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IMSL_BETACDF

# IMSL_BETACDF

The IMSL_BETACDF function evaluates the beta probability distribution function.

The IMSL_BETACDF function evaluates the distribution function of a beta random variable with parameters pin and qin. This function is sometimes called the incomplete beta ratio and is denoted by Ix(p, q), where p = pin and q = qin. It is given by:

where Î(Â·) is the gamma function. The value of the distribution function by Ix(p, q) is the probability that the random variable takes a value less than or equal to x.

The integral in the expression above is called the incomplete beta function and is denoted by Î²x(p, q). The constant in the expression is the reciprocal of the beta function (the incomplete function evaluated at 1) and is denoted by Î²x(p, q).

If the keyword INVERSE is specified, the IMSL_BETACDF function evaluates the inverse distribution function of a beta random variable with parameters pin and qin.

With P = x, p = pin and q = qin, it returns x such that:

where Î(Â·) is the gamma function. The probability that the random variable takes a value less than or equal to x is P.

The BETCDF function uses the method of Bosten and Battiste (1974).