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StatsBetaPDF

StatsBetaPDF (x, p, q [, a, b])​

Returns the beta probability distribution function (PDF) given by

F(x;p,q,a,b)=(x−a)p−1(b−x)q−1B(p,q)(b−a)p+q−1,a≤x≤bp,q>0\displaystyle F(x;p,q,a,b)=\frac{({x - a})^{p - 1}(b-x)^{q-1}}{B(p, q)(b-a)^{p+q-1}}, \quad \begin{array}{c} a \leq x \leq b \\ p,q > 0 \end{array}

where B(p,q) is the beta function

B(p,q)=∫01tp−1(1−t)q−1dt.\displaystyle B(p, q)=\int_{0}^{1} t^{p-1}(1-t)^{q-1} d t.

The defaults (a =0 and b =1) correspond to the standard beta distribution were a is the location parameter, (b -a ) is the scale parameter, and p and q are shape parameters. When p <1 f (x =a ) returns Inf.

References​

Evans, M., N. Hastings, and B. Peacock, Statistical Distributions, 3rd ed., Wiley, New York, 2000.

See Also​

Statistical Analysis, StatsBetaCDF, StatsInvBetaCDF