.14, 0.12, 0.74, 0.18, 0.58, 0.15, 0.34, 0.13)# The log-likelihoodr<-llbb8(c(1.5,0.5),u,v)

## The function is currently defined asfunction(param,u,v){n<-sum(u>=-1)s<-0.for(i in 1:n) { s<-s+log(dcbb8(param[1],param[2],u[i],v[i]));if(is.nan(s)) {break}; }if(is.finite(s)) {res<-s} else {res<- -10**(64)}}

llbb9 23

llbb9 BB9’s log-likelihood function

Description

Calculate the log-likelihood for the BB9 density.

Usage

llbb9(param, u, v)

Arguments

param bidimensional vector with parameters c(theta,delta) (1<theta and 0<delta)

u vector with the first coordenate of the bivariate data

v vector with the second coordenate of the bivariate data (same size asu)

Details

(u,v) margins must have Uniform(0,1) marginal distribution

Value

BB9’s log-likelihood function for the sample

Author(s)

Jesus Garcia, IMECC-UNICAMP and Veronica Gonzalez-Lopez, IMECC-UNICAMP

References

Joe, H., (1997). Multivariate Models and Dependence Concepts. Monogra. Stat. Appl. Probab. 73,London: Chapman and Hall.

Examples

# The data:u <- c( 0.43, 0.1, 0.2, 0.33, 0.24, 0.29, 0.14, 0.4, 0.39, 0.8, 0.63, 0.16, 0.24, 0.14,0.71, 0.39, 0.48, 0.29, 0.38, 0.37)v <- c(0.01, 0.26, 0.2, 0.36, 0.34, 0.43, 0.27, 0.61, 0.08, 0.25, 0.72, 0.15, 0.14, 0.12, 0.74, 0.18, 0.58, 0.15, 0.34, 0.13)# The log-likelihoodr<-llbb9(c(1.5,1.5),u,v)

## The function is currently defined asfunction(param,u,v){n<-sum(u>=-1)s<-0.for(i in 1:n) { s<-s+log(dcbb9(param[1],param[2],u[i],v[i]));if(is.nan(s)) {break}; }if(is.finite(s)) {res<-s} else {res<- -10**(64)}}

24 mlCopulaSelection-package

mlCopulaSelection-packageCopula selection and fitting using maximum likelihood

Description

Use numerical maximum likelihood to choose and fit a bivariate copula model (from a library of 40models) to the data. The copula models in the library correspond to BB1, BB2,...,BB10 from Joe,H., (1997) and its 90, 180 and 270 degree rotations.

Details

Package: mlCopulaSelectionType: PackageVersion: 1.3Date: 2006-08-12License: GPL version 2.

Author(s)

Jesus Garcia, IMECC-UNICAMP and Veronica Gonzalez-Lopez, IMECC-UNICAMP

Maintainer: Jesus Garcia <jg@ime.unicamp.br>

References

Joe, H., (1997). Multivariate Models and Dependence Concepts. Monogra. Stat. Appl. Probab. 73,London: Chapman and Hall.

Examples

# The Data (the margins are uniform)U <- c( 0.43, 0.1, 0.2, 0.33, 0.24, 0.29, 0.14, 0.4, 0.39, 0.8, 0.63, 0.16, 0.24, 0.14,0.71, 0.39, 0.48, 0.29, 0.38, 0.37)V <- c(0.01, 0.26, 0.2, 0.36, 0.34, 0.43, 0.27, 0.61, 0.08, 0.25, 0.72, 0.15, 0.14, 0.12, 0.74, 0.18, 0.58, 0.15, 0.34, 0.13)# find the maximun likelihood estimatesres<-mlcbbsel(U,V)#the best fitting copula model:res$copmax#the parameters for the best fitting copula model:res$parmax#the log-likelihood of the best fitting copula model with those parameters:res$llmax

mlcbb 25

mlcbb Auxiliary function used by the function mlcbbsel

Description

Auxiliary function used by the function mlcbbsel

Author(s)

Jesus Garcia, IMECC-UNICAMP and Veronica Gonzalez-Lopez, IMECC-UNICAMP

References

Joe, H., (1997). Multivariate Models and Dependence Concepts. Monogra. Stat. Appl. Probab. 73,London: Chapman and Hall.

