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

Author

Listed:
  • 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)

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.

Suggested Citation

  • Boughrara Sabrina & Bedouhene Fazia & Zougab Nabil, 2025. "New contribution to Luria–Delbrück distribution. Stability property and estimation," Monte Carlo Methods and Applications, De Gruyter, vol. 31(1), pages 13-28.
    • Handle: RePEc:bpj:mcmeap:v:31:y:2025:i:1:p:13-28:n:1002
    DOI: 10.1515/mcma-2024-2024
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