A Versatile Four Parameter Family of Probability Distributions Suitable for Simulation

TLDR: In this paper, a family of distributions is presented, including those of the exponential, Bernoulli and uniform distributions, and properties of the distribution and methods of parameter determination are developed.

Abstract: Methods are well-known for generating random values from many common statistical distributions. These common distributions are sometimes used in simulation studies due to the lack of convenient methods of generating random values from distributions having more arbitrary shapes. A family of distributions is presented here which assumes many shapes, including those of the exponential, Bernoulli and uniform distributions. Any given first four moments may be obtained through manipulation of four parameters. The inverse cdf exists in closed form, allowing straightforward generation of random values given a source of U(0,1) values. Properties of the distribution and methods of parameter determination are developed.