randlib.c.fdoc

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                                    RANDLIB.C

            Library of C Routines for Random Number Generation








                       Full Documentation of Each Routine








                            Compiled and Written by:

                                 Barry W. Brown
                                  James Lovato
                                   









                     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.

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     void advnst(long k)
               ADV-a-N-ce ST-ate

     Advances the state  of  the current  generator  by 2^K values  and
     resets the initial seed to that value.

     This is  a  transcription from   Pascal to  Fortran    of  routine
     Advance_State from the paper

     L'Ecuyer, P. and  Cote, S. "Implementing  a  Random Number Package
     with  Splitting   Facilities."  ACM  Transactions  on Mathematical
     Software, 17:98-111 (1991)

                              Arguments

     k -> The generator is advanced by2^K values
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     float genbet(float aa,float bb)
               GeNerate BETa random deviate

                              Function

     Returns a single random deviate from the beta distribution with
     parameters A and B.  The density of the beta is
               x^(a-1) * (1-x)^(b-1) / B(a,b) for 0 < x < 1

                              Arguments

     aa --> First parameter of the beta distribution
                         (aa >= 1.0E-37)

     bb --> Second parameter of the beta distribution
                         (bb >= 1.0E-37)       

                              Method

     R. C. H. Cheng
     Generating Beta Variatew with Nonintegral Shape Parameters
     Communications of the ACM, 21:317-322  (1978)
     (Algorithms BB and BC)
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     float genchi(float df)
                Generate random value of CHIsquare variable

                              Function

     Generates random deviate from the distribution of a chisquare
     with DF degrees of freedom random variable.

                              Arguments

     df --> Degrees of freedom of the chisquare
            (Must be positive)
       

                              Method

     Uses relation between chisquare and gamma.
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     float genexp(float av)
                    GENerate EXPonential random deviate

                              Function

     Generates a single random deviate from an exponential
     distribution with mean AV.

                              Arguments

     av --> The mean of the exponential distribution from which
            a random deviate is to be generated.
                              (av >= 0)

                              Method

     Renames SEXPO from TOMS as slightly modified by BWB to use RANF
     instead of SUNIF.
     For details see:
               Ahrens, J.H. and Dieter, U.
               Computer Methods for Sampling From the
               Exponential and Normal Distributions.
               Comm. ACM, 15,10 (Oct. 1972), 873 - 882.
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     float genf(float dfn,float dfd)
                GENerate random deviate from the F distribution

                              Function

     Generates a random deviate from the F (variance ratio)
     distribution with DFN degrees of freedom in the numerator
     and DFD degrees of freedom in the denominator.

                              Arguments

     dfn --> Numerator degrees of freedom
             (Must be positive)

     dfd --> Denominator degrees of freedom
             (Must be positive)

                              Method

     Directly generates ratio of chisquare variates
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     float gengam(float a,float r)
           GENerates random deviates from GAMma distribution

                              Function

     Generates random deviates from the gamma distribution whose
     density is
          (A**R)/Gamma(R) * X**(R-1) * Exp(-A*X)

                              Arguments

     a --> Location parameter of Gamma distribution
                              ( a > 0 )

     r --> Shape parameter of Gamma distribution
                              ( r > 0 )

                              Method

     Renames SGAMMA from TOMS as slightly modified by BWB to use RANF
     instead of SUNIF.
     For details see:
               (Case R >= 1.0)
               Ahrens, J.H. and Dieter, U.
               Generating Gamma Variates by a
               Modified Rejection Technique.
               Comm. ACM, 25,1 (Jan. 1982), 47 - 54.
     Algorithm GD
               (Case 0.0 < R < 1.0)
               Ahrens, J.H. and Dieter, U.
               Computer Methods for Sampling from Gamma,
               Beta, Poisson and Binomial Distributions.
               Computing, 12 (1974), 223-246/
     Adapted algorithm GS.
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     void genmn(float *parm,float *x,float *work)
              GENerate Multivariate Normal random deviate

                              Arguments

     parm --> Parameters needed to generate multivariate normal
               deviates (MEANV and Cholesky decomposition of
               COVM). Set by a previous call to SETGMN.
               1 : 1                - size of deviate, P
               2 : P + 1            - mean vector
               P+2 : P*(P+3)/2 + 1  - upper half of cholesky
                                       decomposition of cov matrix

     x    <-- Vector deviate generated.

     work <--> Scratch array

                              Method

     1) Generate P independent standard normal deviates - Ei ~ N(0,1)
     2) Using Cholesky decomposition find A s.t. trans(A)*A = COVM
     3) trans(A)E + MEANV ~ N(MEANV,COVM)
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     void genmul(int n,float *p,int ncat,int *ix)
     GENerate an observation from the MULtinomial distribution

                              Arguments

     N --> Number of events that will be classified into one of
           the categories 1..NCAT (N >= 0)

     P --> Vector of probabilities.  P(i) is the probability that
           an event will be classified into category i.  Thus, P(i)
           must be [0,1]. Only the first NCAT-1 P(i) must be defined
           since P(NCAT) is 1.0 minus the sum of the first
           NCAT-1 P(i).

     NCAT --> Number of categories.  Length of P and IX. (NCAT > 1)
     IX <-- Observation from multinomial distribution.  All IX(i)
            will be nonnegative and their sum will be N.

                              Method

     Algorithm from page 559 of

     Devroye, Luc

     Non-Uniform Random Variate Generation.  Springer-Verlag,
     New York, 1986.

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     float gennch(float df,float xnonc)
           Generate random value of Noncentral CHIsquare variable

                              Function

     Generates random deviate  from the  distribution  of a  noncentral
     chisquare with DF degrees  of freedom and noncentrality  parameter
     xnonc.

                              Arguments

     df --> Degrees of freedom of the chisquare
            (Must be >= 1.0)

     xnonc --> Noncentrality parameter of the chisquare
               (Must be >= 0.0)

                              Method

     Uses fact that  noncentral chisquare  is  the  sum of a  chisquare
     deviate with DF-1  degrees of freedom plus the  square of a normal
     deviate with mean XNONC and standard deviation 1.
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     float gennf(float dfn,float dfd,float xnonc)
           GENerate random deviate from the Noncentral F distribution

                              Function

     Generates a random deviate from the  noncentral F (variance ratio)
     distribution with DFN degrees of freedom in the numerator, and DFD
     degrees of freedom in the denominator, and noncentrality parameter
     XNONC.

                              Arguments

     dfn --> Numerator degrees of freedom
             (Must be >= 1.0)

     dfd --> Denominator degrees of freedom
             (Must be positive)

     xnonc --> Noncentrality parameter
               (Must be nonnegative)

                              Method

     Directly generates ratio of noncentral numerator chisquare variate
     to central denominator chisquare variate.
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     float gennor(float av,float sd)
         GENerate random deviate from a NORmal distribution

                              Function

     Generates a single random deviate from a normal distribution
     with mean, AV, and standard deviation, SD.

                              Arguments

     av --> Mean of the normal distribution.

     sd --> Standard deviation of the normal distribution.
                              (sd >= 0)

                              Method

     Renames SNORM from TOMS as slightly modified by BWB to use RANF
     instead of SUNIF.
     For details see:
               Ahrens, J.H. and Dieter, U.
               Extensions of Forsythe's Method for Random
               Sampling from the Normal Distribution.
               Math. Comput., 27,124 (Oct. 1973), 927 - 937.
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    void genprm(long *iarray,int larray)
               GENerate random PeRMutation of iarray

                              Arguments