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The beta distribution represents continuous probability distribution parametrized by two positive shape parameters, $ alpha $ and $ beta $, which appear as exponents of the random variable x and control the shape of the distribution.
Probability density function
Probability density function of Beta distribution is given as:
Formula
, where B(alpha,beta) = int_{0}^{1} {t^{alpha-1}(1-t)^{beta-1}dt} }$
Where −
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${ alpha, beta }$ = shape parameters.
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${a, b}$ = upper and lower bounds.
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${B(alpha,beta)}$ = Beta function.
Standard Beta Distribution
In case of having upper and lower bounds as 1 and 0, beta distribution is called the standard beta distribution. It is driven by following formula:
Formula
Cumulative distribution function
Cumulative distribution function of Beta distribution is given as:
Formula
hspace{.2in} 0 le x le 1; p, beta > 0 }$
Where −
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${ alpha, beta }$ = shape parameters.
-
${a, b}$ = upper and lower bounds.
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${B(alpha,beta)}$ = Beta function.
It is also called incomplete beta function ratio.
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