Method of moments

A parameter-estimation method that sets sample moments equal to their theoretical counterparts and solves the resulting equations for the model parameters.

Statistical moment: A numerical summary of a distribution, such as its mean, variance, or skewness. The method matches sample versions of these summaries to model-implied values.
Binomial distribution: The distribution of the number of successes in a fixed number of independent trials with equal success probabilities. Its mean directly relates the success probability to the observed sample average.
Least squares: An estimation procedure that minimizes the sum of squared differences between observed and predicted values. Regression parameters can be fitted by minimizing residuals instead of matching distribution moments.
Consistency (statistics): A property of an estimator whose probability of being close to the true parameter approaches one as sample size grows. Under suitable conditions, sample moments converge and moment estimates approach the true parameters.
Sample mean: The arithmetic average of observations in a dataset. Equating it with the model mean often yields the first parameter estimate.
Poisson distribution: A discrete probability distribution for counts of events occurring independently at a constant average rate. Its mean equals its rate parameter, so the sample mean supplies an estimate.
Bayesian estimation: Parameter estimation that combines a likelihood with a prior distribution to obtain a posterior distribution. It represents parameter uncertainty through a posterior rather than a single moment-matched estimate.
Asymptotic normality: A property in which a suitably scaled estimator converges in distribution to a normal random variable as sample size grows. It supports large-sample uncertainty calculations for moment-based estimates.
Variance: A measure of how widely values in a distribution vary around their mean. Matching sample and theoretical variance can identify parameters beyond the mean.
Exponential distribution: A continuous distribution commonly used for waiting times between independent events occurring at a constant rate. Its theoretical mean gives a direct moment equation for the rate.

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