MParameter

Mparameter, or m-parameter, is a generic term used in mathematics and statistics to denote a parameter or a set of parameters of cardinality m in a parametric model. The concept emphasizes the dimensionality of the parameter space, with m indicating how many independent components define the model.

In statistical modeling, an m-parameter family of distributions is a collection of probability distributions defined by m independent parameters. For example, the normal distribution with both its mean and variance unknown constitutes a two-parameter family (m = 2). More generally, many exponential-family and regression models are described by a parameter vector θ = (θ1, ..., θm) whose dimension is m.

Estimation and inference for m-parameter models involve determining all components of θ from data. Identifiability is a key consideration: different parameter values should yield different probability distributions. Common estimation methods include maximum likelihood estimation, Bayesian inference with priors on θ, and method-of-moments approaches. The numerical properties of estimation can depend strongly on the chosen parameterization.

Reparameterization may be used to improve interpretability or computational stability without changing the underlying model. Different parameterizations can offer advantages in optimization, prior specification, or convergence of iterative algorithms.

See also: parameter, parameterization, identifiability.