Choosing the Appropriate Probability Distribution

Each type of probability distribution has its own properties, which gives every distribution the ability to represent a specific phenomenon. For example, we find that normal distribution may reliably represent concrete strength, while a logistic distribution can usefully represent an increase in population. Before building a model, one must be sure to choose the best probability distribution that represents the parameter of interest.

One may obtain the most suitable probability distribution by returning to previous references or researches, as many statistical studies have been performed for most engineering parameters. Alternatively, studying the phenomenon itself, directly, may provide a more appropriate route for selecting a suitable probability distri­bution. The second is performed through a test more than once, and the results are plotted and compared to the probability distributions.

As mentioned earlier, there is a way to choose the appropri­ate distribution mathematically, but each distribution has certain properties.

If there is raw data, as in the example of concrete strength, do the same procedure to define the frequency tables and curve by trying to choose the best probability distribution that can match with this curve.

One of the commonest methods used to choose the best prob­ability distribution that match the test results of actual measured phenomena is the Chi-Square Test.