**prob**,
a Python code which
handles various discrete and
continuous probability density functions (PDF).

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

then we are asserting that the valueX = 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 or
**I4_UNIFORM**, each of which in turn calls a routine called
**R8_UNIFORM_01**. You may prefer a different random number generator
for this purpose.

The computer code and data files described and made available on this web page are distributed under the GNU LGPL license.

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

log_normal, a Python code which returns quantities associated with the log normal Probability Distribution Function (PDF).

log_normal_truncated_ab, a Python code which returns quantities associated with the log normal Probability Distribution Function (PDF) truncated to the interval [A,B].

normallllllllllllllll, a Python code which samples the normal distribution.

pdflib, a Python code which evaluates Probability Density Functions (PDF's) and produces random samples from them, including beta, binomial, chi, exponential, gamma, inverse chi, inverse gamma, multinomial, normal, scaled inverse chi, and uniform.

test_values, a Python code which contains sample values for a number of distributions.

truncated_normal, a Python code which works with the truncated normal distribution over [A,B], or [A,+oo) or (-oo,B], returning the probability density function (PDF), the cumulative density function (CDF), the inverse CDF, the mean, the variance, and sample values.

uniform, a Python code which samples the uniform distribution.