view release on metacpan or  search on metacpan

cdflib/doc/README  view on Meta::CPAN

indicates that  the answer was  apparently higher than the upper bound
on the search interval.  A return code of 3 indicates that P and Q did
not sum to 1. Other positive codes are routine specific.

BOUND is not  set if status is returned  as 0.  If  STATUS is -I  then
BOUND is   the bound illegally  exceeded by  input  parameter I, where
WHICH  is  counted as 1,  P as 2,  Q as 3,  X as 4, etc.  If STATUS is 
returned as 1 or 2 then bound  is returned as the lower or upper bound
on the search interval respectively.


                                BOUNDS

Below are  the rules that we used  in determining bounds on quantities
to be  calculated.   Those who don't care   can find a summary  of the
bounds in  dcdflib.chs.   Input bounds  are  checked for  legality  of
input.  The search  range  is  the range   of values searched  for  an
answer.

                             Input Bounds

Bounds on input parameters are  checked by the  cdf* routines.   These
bounds were set according to the following rules.

P: If the  domain of the cdf (X) extends to  -infinity  then P must be
greater than 0 otherwise P must be greater than or equal to 0.  P must
always be less than or equal to 1.

Q: If the  domain of the cdf (X) extends to  +infinity  then Q must be
greater than 0 otherwise Q must be greater than or equal to 0.  Q must
always be less than or equal to 1.

Further, P and Q must sum to 1. The smaller of the two P and Q will be
used in calculations to increase accuracy

X:  If  the  domain is infinite  in   either the positive  or negative
direction, no check  is performed in  that direction.  If the left end
of the domain is 0, then X is checked to assure non-negativity.

DF, SD, etc.:  Some auxiliary parameters must  be positive. The lowest
input values accepted for these parameters is 1E-100.


                                Search Bounds

These are the  ranges searched for an  answer.   If the domain  of the
parameter in the cdf  is closed at  some  finite value, e.g., 0,  then
this value is the same endpoint of the search range.  If the domain is
open  at  some finite   endpoint (which only  occurs   for  0 --  some
parameters must be strictly positive) then  the endpoint is 1E-100. If
the  domain is infinite in either  direction then +/- 1E100 is used as
the endpoint of the search range.

                        HOW THE ROUTINES WORK

The cumulative  distribution   functions are computed  directly.   The
normal, gamma,  and  beta functions use the  code  from the references
cited.  Other  cdfs are calculated  by relating them  to one  of these
distributions.  For example, the  binomial and negative binomial  cdfs
can be converted  to a beta cdf.   This is how fractional observations
are handled.  The  formula from Abramowitz  and Stegun  for converting
the cdfs is cited  in the fdoc file.    (We think the formula  for the
negative binomial in A&S is wrong, but there is a correct one which we
used.)

The inverse normal and gamma are also taken  from the references.  For
all other parameters, a search is made for the value that provides the
desired P.  Initial  values are chosen crudely  for the search  (e.g.,
5).  If the domain  of the cdf for the  parameter being calculated  is
infinite, a step doubling strategy is  used to bound the desired value
then the  zero  finder is  employed  to refine the answer.    The zero
finder attempts to obtain the answer accurately to about eight decimal
places.