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A continuous random variable can be defined in terms of a probability density function
(pdf) which is the limit of a histogram as the sample size tends to infinity. One reason
for fitting a pdf to data is extrapolation into the tails to estimate probabilities
associated with extreme events or to make computer simulations realistic. It is necessary
to choose appropriate models for pdfs and a range of distributions that are used in
engineering are described: uniform; normal and lognormal; exponential; gamma; and Gumbel.
Procedures for fitting these distributions to data are given and a method for the graphical
assessment of the goodness of fit is described. Algorithms for the generation of pseudo-random
deviates from continuous distributions are explained and implemented with software functions.
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Table 5.2: Lifetimes of mylar-polyurethane laminated insulation.
Example 5.17: Concrete cubes.
Example 5.18: Gold grades.
Example 5.22: Times between earthquakes.
Example 5.23: Animas River.
Exercise 5.33: Fitting to data.
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