cdfgam - cumulative distribution function gamma distribution

Calling Sequence

[P,Q]=cdfgam("PQ",X,Shape,Scale)

[X]=cdfgam("X",Shape,Scale,P,Q)

[Shape]=cdfgam("Shape",Scale,P,Q,X)

[Scale]=cdfgam("Scale",P,Q,X,Shape)

Parameters

• P,Q,X,Shape,Scale : five real vectors of the same size.
• P,Q (Q=1-P) The integral from 0 to X of the gamma density. Input range: [0,1].
• X : The upper limit of integration of the gamma density. Input range: [0, +infinity). Search range: [0,1E300]
• Shape : The shape parameter of the gamma density. Input range: (0, +infinity). Search range: [1E-300,1E300]
• Scale : The scale parameter of the gamma density. Input range: (0, +infinity). Search range: (1E-300,1E300]

Description

Calculates any one parameter of the gamma distribution given values for the others.

Cumulative distribution function (P) is calculated directly by the code associated with:

DiDinato, A. R. and Morris, A. H. Computation of the incomplete gamma function ratios and their inverse. ACM Trans. Math. Softw. 12 (1986), 377-393.

Computation of other parameters involve a seach for a value that produces the desired value of P. The search relies on the monotinicity of P with the other parameter.

The gamma density is proportional to T**(SHAPE - 1) * EXP(- SCALE * T)

From DCDFLIB: Library of Fortran Routines for Cumulative Distribution Functions, Inverses, and Other Parameters (February, 1994) Barry W. Brown, James Lovato and Kathy Russell. The University of Texas.