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Shape factor asymptotic analysis II

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  • Wang, Frank Xuyan

Abstract

Probability distributions with identical shape factor asymptotic limit formulas are defined as asymptotic equivalent distributions. The GB1, GB2, and Generalized Gamma distributions are examples of asymptotic equivalent distributions, which have similar fitting capabilities to data distribution with comparable parameters values. These example families are also asymptotic equivalent to Kumaraswamy, Weibull, Beta, ExpGamma, Normal, and LogNormal distributions at various parameters boundaries. The asymptotic analysis that motivated the asymptotic equivalent distributions definition is further generalized to contour analysis, with contours not necessarily parallel to the axis. Detailed contour analysis is conducted for GB1 and GB2 distributions for various contours of interest. Methods combing induction and symbolic deduction are crafted to resolve the dilemma over conflicting symbolic asymptotic limit results. From contour analysis build on graphical and analytical reasoning, we find that the upper bound of the GB2 distribution family, having the maximum shape factor for given skewness, is the Double Pareto distribution.

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  • Wang, Frank Xuyan, 2021. "Shape factor asymptotic analysis II," MPRA Paper 110827, University Library of Munich, Germany.
    • Handle: RePEc:pra:mprapa:110827
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    References listed on IDEAS

    as
    1. Masato Okamoto, 2013. "Extension of the κ-generalized distribution: new four-parameter models for the size distribution of income and consumption," LIS Working papers 600, LIS Cross-National Data Center in Luxembourg.
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    Full references (including those not matched with items on IDEAS)

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    More about this item

    Keywords

    shape factor; skewness; kurtosis; asymptotic equivalent distributions; GB1 distribution; ExpGamma distribution; LogNormal distribution; GB2 distribution; Double Pareto distribution; contour analysis; computer algebra system; symbolic analysis;
    All these keywords.

    JEL classification:

    • C02 - Mathematical and Quantitative Methods - - General - - - Mathematical Economics
    • C46 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods: Special Topics - - - Specific Distributions
    • C60 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - General
    • C88 - Mathematical and Quantitative Methods - - Data Collection and Data Estimation Methodology; Computer Programs - - - Other Computer Software
    • G22 - Financial Economics - - Financial Institutions and Services - - - Insurance; Insurance Companies; Actuarial Studies

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