ASA091
Percentage Points of the Chi-Squared Distribution

ASA091 is a FORTRAN77 library which computes the percentage points of the Chi-Squared probability distribution, by Best and Roberts.

ASA091 is Applied Statistics Algorithm 91.

Languages:

ASA091 is available in a C version and a C++ version and a FORTRAN77 version and a FORTRAN90 version and a MATLAB version.

Related Data and Programs:

DCDFLIB, a FORTRAN90 library which evaluates and inverts a number of statistical distributions.

GSL, a C++ library which includes many routines for evaluating probability distributions.

NORMAL, a FORTRAN77 library which samples the normal distribution.

PROB, a FORTRAN90 library which evaluates and inverts many probability distibutions.

TEST_VALUES, a FORTRAN77 library which contains sample values for a number of distributions.

UNIFORM, a FORTRAN77 library which samples the uniform distribution.

Author:

Original FORTRAN77 version by Donald Best and DE Roberts; This FORTRAN77 version by John Burkardt.

Reference:

1. 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.
2. 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.
3. John Hart, Ward Cheney, Charles Lawson, Hans Maehly, Charles Mesztenyi, John Rice, Henry Thacher, Christoph Witzgall,
   Computer Approximations,
   Wiley, 1968,
   LC: QA297.C64.
4. BL Shea,
   Algorithm AS 239: Chi-squared and Incomplete Gamma Integral,
   Applied Statistics,
   Volume 37, Number 3, 1988, pages 466-473.
5. Michael Wichura,
   Algorithm AS 241: The Percentage Points of the Normal Distribution,
   Applied Statistics,
   Volume 37, Number 3, 1988, pages 477-484.

Source Code:

• asa091.f, the source code.
• asa091.sh, commands to compile the source code.

Examples and Tests:

• asa091_prb.f, a sample calling program.
• asa091_prb.sh, commands to compile and run the sample program.
• asa091_prb_output.txt, the output file.

List of Routines:

• ALNGAM computes the logarithm of the gamma function.
• ALNORM computes the cumulative density of the standard normal distribution.
• CHI_SQUARE_CDF_VALUES returns some values of the Chi-Square CDF.
• GAMMAD computes the Incomplete Gamma Integral
• PPCHI2 evaluates the percentage points of the chi-squared PDF.
• PPND produces the normal deviate value corresponding to lower tail area = P.
• TIMESTAMP prints out the current YMDHMS date as a timestamp.

You can go up one level to the FORTRAN77 source codes.