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 chisquare distribution;

the noncentral chisquare 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.
cdflib_test
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:

Milton Abramowitz, Irene Stegun,
Handbook of Mathematical Functions,
National Bureau of Standards, 1964,
ISBN: 0486612724,
LC: QA47.A34.

Jacobus Bus, Jacob Dekker,
Two Efficient Algorithms with Guaranteed Convergence for
Finding a Zero of a Function,
ACM Transactions on Mathematical Software,
Volume 1, Number 4, December 1975, pages 330345.

William Cody,
Algorithm 715:
SPECFUN  A Portable FORTRAN Package of
Special Function Routines and Test Drivers,
ACM Transactions on Mathematical Software,
Volume 19, Number 1, March 1993, pages 2232.

William Cody,
Rational Chebyshev Approximations for the Error Function,
Mathematics of Computation,
Volume 23, Number 107, July 1969, pages 631638.

William Cody, Anthony Strecok, Henry Thacher,
Chebyshev Approximations for the Psi Function,
Mathematics of Computation,
Volume 27, Number 121, January 1973, pages 123127.

Armido DiDinato, Alfred Morris,
Algorithm 708:
Significant Digit Computation of the
Incomplete Beta Function Ratios,
ACM Transactions on Mathematical Software,
Volume 18, Number 3, September 1993, pages 360373.

Armido DiDinato, Alfred Morris,
Computation of the Incomplete Gamma Function Ratios and
their Inverse,
ACM Transactions on Mathematical Software,
Volume 12, Number 4, December 1986, pages 377393.

Phyllis Fox, Andrew Hall, Norman Schryer,
Algorithm 528:
Framework for a Portable Library,
ACM Transactions on Mathematical Software,
Volume 4, Number 2, June 1978, page 176188.

William Kennedy, James Gentle,
Statistical Computing,
Marcel Dekker, 1980,
ISBN: 0824768981,
LC: QA276.4 K46.

Karl Pearson,
Tables of the Incomplete Beta Function,
Cambridge University Press, 1968,
ISBN: 0521059224,
LC: QA351.P38.

Frank Powell,
Statistical Tables for Sociology, Biology and Physical Sciences,
Cambridge University Press, 1982,
ISBN: 0521284732,
LC: QA276.25.S73.

Stephen Wolfram,
The Mathematica Book,
Fourth Edition,
Cambridge University Press, 1999,
ISBN: 0521643147,
LC: QA76.95.W65.

Daniel Zwillinger, editor,
CRC Standard Mathematical Tables and Formulae,
30th Edition,
CRC Press, 1996,
ISBN: 0849324793.
Source Code:
Last revised on 12 June 2019.