# List of statistics articles, Studentized residual, Univariate distribution, Deviation (statistics) and Mathematical statistics

Probability distribution of only one random variable.

- Univariate distributionAbsolute deviation

- List of statistics articlesIt is not simply a matter of the population parameters (mean and standard deviation) being unknown – it is that regressions yield different residual distributions at different data points, unlike point estimators of univariate distributions, which share a common distribution for residuals.

- Studentized residualA probability distribution can either be univariate or multivariate.

- Mathematical statisticsOne way is by dividing by a measure of scale (statistical dispersion), most often either the population standard deviation, in standardizing, or the sample standard deviation, in studentizing (e.g., Studentized residual).

- Deviation (statistics)Mathematical statistics

- List of statistics articlesStudentized residual

- List of statistics articlesUnivariate distribution

- List of statistics articles243 related topics

## Statistics

Discipline that concerns the collection, organization, analysis, interpretation, and presentation of data.

Inferences on mathematical statistics are made under the framework of probability theory, which deals with the analysis of random phenomena.

## Probability distribution

Mathematical function that gives the probabilities of occurrence of different possible outcomes for an experiment.

A probability distribution whose sample space is one-dimensional (for example real numbers, list of labels, ordered labels or binary) is called univariate, while a distribution whose sample space is a vector space of dimension 2 or more is called multivariate.

List of statistical topics

## Mathematics

Area of knowledge that includes such topics as numbers , formulas and related structures (algebra), shapes and the spaces in which they are contained (geometry), and quantities and their changes (calculus and analysis).

In these traditional areas of mathematical statistics, a statistical-decision problem is formulated by minimizing an objective function, like expected loss or cost, under specific constraints: For example, designing a survey often involves minimizing the cost of estimating a population mean with a given level of confidence.

## Standard score

Number of standard deviations by which the value of a raw score is above or below the mean value of what is being observed or measured.

In mathematical statistics, a random variable X is standardized by subtracting its expected value

## Errors and residuals

In statistics and optimization, errors and residuals are two closely related and easily confused measures of the deviation of an observed value of an element of a statistical sample from its "true value" (not necessarily observable).

The distinction is most important in regression analysis, where the concepts are sometimes called the regression errors and regression residuals and where they lead to the concept of studentized residuals.

Suppose there is a series of observations from a univariate distribution and we want to estimate the mean of that distribution (the so-called location model).

## Beta distribution

Family of continuous probability distributions defined on the interval [0, 1] parameterized by two positive shape parameters, denoted by alpha and beta (β), that appear as exponents of the random variable and control the shape of the distribution.

of mathematical statistics.

## Variance

In probability theory and statistics, variance is the expectation of the squared deviation of a random variable from its population mean or sample mean.

## Median

Value separating the higher half from the lower half of a data sample, a population, or a probability distribution.

A median-unbiased estimator minimizes the risk with respect to the absolute-deviation loss function, as observed by Laplace.

## Median absolute deviation

Robust measure of the variability of a univariate sample of quantitative data.

For a univariate data set X1, X2, ..., Xn, the MAD is defined as the median of the absolute deviations from the data's median

## Probability density function

[[Image:Boxplot vs PDF.svg|thumb|350px|[[Box plot]] and probability density function of a normal distribution

A probability density function is most commonly associated with absolutely continuous univariate distributions.