#include "cdflib.h" void cdfgam(int *which,double *p,double *q,double *x,double *shape, double *scale,int *status,double *bound) /********************************************************************** void cdfgam(int *which,double *p,double *q,double *x,double *shape, double *scale,int *status,double *bound) Cumulative Distribution Function GAMma Distribution Function Calculates any one parameter of the gamma distribution given values for the others. Arguments WHICH --> Integer indicating which of the next four argument values is to be calculated from the others. Legal range: 1..4 iwhich = 1 : Calculate P and Q from X,SHAPE and SCALE iwhich = 2 : Calculate X from P,Q,SHAPE and SCALE iwhich = 3 : Calculate SHAPE from P,Q,X and SCALE iwhich = 4 : Calculate SCALE from P,Q,X and SHAPE P <--> The integral from 0 to X of the gamma density. Input range: [0,1]. Q <--> 1-P. Input range: (0, 1]. P + Q = 1.0. 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] STATUS <-- 0 if calculation completed correctly -I if input parameter number I is out of range 1 if answer appears to be lower than lowest search bound 2 if answer appears to be higher than greatest search bound 3 if P + Q .ne. 1 10 if the gamma or inverse gamma routine cannot compute the answer. Usually happens only for X and SHAPE very large (gt 1E10 or more) BOUND <-- Undefined if STATUS is 0 Bound exceeded by parameter number I if STATUS is negative. Lower search bound if STATUS is 1. Upper search bound if STATUS is 2. Method 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. Note The gamma density is proportional to T**(SHAPE - 1) * EXP(- SCALE * T) **********************************************************************/ { #define tol (1.0e-8) #define atol (1.0e-50) #define zero (1.0e-300) #define inf 1.0e300 static int K1 = 1; static double K5 = 0.5e0; static double K6 = 5.0e0; static double xx,fx,xscale,cum,ccum,pq,porq; static int ierr; static unsigned long qhi,qleft,qporq; static double T2,T3,T4,T7,T8,T9; /* .. .. Executable Statements .. */ /* Check arguments */ if(!(*which < 1 || *which > 4)) goto S30; if(!(*which < 1)) goto S10; *bound = 1.0e0; goto S20; S10: *bound = 4.0e0; S20: *status = -1; return; S30: if(*which == 1) goto S70; /* P */ if(!(*p < 0.0e0 || *p > 1.0e0)) goto S60; if(!(*p < 0.0e0)) goto S40; *bound = 0.0e0; goto S50; S40: *bound = 1.0e0; S50: *status = -2; return; S70: S60: if(*which == 1) goto S110; /* Q */ if(!(*q <= 0.0e0 || *q > 1.0e0)) goto S100; if(!(*q <= 0.0e0)) goto S80; *bound = 0.0e0; goto S90; S80: *bound = 1.0e0; S90: *status = -3; return; S110: S100: if(*which == 2) goto S130; /* X */ if(!(*x < 0.0e0)) goto S120; *bound = 0.0e0; *status = -4; return; S130: S120: if(*which == 3) goto S150; /* SHAPE */ if(!(*shape <= 0.0e0)) goto S140; *bound = 0.0e0; *status = -5; return; S150: S140: if(*which == 4) goto S170; /* SCALE */ if(!(*scale <= 0.0e0)) goto S160; *bound = 0.0e0; *status = -6; return; S170: S160: if(*which == 1) goto S210; /* P + Q */ pq = *p+*q; if(!(fabs(pq-0.5e0-0.5e0) > 3.0e0*spmpar(&K1))) goto S200; if(!(pq < 0.0e0)) goto S180; *bound = 0.0e0; goto S190; S180: *bound = 1.0e0; S190: *status = 3; return; S210: S200: if(*which == 1) goto S240; /* Select the minimum of P or Q */ qporq = *p <= *q; if(!qporq) goto S220; porq = *p; goto S230; S220: porq = *q; S240: S230: /* Calculate ANSWERS */ if(1 == *which) { /* Calculating P */ *status = 0; xscale = *x**scale; cumgam(&xscale,shape,p,q); if(porq > 1.5e0) *status = 10; } else if(2 == *which) { /* Computing X */ T2 = -1.0e0; gaminv(shape,&xx,&T2,p,q,&ierr); if(ierr < 0.0e0) { *status = 10; return; } else { *x = xx/ *scale; *status = 0; } } else if(3 == *which) { /* Computing SHAPE */ *shape = 5.0e0; xscale = *x**scale; T3 = zero; T4 = inf; T7 = atol; T8 = tol; dstinv(&T3,&T4,&K5,&K5,&K6,&T7,&T8); *status = 0; dinvr(status,shape,&fx,&qleft,&qhi); S250: if(!(*status == 1)) goto S290; cumgam(&xscale,shape,&cum,&ccum); if(!qporq) goto S260; fx = cum-*p; goto S270; S260: fx = ccum-*q; S270: if(!(qporq && cum > 1.5e0 || !qporq && ccum > 1.5e0)) goto S280; *status = 10; return; S280: dinvr(status,shape,&fx,&qleft,&qhi); goto S250; S290: if(!(*status == -1)) goto S320; if(!qleft) goto S300; *status = 1; *bound = zero; goto S310; S300: *status = 2; *bound = inf; S320: S310: ; } else if(4 == *which) { /* Computing SCALE */ T9 = -1.0e0; gaminv(shape,&xx,&T9,p,q,&ierr); if(ierr < 0.0e0) { *status = 10; return; } else { *scale = xx/ *x; *status = 0; } } return; #undef tol #undef atol #undef zero #undef inf } /* END */