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cdfgam — cumulative distribution function gamma distribution
[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)
| 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] |
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.
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