Beta Distributions for a Given Mean, Median or Mode

plot paramater

mode

mean

median

mode

FE`userMode$$8370446560649006078357750477513218012226

mean

FE`userMean$$8370446560649006078357750477513218012226

median

FE`userMedian$$8370446560649006078357750477513218012226

α

FE`\:03b1$$8370446560649006078357750477513218012226

f

max

FE`fMax$$8370446560649006078357750477513218012226

restore initial settings

The beta distribution

f

α,β

(x)

of a random variable

x

, where

0≤x≤1

and

α,β⩾1

, has mode

x

mode

, mean

x

mean

, median

x

median

and variance

2

σ

, which are determined by

α

and

β

in a nonintuitive manner. However, once

x

mode

,

x

mean

or

x

median

has been chosen,

β

can be expressed as a function of its value and

α

becomes the sole determinant of the distribution's spread. This Demonstration calculates and plots the beta distribution's probability density function (PDF) and cumulative distribution function (CDF) for chosen values of the mode, mean or median and displays the numerical values of all three, as well as the corresponding variance.