prob

prob, a Fortran77 code which handles various discrete and continuous probability density functions ("PDF's").

For a discrete variable X, PDF(X) is the probability that the value X will occur; for a continuous variable, PDF(X) is the probability density of X, that is, the probability of a value between X and X+dX is PDF(X) * dX.

The corresponding cumulative density functions or "CDF"'s are also handled. For a discrete or continuous variable, CDF(X) is the probability that the variable takes on a value less than or equal to X.

In some cases, the inverse of the CDF can easily be computed. If

        X = CDF_INV ( P )
      

For most distributions, the mean or "average value" or "expected value" is also available. For a discrete variable, MEAN is simply the sum of the products X * PDF(X); for a continuous variable, MEAN is the integral of X * PDF(X) over the range. For the distributions covered here, the means are known beforehand, and no summation or integration is required.

For most distributions, the variance is available. For a discrete variable, the variance is the sum of the products ( X - MEAN )^2 * PDF(X); for a continuous variable, the variance is the integral of ( X - MEAN )^2 * PDF(X) over the range. The square root of the variance is known as the standard deviation. For the distributions covered here, the variances are often known beforehand, and no summation or integration is required.

For many of the distributions, it is possible to repeatedly request "samples", that is, a pseudorandom sequence of realizations of the PDF. These samples are always associated with an integer seed, which controls the calculation. Using the same seed as input will guarantee the same sample value on output. Ultimately, a random number generator must be invoked internally. In most cases, the current code will call a routine called R8_UNIFORM_01, which uses a very basic, and old, random number generator. You may prefer a different random number generator for this purpose.

Licensing:

The information on this web page is distributed under the MIT license.

Languages:

prob is available in a C version and a C++ version and a Fortran77 version and a Fortran90 version and a MATLAB version and an Octave version and a Python version.

Related Data and Programs:

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asa066, a Fortran77 library which evaluates the CDF of the normal distribution.

ASA076, a Fortran77 library which evaluates the Owen's T function, needed to compute the CDF of the noncentral T distribution.

ASA091, a Fortran77 library which evaluates the percentage points of the Chi-Squared distribution.

ASA111, a Fortran77 library which evaluates the percentage points of the normal distribution.

ASA152, a Fortran77 library which evaluates point and cumulative probabilities associated with the hypergeometric distribution; this is Applied Statistics Algorithm 152;

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ASA243, a Fortran77 library which evaluates the CDF of the noncentral T distribution.

ASA266, a Fortran77 library which evaluates various properties of the Dirichlet probability density function; this is Applied Statistics Algorithm 266;

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TOMS441, a Fortran77 library which samples the dipole distribution;
this is ACM TOMS algorithm 441.

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Source Code:

• prob.f, the source code;
• prob.sh, commands to compile the source code;