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
4 - Location and dispersion
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: The mean is introduced as a measure of the location of a statistical distribution and the variance as a measure of dispersion around that mean. These concepts are essential to the understanding of much of the material in later chapters. Expectations, moments and skewness are also discussed. More advanced topics treated include conditional means and variances.
Measures of location – mean, median and mode
A distribution of claim frequency is given in table 4.1.1 and depicted in fig. 4.1.1. It is immediately apparent that the probability that the number of claims will lie between 5 and 15, inclusive, is very high (over 90%). In other words, we would expect the number of claims to be somewhere near a central value of about 10 with a high probability. Three different statistics or measures are commonly used to describe the centre of such a distribution. These are the mode, the median and the mean.
The mode is the value most likely to occur (10 in our example). The median is the value which divides the distribution in half. In other words, it is just as likely that the random variable will take a value less than the median as it is for it to take a value greater than the median. In our example F(9) = 0.421 and F(10) = 0.545, and, by convention, we take 10 as the median.
The mean, however, is the most commonly used measure of central tendency in general insurance work, and the only one we use in this book.
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- Information
- Publisher: Cambridge University PressPrint publication year: 1999