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The Gompertz distribution and its applications.

J H Pollard, E J Valkovics

    Genus
    |July 1, 1992
    PubMed
    Summary
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    This study explores the Gompertz distribution, revealing its fixed skewness and kurtosis. These constants explain challenges in fitting the Gompertz curve to fertility data.

    Area of Science:

    • Statistics
    • Probability Theory
    • Biostatistics

    Background:

    • The Gompertz distribution is a valuable statistical model.
    • Its properties and applications, particularly in fertility data analysis, require further elucidation.
    • Previous attempts to fit the Gompertz curve to fertility data have yielded mixed results.

    Purpose of the Study:

    • To thoroughly investigate the underlying Gompertz distribution.
    • To derive formulas for its moments and other key characteristics.
    • To explain the observed successes and failures in fitting the distribution to fertility data.

    Main Methods:

    • Mathematical derivation of formulae for distribution moments.
    • Analysis of skewness and kurtosis properties.
    Keywords:
    Demographic FactorsEvaluationEvaluation MethodologyFertilityMathematical ModelMeasurementModels, TheoreticalPopulationPopulation DynamicsReliabilityResearch MethodologyWorld

    Related Experiment Videos

  • Investigation of the distribution of the minimum of independent Gompertz variables.

    • Main Results:

    • Formulas for the moments and characteristics of the Gompertz distribution were developed.
    • Skewness and kurtosis were found to be fixed constants, independent of distribution parameters.
    • The distribution of the minimum of n independent Gompertz variables (with identical c-parameters) is also a Gompertz variable with the same c-parameter.

    Conclusions:

    • The fixed skewness and kurtosis of the Gompertz distribution are identified as the reason for challenges in fitting fertility data.
    • The study provides a deeper understanding of the Gompertz distribution's mathematical properties.
    • The findings offer insights into the behavior of minimums of Gompertz-distributed variables.