Parameter (statistics)

A parameter is a fixed numerical characteristic of a population or probability distribution, such as its mean, variance, or success probability.

Population (statistics): The complete set of individuals or measurements a statistical study aims to describe. A parameter characterizes this full set rather than just the observed cases.
Point estimation: The use of sample data to produce a single estimate of an unknown parameter. It converts observed data into a specific proposed value for a population quantity.
Parameter space: The set of all allowed values for the parameters of a statistical model. Inference searches this space for values compatible with the observed data.
Estimand: The precise population quantity a statistical analysis aims to estimate or compare. An estimand states the target, while a parameter is a model or population quantity that may represent it.
Statistical sample: A subset of observations selected from a population for analysis. Sample statistics are computed from these observations to learn about population parameters.
Confidence interval: A procedure that produces an interval designed to cover a population parameter at a stated long-run rate. It expresses parameter uncertainty with a range rather than one estimate.
Likelihood function: A function of model parameters proportional to the probability or density of observed data. It measures how well different parameter values account for a fixed dataset.
Hyperparameter: A parameter governing a prior distribution or another higher-level component of a statistical model. It controls assumptions about parameters rather than directly describing the sampled population.
Statistic: A numerical summary calculated from sample data, such as the sample mean. Unlike a parameter, a statistic varies across samples and can estimate a fixed population value.
Hypothesis test: A statistical procedure that evaluates data against a specified claim about a probability model or population. Many tests ask whether evidence conflicts with a proposed parameter value.

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