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Gamma Distribution: This family has two parameters a (the shape parameter) and b (the scale parameter), and leads to a wide variety of skewed shapes for the pdf curve depending on the values of a and b. It has numerous applications.

Chi-Squared Distribution: A special case of the gamma distribution with b =2. It thus has one parameter. This is used widely in statistical inference.

Erlang Distribution: A special case of the gamma distribution with a being a positive integer. Has applications in queueing models.

Weibull Distribution: This family again has two parameters a and b with applications in several areas (e.g., reliability modeling).

Lognormal Distribution: Related to the Normal distribution - X is lognormal if ln(X) is Normal.

Beta Distribution: This distribution has four parameters: a and b (both positive) and A and B. Like the Uniform distribution the curve is zero at points outside the range A to B. Commonly used in PERT (project planning) to estimate the durations of project activities.

Student’s t-Distribution: This is an artificial distribution derived from the Normal distribution and also has lots of applications in statistical inference.

Exponential Distribution: We have already seen this independently, but it is interesting that it may also be viewed as a special case of both the gamma as well as the Weibull distribution.

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