lse_distribution theory.pdf

8/10/2019 LSE_Distribution Theory.pdf

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U ndergraduate study in

Economics, Management,

Finance and the Social Sciences

Advanced statistics:

distribution theory

J. Penzer

ST3133,2790133

2011

This subject guide is for a 300 course offered as part of the U niversity of London

International Program m es in Econom ics, M anagem ent, Finance and the Social Sciences.

This is equivalent to Level 6 w ithin the Fram ew ork for H igher Education Q uali cations in

England, W ales and N orthern Ireland (FH EQ ).

For m ore inform ation about the U niversity of London International Program m es

undergraduate study in Econom ics, M anagem ent, Finance and the Social Sciences, see:

w w w .londoninternational.ac.uk


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Chapter 1: Introduction

1

Chapter 1

Introduction

133 Advanced statistics: distribution theoryis a 300 courseoffered on the Economics, Management, Finance and the Social Sciences

(EMFSS) suite of progra mmes.

Uncertainty is part of life. If we w ere never in any d oubt a bout the

outcomes of our actions, our time on the plan et w ould be very dull. We all

possess an intuitive sense that some things are more certain than others. If

I knock over a glass of water, I can be pretty sure the contents will spill out;

if I throw a d art a t a d artboa rd, I might hope to hit treble tw enty but there

are many other (more likely) outcomes. Science requires us to do more than

make vague sta tements like I can be prett y sure and there a re more likely

outcomes. We need to be able to quantify our uncertainty by at ta ching

numbers to possible events. Probability is the mechanism by which wequa ntify uncertainty; distribution theory provides us w ith the t ools for

building probabilistic models of real world phenomena.

It is important t o understand t hat distribution theory provides a foundation.

The true va lue of the subject becomes apparent w hen it is applied to

questions of inference. A couple of examples of inferential q uestions follow.

1. In the UK, the process of stopping people in the street and searching

them for weapons, drugs or tools for committing burglary is referred

to a s stop and sea rch. The police collect informat ion on th e number of

crimes and the number of people they have searched each month. Their

hypothesis is that, if they reduce the number of people that they search,

crime goes up. There are a number of questions that w e might w ant to

answer. What distribution provides a reasonable model for the number

of crimes? What is the nat ure of the a ssociation betw een the number of

crimes and the number of searches? Is there a pattern in the number of

crimes over time?

2. A storm hits northern France. We have measurements of the wind speed

from 100 weat her stations and the value of insurance claims from

100,000 locations. Can we use the insurance claims information to build

a more accurate picture of w hat the w ind speeds were a cross the region

during the storm?

These are questions about w hat can be inferred from da ta . We approach these

questions using the ma thematical framework provided by distribution theory.

An a bility to q uantify uncertainty provides an evolutionary a dvanta ge;

an a nimal that can a ccurately assess the risk (becoming prey) and bene t

(catching dinner) of leaving its burrow is more likely to survive than

one that goes out hunting regardless of the danger. Although you might

not be asked to risk your skin in the world of work, a sound knowledge

of distribution theory w ill give you a competitive a dvanta ge in a ny

quantitative job. Examples of areas of industry where distribution theory

plays a key role include investment banking (particularly quantitative

an alyst jobs), insurance and ma rket research. There is also grea t dema nd

for skilled stat istician s in the public sector; for example, government

statistical services, government departments and law enforcement agencies.

Finally, distribution theory is fundamental to the models used in the

scientific professions. Medical researchers, climate researchers, social


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lse_distribution theory.pdf

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