DCDFLIB               Library of C Routines for Cumulative Distribution                 Functions, Inverses, and Other Parameters                                  Version 1.1                                (November, 1997)                       Full Documentation of Each Routine                            Compiled and Written by:                                 Barry W. Brown                                  James Lovato                                  Kathy Russell                     Department of Biomathematics, Box 237                     The University of Texas, M.D. Anderson Cancer Center                     1515 Holcombe Boulevard                     Houston, TX      77030 This work was supported by grant CA-16672 from the National Cancer Institute./**********************************************************************      void cdfbet(int *which,double *p,double *q,double *x,double *y,	          double *a,double *b,int *status,double *bound)               Cumulative Distribution Function                         BETa Distribution                              Function     Calculates any one parameter of the beta 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,Y,A and B               iwhich = 2 : Calculate X and Y from P,Q,A and B               iwhich = 3 : Calculate A from P,Q,X,Y and B               iwhich = 4 : Calculate B from P,Q,X,Y and A     P <--> The integral from 0 to X of the chi-square            distribution.            Input range: [0, 1].     Q <--> 1-P.            Input range: [0, 1].            P + Q = 1.0.     X <--> Upper limit of integration of beta density.            Input range: [0,1].            Search range: [0,1]     Y <--> 1-X.            Input range: [0,1].            Search range: [0,1]            X + Y = 1.0.     A <--> The first parameter of the beta density.            Input range: (0, +infinity).            Search range: [1D-100,1D100]     B <--> The second parameter of the beta density.            Input range: (0, +infinity).            Search range: [1D-100,1D100]     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                4 if X + Y .ne. 1     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     code associated with the following reference.     DiDinato, A. R. and Morris,  A.   H.  Algorithm 708: Significant     Digit Computation of the Incomplete  Beta  Function Ratios.  ACM     Trans. Math.  Softw. 18 (1993), 360-373.     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 beta density is proportional to               t^(A-1) * (1-t)^(B-1)**********************************************************************//**********************************************************************      void cdfbin(int *which,double *p,double *q,double *s,double *xn,	          double *pr,double *ompr,int *status,double *bound)               Cumulative Distribution Function                         BINomial distribution                              Function     Calculates any one parameter of the binomial     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 S,XN,PR and OMPR               iwhich = 2 : Calculate S from P,Q,XN,PR and OMPR               iwhich = 3 : Calculate XN from P,Q,S,PR and OMPR               iwhich = 4 : Calculate PR and OMPR from P,Q,S and XN     P <--> The cumulation from 0 to S of the binomial distribution.            (Probablility of S or fewer successes in XN trials each            with probability of success PR.)            Input range: [0,1].     Q <--> 1-P.            Input range: [0, 1].            P + Q = 1.0.     S <--> The number of successes observed.            Input range: [0, XN]            Search range: [0, XN]     XN  <--> The number of binomial trials.              Input range: (0, +infinity).              Search range: [1E-100, 1E100]     PR  <--> The probability of success in each binomial trial.              Input range: [0,1].              Search range: [0,1]     OMPR  <--> 1-PR              Input range: [0,1].              Search range: [0,1]              PR + OMPR = 1.0     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                4 if PR + OMPR .ne. 1     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     Formula  26.5.24    of   Abramowitz  and    Stegun,  Handbook   of     Mathematical   Functions (1966) is   used  to reduce the  binomial     distribution  to  the  cumulative incomplete    beta distribution.     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.**********************************************************************//**********************************************************************      void cdfchi(int *which,double *p,double *q,double *x,double *df,	          int *status,double *bound)               Cumulative Distribution Function               CHI-Square distribution                              Function     Calculates any one parameter of the chi-square     distribution given values for the others.                              Arguments     WHICH --> Integer indicating which of the next three argument               values is to be calculated from the others.               Legal range: 1..3               iwhich = 1 : Calculate P and Q from X and DF               iwhich = 2 : Calculate X from P,Q and DF               iwhich = 3 : Calculate DF from P,Q and X     P <--> The integral from 0 to X of the chi-square            distribution.            Input range: [0, 1].     Q <--> 1-P.            Input range: (0, 1].            P + Q = 1.0.     X <--> Upper limit of integration of the non-central            chi-square distribution.            Input range: [0, +infinity).            Search range: [0,1E100]     DF <--> Degrees of freedom of the             chi-square distribution.             Input range: (0, +infinity).             Search range: [ 1E-100, 1E100]     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 indicates error returned from cumgam.  See                  references in cdfgam     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     Formula    26.4.19   of Abramowitz  and     Stegun, Handbook  of     Mathematical Functions   (1966) is used   to reduce the chisqure     distribution to the incomplete distribution.     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.**********************************************************************//**********************************************************************      void cdfchn(int *which,double *p,double *q,double *x,double *df,	          double *pnonc,int *status,double *bound)               Cumulative Distribution Function               Non-central Chi-Square                              Function     Calculates any one parameter of the non-central chi-square     distribution given values for the others.                              Arguments     WHICH --> Integer indicating which of the next three argument               values is to be calculated from the others.               Input range: 1..4               iwhich = 1 : Calculate P and Q from X and DF               iwhich = 2 : Calculate X from P,DF and PNONC               iwhich = 3 : Calculate DF from P,X and PNONC               iwhich = 3 : Calculate PNONC from P,X and DF     P <--> The integral from 0 to X of the non-central chi-square            distribution.            Input range: [0, 1-1E-16).     Q <--> 1-P.            Q is not used by this subroutine and is only included            for similarity with other cdf* routines.     X <--> Upper limit of integration of the non-central            chi-square distribution.            Input range: [0, +infinity).            Search range: [0,1E100]     DF <--> Degrees of freedom of the non-central             chi-square distribution.             Input range: (0, +infinity).             Search range: [ 1E-100, 1E100]     PNONC <--> Non-centrality parameter of the non-central                chi-square distribution.                Input range: [0, +infinity).                Search range: [0,1E4]