Beta Distribution

Beta distribution is a very important topics of statistics

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In probability theory and statistics, the beta distribution is a family of continuous probability distributions defined on the interval [0, 1] parametrized by two positive shape parameters, denoted by and , that appear as exponents of the random variable and control the shape of the distribution. The beta distribution has been applied to model the behavior of random variables limited to intervals of finite length in a wide variety of disciplines. In population genetics it has been employed for a statistical description of the allele frequencies in the components of a sub-divided population.[1] It has been utilized in PERT,[2] critical path method (CPM) and other project management / control systems to describe the statistical distributions of the time to completion and the cost of a task.

Let us see about mean beta distribution. The beta distribution is a relation of prospect theory and statistics. It is specified by . The beta distribution should contain the intervals between (0, 1). The beta function is also described as Euler integral. The beta distribution models are inhibited to take place within an interval like minimum to maximum value. The mean of beta distribution is from minimum to maximum. In mean function, and value should have positive parameters.

Beta Distribution Formula

The probable distribution of a arbitrary variable with density function (x) = [x-1(1-x)-1]/B(,), where B represents the beta function, and are positive real numbers, and 0

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