Distribution

• normal

• exponential

• linear

• Cauchy

Probability distribution

Probability distribution is a description of a random phenomenon in terms of the probabilities of events.

In probability theory and statistics, a probability distribution is a mathematical function that provides the probabilities of occurrence of different possible outcomes in an experiment.

For instance, in a fair coin toss experiment, if the random variable $X$ is used to denote the outcome of a coin toss, then the probability distribution of $X$ would take the value 0.5 for X = heads, and 0.5 for X = tails.

Examples of random phenomena can include the results of an experiment or survey.

A probability distribution is specified in terms of an underlying sample space, which is the set of all possible outcomes of the random phenomenon being observed. The sample space may be the set of real numbers, vectors, a list of non-numerical values; the sample space of a coin toss would be {heads, tails}.

Probability distributions are generally divided into 2 classes:

• discrete probability distribution

• continuous probability distribution

Discrete probability distribution, applicable to the experiments where the set of possible outcomes is discrete, can be represented by a discrete list of the probabilities of the outcomes, known as a probability mass function.

Continuous probability distribution, applicable to the experiments where the set of possible outcomes can take on values in a continuous range, is typically described by probability density functions (with the probability of any individual outcome actually being 0).

The normal distribution (aka Gaussian, Gauss, Laplace–Gauss distribution) is a very common continuous probability distribution. Normal distributions are important in statistics and are often used in the natural and social sciences to represent real-valued random variables whose distributions are not known.

A random variable with a normal distribution is said to be normally distributed and is called a normal deviate.

More complex experiments, such as those involving stochastic processes defined in continuous time, may demand the use of more general probability measures.

Univariate distribution is a probability distribution whose sample space is one dimensional (e.g. real numbers, list of labels, ordered labels or binary). A univariate distribution gives the probabilities of a single random variable taking on various alternative values. Important and commonly encountered univariate probability distributions include binomial distribution,hypergeometric distribution and normal distribution.

Multivariate distribution is a probability distribution whose sample space is a vector space of two or more dimensions. A multivariate distribution (a joint probability distribution) gives the probabilities of a random vector – a list of two or more random variables – taking on various combinations of values. Commonly encountered multivariate distribution is multivariate normal distribution