The 4 Parameter Beta Distribution 7 Formulas

The 4 Parameter Beta Distribution 7 Formulas

This is part of a short series on the common life data distributions.

The Beta distribution is a univariate continuous distribution. This short article focuses on 7 formulas of the Beta Distribution.

If you want to know more about fitting a set of data to a distribution, well that is in another article.

The Beta function is not used to describe life data very often yet is used to describe model parameters that are contained within an interval. For example given a probability parameter constrained from 0 ≤ p ≤ 1 the use of the Beta distribution is well suited to model such a parameter.

The Beta distribution is also known as a Pearson Type I distribution.

Parameters

The shape parameter, α, is always greater than zero. As is the second shape parameter, β, also always great then zero

The location parameter, known as the lower bound, a-sub L ranges from -∞ < a-sub L < b. For a standard Beta distribution, a-sub L = 0.

The final parameter, known as the upper bound, b-sub U ranges from a < b-sub U < ∞. For a standard Beta distribution, b-sub U = 1.