This function evaluates the beta probability density function.

Function Return Value

BETPR — Function value, the value of the probability density function.   (Output)

Required Arguments

X — Argument for which the beta probability density function is to be evaluated.   (Input)

PIN — First beta distribution parameter.   (Input)
PIN must be positive.

QIN — Second beta distribution parameter.   (Input)
QIN must be positive.

FORTRAN 90 Interface

Generic:                              BETPR (X, PIN, QIN)

Specific:                             The specific interface names are S_BETPR and D_BETPR.

FORTRAN 77 Interface

Single:                                BETPR (X, PIN, QIN)

Double:                              The double precision name is DBETPR.

Description

The function BETPR evaluates the beta probability density function with parameters PIN and QIN.  Using x = X, a = PIN and b = QIN, the beta distribution is defined as

The reciprocal of the beta function used as the normalizing factor is computed using IMSL function BETA (see Special Functions/Chapter 4, Gamma and Related Funtions).

Example

In this example, we evaluate the probability function at X = 0.75, PIN = 2.0, QIN = 0.5.

 

      USE UMACH_INT
      USE BETPR_INT
      IMPLICIT NONE

      INTEGER NOUT

      REAL X, PIN, QIN, PR

      CALL UMACH(2, NOUT)

      X = .75

      PIN = 2.0

      QIN = 0.5

      PR = BETPR(X, PIN, QIN)

      WRITE (NOUT, 99999) X, PIN, QIN, PR

99999 FORMAT (' BETPR(', F4.2, ', ', F4.2, ', ', F4.2, ') = ', F6.4)

      END

Output

 

 BETPR(0.75, 2.00, 0.50) = 1.1250

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