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Math::CDF
Math::CDF - Generate probabilities and quantiles from several
statistical probability functions
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);
$prob = pnorm(1.96);
This module provides a perl interface to the DCDFLIB. See the section on
DCDFLIB for more information.
Functions are available for 7 continuous distributions (Beta,
Chi-square, F, Gamma, Normal, Poisson and T-distribution) and for
two discrete distributions (Binomial and Negative Binomial). Optional
non-centrality parameters are available for the Chi-square, F and
T-distributions. Cumulative probabilities are available for all 9
distributions and quantile functions are available for the 7 continuous
distributions.
All cumulative probability function names begin with the character ``p''.
They give the probability of being less than or equal to the given value
[ P(X <= x) ]
All quantile function names begin with the character q. They give a value
of x such that P(X <= x) = p where the value of p is provided to the function.
Non-centrality parameters are always the last function argument when
available. You do not need to supply the non-centrality parameter in which case
it will be assumed to be 0.
All functions will return an undefined value if the function fails
(probably due to parameters being out of allowed range) but will not otherwise
generate an error message. The user should check for valid output from the
Math::CDF functions with the defined() function as demonstrated in the
SYNOPSIS section.
In all, 16 functions are available via Math::CDF:
pbeta(), qbeta() [Beta Distribution]
pchisq(), qchisq() [Chi-square Distribution]
pf(), qf() [F Distribution]
pgamma(), qgamma() [Gamma Distribution]
pnorm(), qnorm() [Standard Normal Dist]
ppois(), qpois() [Poisson Distribution]
pt(), qt() [T-distribution]
pbinom() [Binomial Distribution]
pnbinom() [Negative Binomial Distribution]
pbeta($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 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
downloaded via ftp from odin.mda.uth.tmc.edu as /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 the source
distribution of Math::CDF for more information.
Math::CDF was put together by Ed Callahan, callahan@envstat.com
Environmental Statistics
PO Box 563
Fountain City, WI 54629
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
the Math::Random manpage, the Statistics::ChiSquare manpage, the Statistics::OLS manpage
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