Examples

## The function is currently defined asfunction(u,v,thetamin,deltamin,thetamax,deltamax, copulamodel=c("CBB1","CBB2" , "CBB3","CBB4","CBB5","CBB6", "CBB7","CBB8", "CBB9", "CBB10","CMM1", "CMM2", "CMM3", "CMM4", "CMM5", "CMM6", "CMM7", "CMM8", "CMM9", "CMM10","CBM1", "CBM2", "CBM3", "CBM4", "CBM5", "CBM6", "CBM7", "CBM8", "CBM9", "CBM10","CMB1", "CMB2", "CMB3", "CMB4", "CMB5", "CMB6", "CMB7", "CMB8", "CMB9", "CMB10")){PMAX<-0

DMAX<-20TMAX<-20if(missing(deltamax)){deltamax<- DMAX}if(missing(thetamax)){thetamax<- TMAX}

if(missing(deltamin) && copulamodel=="CBB1"){deltamin<-1.005};if(missing(deltamin) && copulamodel=="CBB2"){deltamin<-0.005};if(missing(deltamin) && copulamodel=="CBB3"){deltamin<-1.005};if(missing(deltamin) && copulamodel=="CBB4"){deltamin<-0.005};if(missing(deltamin) && copulamodel=="CBB5"){deltamin<-0.005};if(missing(deltamin) && copulamodel=="CBB6"){deltamin<-1.005};if(missing(deltamin) && copulamodel=="CBB7"){deltamin<-0.005};if(missing(deltamin) && copulamodel=="CBB8"){deltamin<-0.005};if(missing(deltamax) && copulamodel=="CBB8"){deltamax<-0.995};if(deltamax==DMAX && copulamodel=="CBB8"){deltamax<-0.995}if(missing(deltamin) && copulamodel=="CBB9"){deltamin<-0.005};if(missing(deltamin) && copulamodel=="CBB10"){deltamin<-0.005};

if(missing(deltamin) && copulamodel=="CMM1"){deltamin<-1.005};if(missing(deltamin) && copulamodel=="CMM2"){deltamin<-0.005};if(missing(deltamin) && copulamodel=="CMM3"){deltamin<-1.005};if(missing(deltamin) && copulamodel=="CMM4"){deltamin<-0.005};if(missing(deltamin) && copulamodel=="CMM5"){deltamin<-0.005};if(missing(deltamin) && copulamodel=="CMM6"){deltamin<-1.005};if(missing(deltamin) && copulamodel=="CMM7"){deltamin<-0.005};if(missing(deltamin) && copulamodel=="CMM8"){deltamin<-0.005};if(missing(deltamax) && copulamodel=="CMM8"){deltamax<-0.995};if(deltamax==DMAX && copulamodel=="CMM8"){deltamax<-0.995}if(missing(deltamin) && copulamodel=="CMM9"){deltamin<-0.005};if(missing(deltamin) && copulamodel=="CMM10"){deltamin<-0.005};

26 mlcbb

if(missing(deltamin) && copulamodel=="CBM1"){deltamin<-1.005};if(missing(deltamin) && copulamodel=="CBM2"){deltamin<-0.005};if(missing(deltamin) && copulamodel=="CBM3"){deltamin<-1.005};if(missing(deltamin) && copulamodel=="CBM4"){deltamin<-0.005};if(missing(deltamin) && copulamodel=="CBM5"){deltamin<-0.005};if(missing(deltamin) && copulamodel=="CBM6"){deltamin<-1.005};if(missing(deltamin) && copulamodel=="CBM7"){deltamin<-0.005};if(missing(deltamin) && copulamodel=="CBM8"){deltamin<-0.005};if(missing(deltamax) && copulamodel=="CBM8"){deltamax<-0.995};if(deltamax==DMAX && copulamodel=="CBM8"){deltamax<-0.995}if(missing(deltamin) && copulamodel=="CBM9"){deltamin<-0.005};if(missing(deltamin) && copulamodel=="CBM10"){deltamin<-0.005};

