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```CDF(3)		      User Contributed Perl Documentation		CDF(3)

NAME
Math::CDF - Generate probabilities and quantiles	from several
statistical probability functions

SYNOPSIS
use Math::CDF;

\$prob = "&Math::CDF::pnorm(1.96)";

"if( not	defined(\$z = &Math::CDF::qnorm(0.975)) )" {
die ""qnorm()" failed"; }

or

use Math::CDF "qw(:all)";

\$prob = "pnorm(1.96)";

DESCRIPTION
This module provides a perl interface to	the DCDFLIB. See the section

Functions are available for 7 continuous	distributions (Beta, Chi-
square, F, Gamma, Normal, Poisson and T-distribution) and for two
discrete	distributions (Binomial	and Negative Binomial).	Optional non-
centrality parameters are available for the Chi-square, F and
T-distributions.	Cumulative probabilities are available for all 9
distributions and quantile functions are	available for the 7 continuous
distributions.

All cumulative probability function names begin with the	character "p".
They give the probability of being less than or equal to	the given
value [A	"P(XA <=A x)"A ]

All quantile function names begin with the character q. They give a
value of	x such that "P(XA <=A x)"A =A p	where the value	of p is
provided	to the function.

Non-centrality parameters are always the	last function argument when
available. You do not need to supply the	non-centrality parameter in
which case it will be assumed to	be 0.

All functions will return an undefined value if the function fails
(probably due to	parameters being out of	allowed	range) but will	not
otherwise generate an error message. The	user should check for valid
output from the Math::CDF functions with	the "defined()"	function as
demonstrated in the SYNOPSIS section.

FUNCTION DESCRIPTIONS
In all, 16 functions are	available via Math::CDF:

pbeta(), qbeta()	     [Beta Distribution]
pchisq(), qchisq()	     [Chi-square Distribution]
pf(), qf()		     [F	Distribution]
pgamma(), qgamma()	     [Gamma Distribution]
pnorm(), qnorm()	     [Standard Normal Dist]
ppois(), qpois()	     [Poisson Distribution]
pt(), qt()		     [T-distribution]
pbinom()		     [Binomial Distribution]
pnbinom()		     [Negative Binomial	Distribution]

"pbeta(\$x, \$a, \$b), qbeta(\$p, \$a, \$b)"
Generates cumulative	probabilities and quantiles from the Beta
distribution.  \$x should be in the range of [0,1] and \$p should be
in [0,1].  \$a and \$b	are parameters of the beta distribution.  Both
\$a and \$b must be in	the range [0,Inf).

"pchisq(\$x, \$df,	\$ncp), qbeta(\$p, \$df, \$ncp)"
Generates cumulative	probabilities and quantiles from the Chi-
square distribution.	 \$x should be in the range of [0,Inf) and \$p
should be in	[0,1].	\$df is the degrees of freedom of the
distribution	and must be in the range (0,Inf).  \$ncp	is the
optional non-centrality parameter and must be in the	range [0,Inf).
The non-centrality parameter	need not be specified and the calls
"pchisq(5, 5, 0.0)" and "pchisq(5, 5)" will return identical
values.

"pf(\$x, \$dfn, \$dfd, \$ncp), qf(\$p, \$dfn, \$dfd, \$ncp)"
Generates cumulative	probabilities and quantiles from the F
distribution.  \$x should be in the range of [0,Inf) and \$p should
be in [0,1].	 \$dfn and \$dfd are the numerator and denominator
degrees of freedom, respectively. Both must be in the range
(0,Inf).  \$ncp is the optional non-centrality parameter and must be
in the range	[0,Inf).  The non-centrality parameter need not	be
specified and the calls [CS]<pf(5, 2, 3, 0.0)> and [CS]<pf(5, 2,
3)> will return identical values.

"pgamma(\$x, \$shape, \$scale), qgamma(\$p, \$shape, \$scale)"
Generates cumulative	probabilities and quantiles from the Gamma
distribution. The gamma density is proportional to [CS]<\$x**(\$shape
- 1)	* EXP(-	\$scale * \$x)> \$x should	be in the range	of [0,Inf) and
\$p should be	in [0,1].  \$shape and \$scale are parameters of the
Gamma distribution and both must be in the range (0,Inf).

"pnorm(\$x), qnorm(\$p)"
Generates cumulative	probabilities and quantiles from the standard
Normal distribution.	 \$x should be in the range of (-Inf,Inf) and
\$p should be	in [0,1].

"ppois(\$x, \$lambda), qpois(\$p, \$lambda)"
Generates cumulative	probabilities and quantiles from the Poisson
distribution.  \$x should be in the range of [0,Inf) and \$p should
be in [0,1].	 \$lambda is the	parameter of the Poisson distribution
and must be in the range [0,Inf).

"pt(\$x, \$df, \$ncp), qt(\$p, \$df, \$ncp)"
Generates cumulative	probabilities and quantiles from the T
distribution.  \$x should be in the range of (-Inf,Inf) and \$p
should be in	[0,1].	\$df is the degree of freedom of	the
distribution	and must be in the range (0,Inf).  \$ncp	is the
optional non-centrality parameter and must be in the	range
(-Inf,Inf).	The non-centrality parameter need not be specified and
the calls [CS]<pt(0,	3, 0.0)> and [CS]<pt(0,	3)> will return
identical values.

"pbinom(\$x, \$n, \$p)"
Generates cumulative	probabilities from the Binomial	distribution.
This	is the probability of having \$x	or fewer successes in \$n
trials when each trial has a	\$p probability of success.  \$x should
be in the range of [0,\$n], \$n should	be in the range	(0,Inf)	and \$p
should be in	[0,1].

"pnbinom(\$x, \$n,	\$p)"
Generates cumulative	probabilities from the Negative	Binomial
distribution.  The is the probability of having \$x or fewer
failures before the \$n'th success when each trial has a \$p
probability of success.  \$x should be in the	range of [0,Inf), \$n
should be in	the range (0,Inf) and \$p should	be in [0,1].

DCDFLIB
DCDFLIB is a library of C routines for cumulative distribution
functions, inverses, and	other parameters written by Barry W. Brown,
James Lovato and	Kathy Russell of the Department	of Biomathematics at
The University of Texas M.D. Anderson Cancer Center in Houston Texas.

Version 1.1 of DCDFLIB is included with this distribution and can be
/pub/src/dcdflib.c-1.1.tar.gz.  The library is also available in
Fortran source.

Documentation for DCDFLIB is found in the cdflib/doc/ directory of the
source distribution of Math::CDF

DCDFLIB has been	put in the public domain. However, some	of the
Algorithms are from the ACM publication and is under their copyright.
Generally this means that those algorithms can be distributed and used
freely for non-commercial purposes. See the file	cdflib/doc/README in

AUTHOR
o   Math::CDF was put together by Ed Callahan, callahan@envstat.com

Environmental Statistics PO Box 563 Fountain	City, WI  54629

o   DCDFLIB was written by Barry	W. Brown (bwb@odin.mdacc.tmc.edu),
James Lovato	and Kathy Russell

Department of Biomathematics, Box 237 The University	of Texas, M.D.
Anderson Cancer Center 1515 Holcombe	Boulevard Houston, TX  77030