Book contents
- Frontmatter
- Contents
- Preface to first edition
- Preface to second edition
- 1 Introduction and mathematical preliminaries
- 2 Elementary probability
- 3 Random variables and their distributions
- 4 Location and dispersion
- 5 Statistical distributions useful in general insurance work
- 6 Inferences from general insurance data
- 7 The risk premium
- 8 Experience rating
- 9 Simulation
- 10 Estimation of outstanding claim provisions
- 11 Elementary risk theory
- References
- Solutions to exercises
- Author index
- Subject index
6 - Inferences from general insurance data
Published online by Cambridge University Press: 05 June 2012
- Frontmatter
- Contents
- Preface to first edition
- Preface to second edition
- 1 Introduction and mathematical preliminaries
- 2 Elementary probability
- 3 Random variables and their distributions
- 4 Location and dispersion
- 5 Statistical distributions useful in general insurance work
- 6 Inferences from general insurance data
- 7 The risk premium
- 8 Experience rating
- 9 Simulation
- 10 Estimation of outstanding claim provisions
- 11 Elementary risk theory
- References
- Solutions to exercises
- Author index
- Subject index
Summary
Summary. In this short chapter we show how the theoretical distributions, described in chapter 5, can be used to make inferences about claim frequencies and claim sizes. We briefly outline the theory behind the testing of statistical hypotheses and give several examples. The basic concepts of point and interval estimation of claim frequency and claim size parameters are also explained. The chapter concludes with a short introduction to multivariate modelling of claim frequency rates.
Hypothesis testing
We saw in section 2.1 that many of the basic concepts of probability and statistics are readily explained in terms of games of chance. This is certainly true in respect of hypothesis testing, and we start with a coin-tossing example.
A scientist has recently been given a coin and wishes to test whether it is unbiased. The obvious experiment to carry out is to toss the coin a number of times and observe the number of ‘head’ and ‘tail’ outcomes. The scientist decides to toss the coin 1000 times. For an unbiased coin, the probability of a ‘head’ p = ½, and the expected number of ‘heads’ from the experiment is 500 (section 5.8). If the number of ‘heads’ turns out to be 511, the scientist will probably conclude that the coin is unbiased (511 is near 500); if, on the other hand, the number of ‘heads’ turns out to be 897, the scientist will be rather convinced that the coin is biased, and will reject any suggestion that it is unbiased.
- Type
- Chapter
- Information
- Introductory Statistics with Applications in General Insurance , pp. 103 - 121Publisher: Cambridge University PressPrint publication year: 1999