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A "parameter" is to a population as a "statistic" is to a sample; that is to say, a parameter describes the true value calculated from the full population (such as the population mean), whereas a statistic is an estimated measurement of the parameter based on a sample (such as the sample mean). Thus a "statistical parameter" can be more ...
A statistic (singular) or sample statistic is any quantity computed from values in a sample which is considered for a statistical purpose. Statistical purposes include estimating a population parameter, describing a sample, or evaluating a hypothesis. The average (or mean) of sample values is a statistic. The term statistic is used both for the ...
Parametric statistics is a branch of statistics which leverages models based on a fixed (finite) set of parameters. [1] Conversely nonparametric statistics does not assume explicit (finite-parametric) mathematical forms for distributions when modeling data. However, it may make some assumptions about that distribution, such as continuity or ...
A statistic is a numerical characteristic of a sample that can be used as an estimate of the corresponding parameter, the numerical characteristic of the population from which the sample was drawn. For example, the sample mean (estimator), denoted X ¯ {\displaystyle {\overline {X}}} , can be used as an estimate of the mean parameter (estimand ...
Greek letters (e.g. θ, β) are commonly used to denote unknown parameters (population parameters). [3]A tilde (~) denotes "has the probability distribution of". Placing a hat, or caret (also known as a circumflex), over a true parameter denotes an estimator of it, e.g., ^ is an estimator for .
The Beta distribution on [0,1], a family of two-parameter distributions with one mode, of which the uniform distribution is a special case, and which is useful in estimating success probabilities. The four-parameter Beta distribution, a straight-forward generalization of the Beta distribution to arbitrary bounded intervals [,].
In statistics, sufficiency is a property of a statistic computed on a sample dataset in relation to a parametric model of the dataset. A sufficient statistic contains all of the information that the dataset provides about the model parameters.
For example, with the univariate Gaussian distribution, is formally a single parameter with dimension 2, but it is often regarded as comprising 2 separate parameters—the mean and the standard deviation. A statistical model is nonparametric if the parameter set is infinite