Unknown properties of bimodal power Laplace distribution

Piotr Sulewski; Jakub Bilski

doi:https://doi.org/10.59139/ws.2025.12.1

Piotr Sulewski Uniwersytet Pomorski w Słupsku, Instytut Nauk Ścisłych i Technicznych, Zakład Informatyki, Polska / Pomeranian University in Słupsk, Institute of Exact and Technical Sciences, Department of Computer Science, Poland ORCID: https://orcid.org/0000-0002-0788-6567 , Jakub Bilski Uniwersytet Pomorski w Słupsku, Instytut Nauk Ścisłych i Technicznych, Zakład Informatyki, Polska / Pomeranian University in Słupsk, Institute of Exact and Technical Sciences, Department of Computer Science, Poland ORCID: https://orcid.org/0009-0000-8339-4698 Wiadomości Statystyczne. The Polish Statistician, vol. 70, 2025, 12, s. 1-34 Opublikowano online: 31 grudnia 2025 DOI https://doi.org/10.59139/ws.2025.12.1 Sposób cytowania: Sulewski, P., Bilski, J. (2025). Unknown properties of bimodal power Laplace distribution. Wiadomości Statystyczne. The Polish Statistician, 70(12), 1–34. https://doi.org/10.59139/ws.2025.12.1.

65 Wyświetlenia 26 Pobrania

ARTYKUŁ

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STRESZCZENIE

The main goal of this article is to present the unknown properties of the bimodal power Laplace (BPL) distribution such as: inflection points, Moors’ measure, pseudorandom number generator, entropy and Fisher information matrix. The secondary goals involve: a chronological overview of the large family of Laplace distributions, a brief review of the known properties of the analysed distribution and an estimation of the unknown parameters of the BPL distribution.
The BPL distribution has been defined by means of the standard Laplace distribution. The research has shown that the probability density function of the BPL distribution can also be obtained by applying the Fernández-Steel transformation to the Weibull distribution with a scale parameter equal to 1. Real data examples demonstrate that the BPL distribution is a flexible model that proves to be a valuable addition to the existing distributions for modelling bimodal data.

SŁOWA KLUCZOWE

Laplace distribution, double Weibull distribution, modelling bimodal data

JEL

C02, C10, C13, C15, C50

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