dcdflib.fdoc

有关SAR的一个工具箱

     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

     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  26.4.25   of   Abramowitz   and   Stegun,  Handbook  of
     Mathematical  Functions (1966) is used to compute the cumulative
     distribution function.

     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.


                            WARNING

     The computation time  required for this  routine is proportional
     to the noncentrality  parameter  (PNONC).  Very large  values of
     this parameter can consume immense  computer resources.  This is
     why the search range is bounded by 10,000.

**********************************************************************/
/**********************************************************************

      void cdff(int *which,double *p,double *q,double *f,double *dfn,
	        double *dfd,int *status,double *bound)

               Cumulative Distribution Function
               F distribution


                              Function


     Calculates any one parameter of the F 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 F,DFN and DFD
               iwhich = 2 : Calculate F from P,Q,DFN and DFD
               iwhich = 3 : Calculate DFN from P,Q,F and DFD
               iwhich = 4 : Calculate DFD from P,Q,F and DFN

       P <--> The integral from 0 to F of the f-density.
              Input range: [0,1].

       Q <--> 1-P.
              Input range: (0, 1].
              P + Q = 1.0.

       F <--> Upper limit of integration of the f-density.
              Input range: [0, +infinity).
              Search range: [0,1E100]

     DFN < --> Degrees of freedom of the numerator sum of squares.
               Input range: (0, +infinity).
               Search range: [ 1E-100, 1E100]

     DFD < --> Degrees of freedom of the denominator sum of squares.
               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

     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   26.6.2   of   Abramowitz   and   Stegun,  Handbook  of
     Mathematical  Functions (1966) is used to reduce the computation
     of the  cumulative  distribution function for the  F  variate to
     that of an incomplete beta.

     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.

                              WARNING

     The value of the  cumulative  F distribution is  not necessarily
     monotone in  either degrees of freedom.  There  thus may  be two
     values  that  provide a given CDF  value.   This routine assumes
     monotonicity and will find an arbitrary one of the two values.

**********************************************************************/
/**********************************************************************

      void cdffnc(int *which,double *p,double *q,double *f,double *dfn,
	          double *dfd,double *phonc,int *status,double *bound) 

               Cumulative Distribution Function
               Non-central F distribution


                              Function


     Calculates any one parameter of the Non-central F
     distribution given values for the others.


                              Arguments


     WHICH --> Integer indicating which of the next five argument
               values is to be calculated from the others.
               Legal range: 1..5
               iwhich = 1 : Calculate P and Q from F,DFN,DFD and PNONC
               iwhich = 2 : Calculate F from P,Q,DFN,DFD and PNONC
               iwhich = 3 : Calculate DFN from P,Q,F,DFD and PNONC
               iwhich = 4 : Calculate DFD from P,Q,F,DFN and PNONC
               iwhich = 5 : Calculate PNONC from P,Q,F,DFN and DFD

       P <--> The integral from 0 to F of the non-central f-density.
              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.

       F <--> Upper limit of integration of the non-central f-density.
              Input range: [0, +infinity).
              Search range: [0,1E100]

     DFN < --> Degrees of freedom of the numerator sum of squares.
               Input range: (0, +infinity).
               Search range: [ 1E-100, 1E100]

     DFD < --> Degrees of freedom of the denominator sum of squares.
               Must be in range: (0, +infinity).
               Input range: (0, +infinity).
               Search range: [ 1E-100, 1E100]

     PNONC <-> The non-centrality parameter
               Input range: [0,infinity)
               Search range: [0,1E4]

     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

     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  26.6.20   of   Abramowitz   and   Stegun,  Handbook  of
     Mathematical  Functions (1966) is used to compute the cumulative
     distribution function.

     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.

                            WARNING

     The computation time  required for this  routine is proportional
     to the noncentrality  parameter  (PNONC).  Very large  values of
     this parameter can consume immense  computer resources.  This is
     why the search range is bounded by 10,000.

                              WARNING

     The  value  of the  cumulative  noncentral F distribution is not
     necessarily monotone in either degrees  of freedom.  There  thus
     may be two values that provide a given  CDF value.  This routine
     assumes monotonicity  and will find  an arbitrary one of the two
     values.

**********************************************************************/
/**********************************************************************

      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: [0,1E100]

     SHAPE <--> The shape parameter of the gamma density.
                Input range: (0, +infinity).
                Search range: [1E-100,1E100]

     SCALE <--> The scale parameter of the gamma density.
                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 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)

**********************************************************************/
/**********************************************************************

      void cdfnbn(int *which,double *p,double *q,double *s,double *xn,
	          double *pr,double *ompr,int *status,double *bound)

               Cumulative Distribution Function
               Negative BiNomial distribution


                              Function


     Calculates any one parameter of the negative binomial
     distribution given values for the others.

     The  cumulative  negative   binomial  distribution  returns  the
     probability that there  will be  F or fewer failures before  the
     XNth success in binomial trials each of which has probability of
     success PR.

     The individual term of the negative binomial is the probability of
     S failures before XN successes and is
          Choose( S, XN+S-1 ) * PR^(XN) * (1-PR)^S


                              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  negative
            binomial distribution.
            Input range: [0,1].

     Q <--> 1-P.
            Input range: (0, 1].
            P + Q = 1.0.

     S <--> The upper limit of cumulation of the binomial distribution.
            There are F or fewer failures before the XNth success.
            Input range: [0, +infinity).
            Search range: [0, 1E100]