asa266
asa266,
a FORTRAN77 code which
estimates the parameters of a Dirichlet probability density function.
This is a version of Applied Statistics Algorithm 266.
The assumption is that a given process is governed by a Dirichlet
distribution with parameters ALPHA(I), I = 1 to N, positive quantities
which are required to sum to 1. Each observation of the process yields
a vector of N data values. After a number of observations of this sort,
it is desired to estimate the the underlying parameters ALPHA of
the Dirichlet distribution.
There are a considerable number of routines required to get DIRICH
to work. In some cases, there are several versions of the routines,
and they all were included, in order to provide a way to check
results.
Also included is a routine DIRICHLET_SAMPLE, with which experiments
can be carried out. Values for the parameters ALPHA can be chosen,
and data generated by DIRICHLET_SAMPLE. Then DIRICH can analyze this
data and attempt to determine the values of ALPHA.
Another routine, DIRICHLET_MIX_SAMPLE, allows you to sample a
probability distribution that is a weighted mixture of Dirichlet
distributions.
Licensing:
The computer code and data files described and made available on this web page
are distributed under
the MIT license
Languages:
asa266 is available in
a C version and
a C++ version and
a Fortran90 version and
a MATLAB version and
an Octave version.
Related Data and Programs:
asa266_test
asa032,
a FORTRAN77 library which
evaluates the incomplete Gamma integral.
ASA066,
a FORTRAN77 library which
evaluates the percentage points of the normal distribution.
ASA091,
a FORTRAN77 library which
evaluates the percentage points of the Chi-Squared distribution.
ASA103,
a FORTRAN77 library
which evaluates the digamma or psi function.
ASA111,
a FORTRAN77 library
which evaluates the percentage points of the normal distribution.
ASA121,
a FORTRAN77 library
which evaluates the trigamma function.
ASA147,
a FORTRAN77 library
which evaluates the incomplete Gamma function.
ASA239,
a FORTRAN77 library
which evaluates the percentage points of the Chi-Squared distribution
and the incomplete Gamma function.
ASA241,
a FORTRAN77 library
which evaluates the percentage points of the normal distribution.
ASA245,
a FORTRAN77 library
which evaluates the logarithm of the Gamma function.
BDMLIB,
a FORTRAN77 library which
estimates the weights in a Dirichlet mixtured based on sample data;
NORMAL,
a FORTRAN77 library which
samples the normal distribution.
PROB,
a FORTRAN77 library which
evaluates the PDF, CDF, mean and variance for a number of probability
density functions.
TEST_VALUES,
a FORTRAN77 library which
contains sample values
for a number of distributions.
TOMS291,
a FORTRAN77 library
which evaluates the logarithm of the Gamma function.
UNIFORM,
a FORTRAN77 library which
samples the uniform distribution.
Reference:
-
AG Adams,
Algorithm 39:
Areas Under the Normal Curve,
Computer Journal,
Volume 12, Number 2, May 1969, pages 197-198.
-
Joachim Ahrens, Ulrich Dieter,
Computer Methods for Sampling from Gamma, Beta, Poisson and
Binomial Distributions,
Computing,
Volume 12, Number 3, September 1974, pages 223-246.
-
Joachim Ahrens, Ulrich Dieter,
Generating Gamma Variates by a Modified Rejection Technique,
Communications of the ACM,
Volume 25, Number 1, January 1982, pages 47-54.
-
Jerry Banks, editor,
Handbook of Simulation,
Wiley, 1998,
ISBN: 0471134031,
LC: T57.62.H37.
-
JD Beasley, SG Springer,
Algorithm AS 111:
The Percentage Points of the Normal Distribution,
Applied Statistics,
Volume 26, Number 1, 1977, pages 118-121.
-
Jose Bernardo,
Algorithm AS 103:
Psi ( Digamma ) Function,
Applied Statistics,
Volume 25, Number 3, 1976, pages 315-317.
-
Donald Best, DE Roberts,
Algorithm AS 91:
The Percentage Points of the Chi-Squared Distribution,
Applied Statistics,
Volume 24, Number 3, 1975, pages 385-390.
-
G Bhattacharjee,
Algorithm AS 32:
The Incomplete Gamma Integral,
Applied Statistics,
Volume 19, Number 3, 1970, pages 285-287.
-
William Cody, Kenneth Hillstrom,
Chebyshev Approximations for the Natural Logarithm of the
Gamma Function,
Mathematics of Computation,
Volume 21, Number 98, April 1967, pages 198-203.
-
William Cody, Anthony Strecok, Henry Thacher,
Chebyshev Approximations for the Psi Function,
Mathematics of Computation,
Volume 27, Number 121, January 1973, pages 123-127.
-
John Hart, Ward Cheney, Charles Lawson, Hans Maehly,
Charles Mesztenyi, John Rice, Henry Thacher,
Christoph Witzgall,
Computer Approximations,
Wiley, 1968,
LC: QA297.C64.
-
David Hill,
Algorithm AS 66:
The Normal Integral,
Applied Statistics,
Volume 22, Number 3, 1973, pages 424-427.
-
Cornelius Lanczos,
A precision approximation of the gamma function,
SIAM Journal on Numerical Analysis, B,
Volume 1, 1964, pages 86-96.
-
Chi Leung Lau,
Algorithm AS 147:
A Simple Series for the Incomplete Gamma Integral,
Applied Statistics,
Volume 29, Number 1, 1980, pages 113-114.
-
Allan Mcleod,
Algorithm AS 245:
A Robust and Reliable Algorithm for the Logarithm
of the Gamma Function,
Applied Statistics,
Volume 38, Number 2, 1989, pages 397-402.
-
A. Naryanan,
Algorithm AS 266:
Maximum Likelihood Estimation of the Parameters of the
Dirichlet Distribution,
Applied Statistics,
Volume 40, Number 2, 1991, pages 365-374.
-
Malcolm Pike, David Hill,
Algorithm 291:
Logarithm of Gamma Function,
Communications of the ACM,
Volume 9, Number 9, September 1966, page 684.
-
BE Schneider,
Algorithm AS 121:
Trigamma Function,
Applied Statistics,
Volume 27, Number 1, 1978, pages 97-99.
-
BL Shea,
Algorithm AS 239:
Chi-squared and Incomplete Gamma Integral,
Applied Statistics,
Volume 37, Number 3, 1988, pages 466-473.
-
Michael Wichura,
Algorithm AS 241:
The Percentage Points of the Normal Distribution,
Applied Statistics,
Volume 37, Number 3, 1988, pages 477-484.
Source Code:
Last revised on 27 August 2023.