R Programming for Actuarial Science

5 Fundamental Statistics: A Selection of Key Topics

Dr Alfred Kume

library(moments)
library(psych)
library(tseries)
library(nortest)
library(MASS)

5.1 Introduction

This chapter covers many of the key statistical techniques used in this book, and loosely follows some of the key concepts set out in various introductory actuarial and statistical resources. In particular, a number of topics discussed are included in statistics modules in the first year of a typical undergraduate maths-related degree. Most topics are covered relatively briefly, with the use of examples highlighting where common misunderstandings often arise. As with several chapters in this book, we recommend that the reader consults a standard statistical textbook. A number of recommended texts are included at the end of this chapter. Several references are made in this chapter which will be relevant to other parts of the book. A certain amount of background knowledge is assumed however, such as probability definitions and basic statistical theory regarding concepts of the mean and variance of a random variable.

5.2 Basic Distributions in Statistics

In general, the random variables used in probability and statistics are of two types: discrete and continuous. A random variable is discrete if it takes only a finite number of possible values with positive probability, as in the case of the Binomial distribution with ...