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When is an Exponentiated Pareto distribution infinitely divisible?

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  • Sarkar, Pritam
  • Chakraborty, Soumi Thakur
  • Pal, Ayan

Abstract

We investigate the conditions of infinite divisibility of the Exponentiated Pareto (EP) distribution supported on the entire positive half-line (0,∞), along with its discrete analogue defined on the set of non-negative integers. The EP distribution is defined via the cumulative distribution function (CDF) [F(x)]α , where α>0 and F(x)=1−(1+x)−λ,x>0, is the CDF of Pareto Type II (Lomax) distribution with tail parameter λ>0. The discrete counterpart is defined as the integer part of a random variable X following the EP distribution. The main results assert that both the continuous and discrete versions of the EP distribution are infinitely divisible if α∈(0,1]. A brief discussion of the Lévy process corresponding to the infinitely divisible case for α∈(0,1] is provided along with a real world data illustration.

Suggested Citation

  • Sarkar, Pritam & Chakraborty, Soumi Thakur & Pal, Ayan, 2026. "When is an Exponentiated Pareto distribution infinitely divisible?," Statistics & Probability Letters, Elsevier, vol. 232(C).
    • Handle: RePEc:eee:stapro:v:232:y:2026:i:c:s0167715226000192
    DOI: 10.1016/j.spl.2026.110655
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    References listed on IDEAS

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