if(missing(deltamin) && copulamodel=="CMB1"){deltamin<-1.005};if(missing(deltamin) && copulamodel=="CMB2"){deltamin<-0.005};if(missing(deltamin) && copulamodel=="CMB3"){deltamin<-1.005};if(missing(deltamin) && copulamodel=="CMB4"){deltamin<-0.005};if(missing(deltamin) && copulamodel=="CMB5"){deltamin<-0.005};if(missing(deltamin) && copulamodel=="CMB6"){deltamin<-1.005};if(missing(deltamin) && copulamodel=="CMB7"){deltamin<-0.005};if(missing(deltamin) && copulamodel=="CMB8"){deltamin<-0.005};if(missing(deltamax) && copulamodel=="CMB8"){deltamax<-0.995};if(deltamax==DMAX && copulamodel=="CMB8"){deltamax<-0.995}if(missing(deltamin) && copulamodel=="CMB9"){deltamin<-0.005};if(missing(deltamin) && copulamodel=="CMB10"){deltamin<-0.005};

if(missing(thetamin) && copulamodel=="CBB1"){thetamin<-0.005};if(missing(thetamin) && copulamodel=="CBB2"){thetamin<-0.005};if(missing(thetamin) && copulamodel=="CBB3"){thetamin<-0.005};if(missing(thetamin) && copulamodel=="CBB4"){thetamin<-0.005};if(missing(thetamin) && copulamodel=="CBB5"){thetamin<-1.005};if(missing(thetamin) && copulamodel=="CBB6"){thetamin<-1.005};if(missing(thetamin) && copulamodel=="CBB7"){thetamin<-1.005};if(missing(thetamin) && copulamodel=="CBB8"){thetamin<-1.005};if(missing(thetamin) && copulamodel=="CBB9"){thetamin<-1.005};if(missing(thetamin) && copulamodel=="CBB10"){thetamin<-0.005};if(missing(thetamax) && copulamodel=="CBB10"){thetamax<-0.995};if(thetamax==TMAX && copulamodel=="CBB10"){thetamax<-0.995}

if(missing(thetamin) && copulamodel=="CMM1"){thetamin<-0.005};if(missing(thetamin) && copulamodel=="CMM2"){thetamin<-0.005};if(missing(thetamin) && copulamodel=="CMM3"){thetamin<-0.005};if(missing(thetamin) && copulamodel=="CMM4"){thetamin<-0.005};if(missing(thetamin) && copulamodel=="CMM5"){thetamin<-1.005};if(missing(thetamin) && copulamodel=="CMM6"){thetamin<-1.005};if(missing(thetamin) && copulamodel=="CMM7"){thetamin<-1.005};if(missing(thetamin) && copulamodel=="CMM8"){thetamin<-1.005};if(missing(thetamin) && copulamodel=="CMM9"){thetamin<-1.005};if(missing(thetamin) && copulamodel=="CMM10"){thetamin<-0.005};if(missing(thetamax) && copulamodel=="CMM10"){thetamax<-0.995};if(thetamax==TMAX && copulamodel=="CMM10"){thetamax<-0.995}

mlcbbsel 27

if(missing(thetamin) && copulamodel=="CBM1"){thetamin<-0.005};if(missing(thetamin) && copulamodel=="CBM2"){thetamin<-0.005};if(missing(thetamin) && copulamodel=="CBM3"){thetamin<-0.005};if(missing(thetamin) && copulamodel=="CBM4"){thetamin<-0.005};if(missing(thetamin) && copulamodel=="CBM5"){thetamin<-1.005};if(missing(thetamin) && copulamodel=="CBM6"){thetamin<-1.005};if(missing(thetamin) && copulamodel=="CBM7"){thetamin<-1.005};if(missing(thetamin) && copulamodel=="CBM8"){thetamin<-1.005};if(missing(thetamin) && copulamodel=="CBM9"){thetamin<-1.005};if(missing(thetamin) && copulamodel=="CBM10"){thetamin<-0.005};if(missing(thetamax) && copulamodel=="CBM10"){thetamax<-0.995};if(thetamax==TMAX && copulamodel=="CBM10"){thetamax<-0.995}

