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Estimating the parameters of a Polya-Aeppli distribution.

H L Sharma

    Rural Demography
    |January 1, 1988
    PubMed
    Summary

    This study derives maximum likelihood equations for the Polya-Aeppli distribution, offering insights into household structures. It details estimators for parameters when group counts are known, aiding demographic analysis.

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    Area of Science:

    • Statistics
    • Demography

    Background:

    • The Polya-Aeppli distribution is used for modeling count data, particularly in biological and social sciences.
    • Understanding household structures is crucial for demographic and socioeconomic analysis.

    Purpose of the Study:

    • To derive maximum likelihood equations for the Polya-Aeppli distribution parameters.
    • To determine asymptotic variances and covariances for these maximum likelihood estimators.
    • To apply the methods to demographic data concerning household structures.

    Main Methods:

    • Derivation of maximum likelihood equations.
    • Calculation of asymptotic variances and covariances for estimators.
    • Application of statistical methods to demographic data.
    Keywords:
    AsiaDemographic FactorsDeveloping CountriesEstimation TechnicsFamily And HouseholdHouseholdsIndiaMigrationModels, TheoreticalPopulationPopulation DynamicsResearch MethodologySouthern Asia

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    Main Results:

    • Expressions for maximum likelihood equations are provided.
    • Asymptotic variances and covariances of estimators are determined.
    • The methodology is illustrated with an example using Indian demographic data on household types.

    Conclusions:

    • The study provides a statistical framework for analyzing Polya-Aeppli distributed data, specifically for household structures.
    • The derived estimators are valuable for demographic research, especially when counts of groups with zero or one object are known.