StatsBetaCDF

StatsBetaCDF (x, p, q [, a, b])

The StatsBetaCDF function returns the beta cumulative distribution function

$$\displaystyle F(x,p,q,a,b)=\frac{1}{{B}({p}, {q})} \int_{0}^{\frac{x-a}{b-a}} t^{p-1}(1-t)^{q-1} d t, \quad \begin{array}{c} p, q>0 \\ a \le x \le b \end{array}$$

where B(p,q) is the beta function

$$\displaystyle B(p, q)=\int_{0}^{1} t^{p-1}(1-t)^{q-1} d t.$$

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.

References

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

See Also

Statistical Analysis, StatsBetaPDF, StatsInvBetaCDF