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--- beta_distribution [2019/11/18 13:34]
127.0.0.1 external edit
+++ beta_distribution [2023/01/23 10:57] (current)
daria
@@ Line 1: / Line 1: @@
 ====== Beta Distribution ======
-In probability theory and statistics, the Beta distribution is a family of continuous probability distributions defined on the interval 0,1 parametrized by two non-negative shape parameters, typically denoted by A and B.
+In probability theory and statistics, the Beta distribution is a family of continuous probability distributions defined on the interval [0,1] parametrized by two non-negative shape parameters, typically denoted by //alpha// and //beta//.
-f(x,A,B) =   x^(A-1)//(1-x^(B-1)/beta(A,B))//
+f(x,alpha,beta) =  // (x^(alpha-1)*(1-x)^(beta-1))/Beta(alpha,beta)//
+where
+//Beta// (the beta function)  is a normalization constant to ensure that the total probability is 1 and has next formula
-where   beta(z,w) = integral from 0 to 1 of t^(z-1)//(1-t)^(w-1) dt.//
+Beta(alpha,beta) = //integral from 0 to 1 of t^(alpha-1)*(1-t)^(beta-1) dt.//
-support 0 <= x <= 1
 ^Parameter^Description               ^Default value^Restriction^
-|A        |The first shape parameter |2.0          |A>0        |
+|alpha        |The first shape parameter |2.0          |alpha>0        |
-|B        |The second shape parameter|2.0          |B>0        |
+|beta         |The second shape parameter|2.0          |beta>0         |

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