CDFLIB Cumulative Density Functions

CDFLIB, a C library which evaluates cumulative probability density functions.

CDFLIB includes routines for evaluating the cumulative density functions of a variety of standard probability distributions. An unusual feature of this library is its ability to easily compute any one parameter of the CDF given the others. This means that a single routine can evaluate the CDF given the usual parameters, or determine the value of a parameter that produced a given CDF value.

The probability distributions covered include:

• the Beta distribution;
• the binomial distribution;
• the chi-square distribution;
• the noncentral chi-square distribution;
• the F distribution;
• the noncentral F distribution;
• the Gamma distribution;
• the negative binomial distribution;
• the normal distribution;
• the Poisson distribution;
• the T distribution;

Note that the F and noncentral F distributions are not necessarily monotone in either degree of freedom argument. Consequently, there may be two degree of freedom arguments that satisfy the specified condition. An arbitrary one of these will be found by the routines.

The amount of computation required for the noncentral chisquare and noncentral F distribution is proportional to the value of the noncentrality parameter. Very large values of this parameter can require immense numbers of computation. Consequently, when the noncentrality parameter is to be calculated, the upper limit searched is 10,000.

Languages:

CDFLIB is available in a C version and a C++ version and a FORTRAN90 version.

Related Data and Programs:

ASA310, a C library which computes the CDF of the noncentral Beta distribution.

BETA_NC, a C library which evaluates the CDF of the noncentral Beta distribution.

NORMAL, a C library which contains routines for sampling the normal distribution.

PROB, a C library which contains routines for evaluating and inverting the normal CDF, and many other distributions.

TEST_VALUES, a C library which contains routines that store selected values of the normal CDF, and many other statistical distributions.

UNIFORM, a C library which contains routines for sampling the uniform distribution.

Author:

Barry Brown, James Lovato, Kathy Russell,
Department of Biomathematics,
University of Texas,
Houston, Texas.

Reference:

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Source Code:

Last revised on 12 June 2019.