New contribution to Luria–Delbrück distribution. Stability property and estimation

Boughrara Sabrina (), Bedouhene Fazia () and Zougab Nabil ()
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Boughrara Sabrina: Laboratoire de Mathématiques Pures et Appliquées, Mouloud Mammeri University of Tizi-Ouzou, Tizi-Ouzou, Algeria
Bedouhene Fazia: Laboratoire de Mathématiques Pures et Appliquées, Mouloud Mammeri University of Tizi-Ouzou, Tizi-Ouzou, Algeria
Zougab Nabil: Department of Electrical Engineering, Faculty of Technology and Research unit LaMOS, University of Bejaia, Bejaia, Algeria

Monte Carlo Methods and Applications, 2025, vol. 31, issue 1, 13-28

Abstract: The multiplication of cells leads to consider the cell division model with mutation. Large cell counts therefore appear, implying that the distribution of the final number of mutant cells is a heavy tailed distribution. This distribution can be interpreted as a compound Poisson distribution, which depends on two parameters: the average number of mutations and the fitness parameter (heavy tail index). In this work, we specify some conditions that ensure a stability property of heavy-tailed distributions, namely, the distribution of random sum of random variables is a heavy-tailed distribution. We apply the obtained result to the compound Poisson distribution. To estimate the tail index, the Hill estimator and the generating function method are used. A comparative study is performed using these two estimators.

Keywords: Heavy tailed distribution; compound Poisson distribution; Luria–Delbrück distribution; power law distribution; generating function; Hill estimator (search for similar items in EconPapers)
Date: 2025
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DOI: 10.1515/mcma-2024-2024

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