dcdflib.fdoc

unix环境下计算符合常用概率分布的随机变量的集合

                                    DCDFLIB

               Library of C Routines for Cumulative Distribution
                 Functions, Inverses, and Other Parameters

                               (February, 1994)






                       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-300,1D300]

     B <--> The second parameter of the beta density.
            Input range: (0, +infinity).
            Search range: [1D-300,1D300]

     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-300, 1E300]

     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: [0,1E300]

     DF <--> Degrees of freedom of the
             chi-square distribution.
             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 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