Editing Mathematical statistics (section)

===Probability distributions===
{{main|Probability distribution}}
A [[probability distribution]] is a [[function (mathematics)|function]] that assigns a [[probability]] to each [[measure (mathematics)|measurable subset]] of the possible outcomes of a random [[Experiment (probability theory)|experiment]], [[Survey methodology|survey]], or procedure of [[statistical inference]]. Examples are found in experiments whose [[sample space]] is non-numerical, where the distribution would be a [[categorical distribution]]; experiments whose sample space is encoded by discrete [[random variables]], where the distribution can be specified by a [[probability mass function]]; and experiments with sample spaces encoded by continuous random variables, where the distribution can be specified by a [[probability density function]]. More complex experiments, such as those involving [[stochastic processes]] defined in [[continuous time]], may demand the use of more general [[probability measure]]s.

A probability distribution can either be [[Univariate distribution|univariate]] or [[Multivariate distribution|multivariate]]. A univariate distribution gives the probabilities of a single [[random variable]] taking on various alternative values; a multivariate distribution (a [[joint probability distribution]]) gives the probabilities of a [[random vector]]—a set of two or more random variables—taking on various combinations of values. Important and commonly encountered univariate probability distributions include the [[binomial distribution]], the [[hypergeometric distribution]], and the [[normal distribution]]. The [[multivariate normal distribution]] is a commonly encountered multivariate distribution.

====Special distributions====
*[[Normal distribution]],  the most common continuous distribution
*[[Bernoulli distribution]], for the outcome of a single Bernoulli trial (e.g. success/failure, yes/no)
*[[Binomial distribution]], for the number of "positive occurrences" (e.g. successes, yes votes, etc.) given a fixed total number of [[independent (statistics)|independent]] occurrences
*[[Negative binomial distribution]], for binomial-type observations but where the quantity of interest is the number of failures before a given number of successes occurs
*[[Geometric distribution]], for binomial-type observations but where the quantity of interest is the number of failures before the first success; a special case of the negative binomial distribution, where the number of successes is one.
*[[Discrete uniform distribution]], for a finite set of values (e.g. the outcome of a fair die)
*[[Continuous uniform distribution]], for continuously distributed values
*[[Poisson distribution]], for the number of occurrences of a Poisson-type event in a given period of time
*[[Exponential distribution]], for the time before the next Poisson-type event occurs
*[[Gamma distribution]], for the time before the next k Poisson-type events occur
*[[Chi-squared distribution]], the distribution of a sum of squared [[standard normal]] variables; useful e.g. for inference regarding the [[sample variance]] of normally distributed samples (see [[chi-squared test]])
*[[Student's t distribution]], the distribution of the ratio of a [[standard normal]] variable and the square root of a scaled [[chi squared distribution|chi squared]] variable; useful for inference regarding the [[mean]] of normally distributed samples with unknown variance (see [[Student's t-test]])
*[[Beta distribution]], for a single probability (real number between 0 and 1); conjugate to the [[Bernoulli distribution]] and [[binomial distribution]]