Editing Beta distribution (section)

===Cumulative distribution function===
[[File:CDF for symmetric Beta distribution vs. x and alpha=beta - J. Rodal.jpg|thumb|CDF for symmetric beta distribution vs. ''x'' and&nbsp;''α''&nbsp;=&nbsp;''β'']]
[[File:CDF for skewed Beta distribution vs. x and beta= 5 alpha - J. Rodal.jpg|thumb|CDF for skewed beta distribution vs. ''x'' and&nbsp;''β''&nbsp;=&nbsp;5''α'']]

The [[cumulative distribution function]] is

:<math>F(x;\alpha,\beta) = \frac{\Beta{}(x;\alpha,\beta)}{\Beta{}(\alpha,\beta)} = I_x(\alpha,\beta)</math>

where <math>\Beta(x;\alpha,\beta)</math> is the [[beta function#Incomplete beta function|incomplete beta function]] and <math>I_x(\alpha,\beta)</math> is the [[regularized incomplete beta function]].

For positive integer <math> \alpha </math>, <math> \beta</math>, the cumulative distribution function of a beta distribution can be expressed in terms of the cumulative distribution function of a [[binomial distribution]] with<ref>{{cite book |last=Wadsworth |first=G. P. |title=Introduction to Probability and Random Variables |year=1960 |publisher=McGraw-Hill |location=New York  |page=[https://archive.org/details/introductiontopr0000wads/page/52 52] |url=https://archive.org/details/introductiontopr0000wads |url-access=registration }}</ref>

:<math>F_{\text{beta}}(x;\alpha,\beta) = F_{\text{binomial}}(\beta-1;\alpha+\beta-1,1-x)</math>.