BETIN
This function evaluates the inverse of the beta cumulative distribution function.
Function Return Value
BETIN — Function value. (Output)
The probability that a beta random variable takes a value less than or equal to BETIN is P.
Required Arguments
P — Probability for which the inverse of the beta distribution function is to be evaluated. (Input)
P must be in the open interval (0.0, 1.0).
PIN — First beta distribution parameter. (Input)
PIN must be positive.
QIN — Second beta distribution parameter. (Input)
QIN must be positive.
FORTRAN 90 Interface
Generic: BETIN (P, PIN, QIN)
Specific: The specific interface names are S_BETIN and D_BETIN.
FORTRAN 77 Interface
Single: BETIN (P, PIN, QIN)
Double: The double precision name is DBETIN.
Description
The function BETIN evaluates the inverse distribution function of a beta random variable with parameters PIN and QIN, that is, with P = P, p = PIN, and q = QIN, it determines x (equal to BETIN (P, PIN, QIN)), 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.
Comments
Informational errors
Type | Code | Description |
|---|
3 | 1 | The value for the inverse Beta distribution could not be found in 100 iterations. The best approximation is used. |
Example
Suppose X is a beta random variable with parameters 12 and 12. (X has a symmetric distribution.) In this example, we find the value x0 such that the probability that X ≤ x0 is 0.9.
USE UMACH_INT
USE BETIN_INT
IMPLICIT NONE
INTEGER NOUT
REAL P, PIN, QIN, X
!
CALL UMACH (2, NOUT)
PIN = 12.0
QIN = 12.0
P = 0.9
X = BETIN(P,PIN,QIN)
WRITE (NOUT,99999) X
99999 FORMAT (' X is less than ', F6.4, ' with probability 0.9.')
END
Output
X is less than 0.6299 with probability 0.9.
