The beta distribution is used to describe outcomes of probabilities or proportions. It works especially well when used to describe things that need a defined start and end, like projects in business management. The beta distribution is also heavily used in Bayesian statistics, which is a way of modeling statistical uncertainty.
The beta distribution can be graphed in many popular math software applications including Mathematics, Maple and Microsoft Excel. For example, Beta.Dist(x,alpha,beta,cumulative,[A],[B]) is a function used in Microsoft Excel to invoke the cumulative probability density function. In Mathematica, the command is BetaDistribution[alpha,beta] and in Maple the beta function is invoked by Beta(nu, omega).
The graph of a beta distribution can look like a straight line, a "U" shape or a simple curve up or down, depending on two letters, α and β, which define the shape of the curve. For example, if α is less than 1 and β is less than 1, the graph's shape will be a "U" and if α and β both equal 1, the graph is a straight line.
The word "Beta" applies to three different things in beta density functions, all of which can become confusing if they aren't carefully defined. Beta refers to the name of the probability distribution, the name of the function in the denominator of the density function, or the name of the second parameter in the density function.