if(missing(thetamin) && copulamodel=="CMB1"){thetamin<-0.005};if(missing(thetamin) && copulamodel=="CMB2"){thetamin<-0.005};if(missing(thetamin) && copulamodel=="CMB3"){thetamin<-0.005};if(missing(thetamin) && copulamodel=="CMB4"){thetamin<-0.005};if(missing(thetamin) && copulamodel=="CMB5"){thetamin<-1.005};if(missing(thetamin) && copulamodel=="CMB6"){thetamin<-1.005};if(missing(thetamin) && copulamodel=="CMB7"){thetamin<-1.005};if(missing(thetamin) && copulamodel=="CMB8"){thetamin<-1.005};if(missing(thetamin) && copulamodel=="CMB9"){thetamin<-1.005};if(missing(thetamin) && copulamodel=="CMB10"){thetamin<-0.005};if(missing(thetamax) && copulamodel=="CMB10"){thetamax<-0.995};if(thetamax==TMAX && copulamodel=="CMB10"){thetamax<-0.995}

n<-sum(u>=-1)m<-5inct<-(thetamax-thetamin)/(m+1)incd<-(deltamax-deltamin)/(m+1)PMAX <- -10**(250)for (tet in 1:m){ for (del in 1:m){teta <- thetamin + tet*inctdelta <- deltamin + del*incd

pvalor<-clibmodel(c(teta,delta),u,v,model=copulamodel)

if (pvalor>PMAX) { PMAX <- pvalor; tlmax<- teta ; dlmax <- delta }} }

result<-optim(c(tlmax,dlmax), method = "L-BFGS-B" , clibmodel,lower = c(thetamin,deltamin), upper = c(thetamax,deltamax) , control=list(fnscale=-1), x=u , y=v , model = copulamodel )

}

mlcbbsel Function for maximum likelihood copula selection and fitting

28 mlcbbsel

Description

Use numerical maximum likelihood to choose and fit a bivariate copula model (from a library of 40models) to the data.

Usage

mlcbbsel(U, V)

Arguments

U vector with the first coordenate of the bivariate data

V vector with the second coordenate of the bivariate data (same size asU)

Details

(U,V) margins must have Uniform(0,1) marginal distribution

Value

It return a LIST with,

copmax the best fitting copula model. The copula models in the library correspond toBB1, BB2,...,BB10 from Joe, H., (1997) and its 90, 180 and 270 degree rota-tions.

parmax the maximum likelihood estimates of the parameters for the best fitting copula

llmax the log-likelihood on the estimated parameters for the best copula

todo contain a matrix with the maximum likelihood ressults for all the copula models.The first column is the copulamodel number (from 1 to 40), the second columnis the maximum log-likelihood for that particular model and the third and fourthcolumn contain the parameters values for which that maximum log-likelihoodwas attained.

Author(s)

Jesus Garcia. IMECC-UNICAMP and Veronica Gonzalez-Lopez. IMECC-UNICAMP

References

Joe, H., (1997). Multivariate Models and Dependence Concepts. Monogra. Stat. Appl. Probab. 73,London: Chapman and Hal l.

Examples

# The Data (the margins are uniform)U <- c( 0.43, 0.1, 0.2, 0.33, 0.24, 0.29, 0.14, 0.4, 0.39, 0.8, 0.63, 0.16, 0.24, 0.14,0.71, 0.39, 0.48, 0.29, 0.38, 0.37)V <- c(0.01, 0.26, 0.2, 0.36, 0.34, 0.43, 0.27, 0.61, 0.08, 0.25, 0.72, 0.15, 0.14, 0.12, 0.74, 0.18, 0.58, 0.15, 0.34, 0.13)# find the maximun likelihood estimatesres<-mlcbbsel(U,V)#the best fitting copula model:res$copmax#the parameters for the best fitting copula model:res$parmax#the log-likelihood of the best fitting copula model with those parameters:

