Distributions

Distributions section includes description of popular probability distributions and their implementations.

A probability mass, probability density, or probability distribution is a function that describes the probability of a random variable taking certain values. For a more precise definition one needs to distinguish between discrete and continuous random variables.

In the discrete case, one can easily assign a probability to each possible value: when throwing a die, each of the six values 1 to 6 has the probability 1/6. In contrast, when a random variable takes values from a continuum, probabilities are nonzero only if they refer to finite intervals: in quality control one might demand that the probability of a "500 g" package containing between 500 g and 510 g should be no less than 98%.

The cumulative distribution function (CDF) describes the probability that a real-valued random variable X with a given probability distribution will be found at a value less than or equal to x.

Random variables can be univariate, multivariate or matrix. Therefore, the distributions descriptions are divided in the following groups by type of random variables:

• Discrete Univariate

• Continious Univariate

• Multivariate

• Matrix