All classes that implement discrete probability distributions inherit from the DiscreteDistribution class. This class defines
methods and properties common to all discrete probability distributions.
Parameters of a distribution
Discrete probability distributions arise from counting events whose
occurrence is in some way probabilistic. One parameter specifies
the probabilistic element of the setup. The remaining parameters specify
specific details about the setup.
Each distribution object has one or more properties corresponding to
the distribution parameters. These properties are read-only.
Properties of distributions
Each distribution object has one or more properties that return
the parameters of the distribution.
In addition, each distribution defines properties that describe
the main traits of the distribution. The
property returns the mean of the distribution.
The StandardDeviation property
returns the standard deviation of the distribution. The Variance property returns the variance. The
Skewness property returns the skewness of
the distribution, and the Kurtosis
property returns the kurtosis supplement of the distribution.
Associated with each distribution are a number of functions
that are commonly used in statistical calculations.
The probability function gives the probability that a random sample
from the distribution takes on a specific value. It is implemented by the
method. This method takes one argument: the value for which the probability is requested.
There is an
that takes two arguments, and returns the total probability that a sample falls
within the interval specified by the arguments. The lower bound is inclusive.
The upper bound is exclusive. This means that passing the same value for
both parameters returns 0.
The distribution function, often called the cumulative distribution function (CDF),
gives the probability that a sample or sample from the distribution
has a value less than or equal to its argument. It is implemented by the
Generating Random Variates
One of the principal applications of probability distributions is
the generation of random numbers that follow a certain distribution.
The discrete distribution classes provide a series of methods to make this happen.
method returns a single random sample from the distribution. It has overloads
as both static (Shared in Visual Basic) and instance methods. The instance method
has only one parameter: the random number generator that will be used to
generate the uniform random number(s) used in the calculation of the sample.
It is of type SystemRandom.
Any of the random number generators from the
can be used for this purpose.
Each class also defines one or more static overloads,
one each for each constructor. The first argument is always the random number generator,
as above. Additional arguments correspond to the arguments of each constructor.
This makes it possible to generate random samples for any distribution
without first constructing a distribution object.
The Sample method
generates a large number of random samples at once. The first argument
is once again the uniform random number generator.
The samples are returned as an integer array.
The array must be supplied as the second argument.
Two additional argument may be provided, which supply the start index
and the length of a segment in the array where the samples are to be copied.