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<p>In this article, we introduce and develop new population distribution parameters estimation method by examining the empirical <i>exponent function</i> against the distribution exponent function. This indeed advances the method of moments and appears to be a powerful estimation procedure, alternative to the maximum likelihood and the empirical characteristic function parameters estimation methods. We put light on families of distributions where maximum likelihood and empirical characteristic function procedures fail to be, or hardly can be applied. Consistency and the limiting distribution of empirical exponent function estimators are established, as well. Our theoretical derivations are illustrated by performing extensive simulation work. Two real work are performed: inter-exceedance times of daily Bitcoin price changes (January 2020–June 2024) and inter-exceedance times of joint extreme water level and precipitation events at NOAA Station, Massachusetts, USA (1976–2022).</p>

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Parameter estimation using exponent function

  • 期刊论文

  • 发表日期：

    2026年2月3日

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  • Heydar Ali Mardani-Fard,
  • Ahmad Reza Soltani

摘要

In this article, we introduce and develop new population distribution parameters estimation method by examining the empirical exponent function against the distribution exponent function. This indeed advances the method of moments and appears to be a powerful estimation procedure, alternative to the maximum likelihood and the empirical characteristic function parameters estimation methods. We put light on families of distributions where maximum likelihood and empirical characteristic function procedures fail to be, or hardly can be applied. Consistency and the limiting distribution of empirical exponent function estimators are established, as well. Our theoretical derivations are illustrated by performing extensive simulation work. Two real work are performed: inter-exceedance times of daily Bitcoin price changes (January 2020–June 2024) and inter-exceedance times of joint extreme water level and precipitation events at NOAA Station, Massachusetts, USA (1976–2022).