GAMIN

This function evaluates the inverse of the gamma cumulative distribution function.

Function Return Value

GAMIN — Function value. (Output)
The probability that a gamma random variable takes a value less than or equal to GAMIN is P.

Required Arguments

P — Probability for which the inverse of the gamma cumulative distribution function is to be evaluated. (Input)
P must be in the open interval (0.0, 1.0).

A — The shape parameter of the gamma distribution. (Input)
This parameter must be positive.

FORTRAN 90 Interface

Generic: GAMIN (P, A)

Specific: The specific interface names are S_GAMIN and D_GAMIN.

FORTRAN 77 Interface

Single: GAMIN (P, A)

Double: The double precision name is DGAMIN.

Description

Function GAMIN evaluates the inverse distribution function of a gamma random variable with shape parameter a, that is, it determines x (= GAMIN(P, A)), 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. See the documentation for routine GAMDF for further discussion of the gamma distribution.

Function GAMIN uses bisection and modified regula falsi to invert the distribution function, which is evaluated using routine GAMDF.

Comments

Informational Error

 

 

Type	Code	Description
4	1	Over 100 iterations have occurred without convergence. Convergence is assumed.

Example

In this example, we find the 95‑th percentage point for a gamma random variable with shape parameter of 4.

 

USE UMACH_INT

USE GAMIN_INT

IMPLICIT NONE

INTEGER NOUT

REAL A, P, X

!

CALL UMACH (2, NOUT)

A = 4.0

P = 0.95

X = GAMIN(P,A)

WRITE (NOUT,99999) X

!

99999 FORMAT (' The 0.05 gamma(4) critical value is ', F6.3, &

'.')

!

END

Output

 

The 0.05 gamma(4) critical value is 7.754.