mlcbbsel 29

res$llmax

## The function is currently defined asfunction(U,V){

model=c("CBB1","CBB2" , "CBB3","CBB4","CBB5","CBB6", "CBB7","CBB8", "CBB9", "CBB10","CMM1", "CMM2", "CMM3", "CMM4", "CMM5", "CMM6", "CMM7", "CMM8", "CMM9", "CMM10","CBM1", "CBM2", "CBM3", "CBM4", "CBM5", "CBM6", "CBM7", "CBM8", "CBM9", "CBM10","CMB1", "CMB2", "CMB3", "CMB4", "CMB5", "CMB6", "CMB7", "CMB8", "CMB9", "CMB10")

respmodel=c("CBB1","CBB2" , "CBB3","CBB4","CBB5","CBB6", "CBB7","CBB8", "CBB9", "CBB10","180 degree rotation of CBB1","180 degree rotation of CBB2" , "180 degree rotation of CBB3","180 degree rotation of CBB4","180 degree rotation of CBB5","180 degree rotation of CBB6", "180 degree rotation of CBB7","180 degree rotation of CBB8", "180 degree rotation of CBB9", "180 degree rotation of CBB10","90 degree rotation of CBB1","90 degree rotation of CBB2" , "90 degree rotation of CBB3","90 degree rotation of CBB4","90 degree rotation of CBB5","90 degree rotation of CBB6", "90 degree rotation of CBB7","90 degree rotation of CBB8", "90 degree rotation of CBB9", "90 degree rotation of CBB10","270 degree rotation of CBB1","270 degree rotation of CBB2" , "270 degree rotation of CBB3","270 degree rotation of CBB4","270 degree rotation of CBB5","270 degree rotation of CBB6", "270 degree rotation of CBB7","270 degree rotation of CBB8", "270 degree rotation of CBB9", "270 degree rotation of CBB10")

ncop<-1

TODOCOP <-c(1:40)TODOPV <-c(1:2)*0TODOTET <-c(1:2)*0TODODEL <-c(1:2)*0PVMAX<- -10**(100)pmax<-10

n<-sum(U != -10**200)

for(nmodel in 1:40){RES <- mlcbb(U,V,copulamodel=model[nmodel])PV <- RES$valuePAR<- RES$parif (PV>PVMAX) {PVMAX<-PV;PARMAX<-PAR;COPMAX<-nmodel;LLMAX<-PV}TODOPV[nmodel]<- PVTODOTET[nmodel] <-PAR[1]TODODEL[nmodel] <-PAR[2]}

ORDEN<-order(TODOPV,TODOCOP,decreasing= TRUE)

TODO<-matrix(c(1:40*4)*0,40,4)

TODO[,1]<-respmodel[TODOCOP[ORDEN]]TODO[,2]<-TODOPV[ORDEN]TODO[,3]<-TODOTET[ORDEN]TODO[,4]<-TODODEL[ORDEN]

result <- list(todo=TODO,copmax=respmodel[COPMAX],parmax=PARMAX,llmax=LLMAX)}

Index

∗Topic documentationmlCopulaSelection-package, 23

∗Topic internalclibmodel, 1llbb, 12mlcbb, 24

∗Topic miscdcbb1, 2dcbb10, 3dcbb2, 4dcbb3, 5dcbb4, 6dcbb5, 7dcbb6, 8dcbb7, 9dcbb8, 10dcbb9, 11llbb1, 13, 15–17llbb10, 14llbb5, 18llbb6, 19llbb7, 20llbb8, 21llbb9, 22mlcbbsel, 26

clibmodel, 1

dcbb1, 2dcbb10, 3dcbb2, 4dcbb3, 5dcbb4, 6dcbb5, 7dcbb6, 8dcbb7, 9dcbb8, 10dcbb9, 11

llbb, 12llbb1, 13, 15–17llbb10, 14llbb2 (llbb1), 15llbb3 (llbb1), 16

llbb4 (llbb1), 17llbb5, 18llbb6, 19llbb7, 20llbb8, 21llbb9, 22

mlcbb, 24mlcbbsel, 26mlCopulaSelection

(mlCopulaSelection-package),23

mlCopulaSelection-package, 23

30