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IMSL_BETACDF

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 Γ(·) 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 βx(p, q). The constant in the expression is the reciprocal of the beta function (the incomplete function evaluated at 1) and is denoted by βx(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 Γ(·) 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).



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