This function evaluates the incomplete beta function ratio.
Function Return Value
BETAI — Probability that a random variable from a beta distribution having parameters PIN and QIN will be less than or equal to X. (Output)
Required Arguments
X — Upper limit
of integration. (Input)
X must be in the
interval (0.0, 1.0) inclusive.
PIN — First beta
distribution parameter. (Input)
PIN must be
positive.
QIN — Second beta
distribution parameter. (Input)
QIN must be
positive.
FORTRAN 90 Interface
Generic: BETAI (X, PIN, QIN)
Specific: The specific interface names are S_BETAI and D_BETAI.
FORTRAN 77 Interface
Single: BETAI (X, PIN, QIN)
Double: The double precision function name is DBETAI.
Description
The incomplete beta function is defined to be
See BETA for the definition of β(p, q).
The parameters p and q must both be greater than zero. The argument x must lie in the range 0 to 1. The incomplete beta function can underflow for sufficiently small x and large p; however, this underflow is not reported as an error. Instead, the value zero is returned as the function value.
The function BETAI is based on the work of Bosten and Battiste (1974).
Example
In this example, I0.61(2.2, 3.7) is computed and printed.
USE BETAI_INT
USE UMACH_INT
IMPLICIT NONE
! Declare variables
INTEGER NOUT
REAL PIN, QIN, VALUE, X
! Compute
X = 0.61
PIN = 2.2
QIN = 3.7
VALUE = BETAI(X, PIN, QIN)
! Print the results
CALL UMACH (2, NOUT)
WRITE (NOUT,99999) X, PIN, QIN, VALUE
99999 FORMAT (' BETAI(', F6.3, ',', F6.3, ',', F6.3, ') = ', F6.4)
END
Output
BETAI( 0.610, 2.200, 3.700) = 0.8822
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