Does the random variable follow a stochastic process with a well-known model?

See also: Fitting distributions to data, Fitting in ModelRisk, Analyzing and using data introduction

Many theoretical distributions have developed as a result of modelling specific types of probability problems. These distributions then find a wider use in other problems that have the same mathematical structure. Examples include: the times between telephone calls at a telephone exchange or fires in a railway system are accurately represented by an Exponential distribution; the time until failure of an electronics component may be represented by a Weibull distribution; how many treble 20s a darts player will score with a specific number of darts by a Binomial distribution; the number of cars going through a road junction in any one hour by a Poisson distribution; and the heights of the tallest and shortest children in UK school classes by Gumbel distributions. If a distribution can be found with the same mathematical basis as the variable being modelled, it only remains to find the appropriate parameters to define the distribution. In order to take advantage of the solutions that many probability distributions provides, you must first be familiar with the different stochastic processes they belong to.

 
 

 

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