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On the Poisson XLindley process

Sakri Amine, Seghier Fatma-Zohra, Vinoth Raman, Zeghdoudi Halim

Mathematica Applicanda

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2023

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Vol. 51, no. 2

273--289

EN

Due to their advantages, non-homogeneous Poisson processes have so far been used extensively in a variety of practical applications. They do, however, also have important application-related limits. A novel counting process model named the Poisson–XLindley Process was created to get around these restrictions. We shall demonstrate that this new model lacks such constraints. These fundamental stochastic properties of the process are derived. Additionally, the dependence structure is examined along with the new idea of positively dependent increments. Generic versions of several of the features derived in this article will be offered. This is an innovative concept related to counting processes, which allows the probability function to be described explicitly. It is one of its major contributions

PL

Niejednorodne procesy Poissona są szeroko stosowane w modelowaniu chociaż mają istotne ograniczenia jesli chcemy uzyskać wysoką zgodność modelu z zjawiskiem. W celu usunięcia tych problemów wprowadzamy zmodyfikowany opis procesu liczącego, nazwany Procesem Poissona XLindleya. W pracy pokazujemy przełamanie istotnych ograniczeń niejednorodnego procesu Poissona przez nowy model. Wyprowadzono podstawowe właściwości probabilistyczne tego procesu, badana jest równiez struktura zależności przyrostów z wykorzystaniem idei przyrostów dodatnio zależnych. W pracy pokazano ogólną wersję funkcjonałów od tego procesu. Ta innowacyjna koncepcja procesu liczącego, pozwalająca na jawny formuły opisujące rozkłady prawdopodobieństwa, jest jednym z jej głównych walorów pracy.

2

On the characterisation of X-Lindley distribution by truncated moments. Properties and application

Metiri Farouk, Zeghdoudi Halim, Ezzebsa Abdelali

Operations Research and Decisions

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2022

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Vol. 32, No. 1

99--109

EN

Several papers introduce the new distributions and their applications, including, among others, those of Ducey and Gove [7], Grine and Zeghdoudi [8], Chouia et al. [5], Seghier et al. [11], Beghriche and Zeghdoudi [4], where characterisation of a probability distribution plays an important role in statistical science. Several researchers studied the characterisations of probability distributions. For example, Su and Huang [12] study the characterisations of distributions based on expectations. In addition, Nanda [10] studies the characterisations by average residual life and the failure rates of functions of absolutely continuous random variables. Ahmadi et al. [1] consider the estimation based on the left-truncated and right randomly censored data arising from a general family of distributions. On the other hand, Ahsanullah et al. [2, 3] present two characterisations of Lindley distribution, standard normal distribution, t-Student’s, exponentiated exponential, power function, Pareto, and Weibull distributions based on the relation of failure rate, reverse failure rate functions with left and right truncated moments. Recently, Haseeb and Yahia [9] studied truncated moments for two general classes of continuous distributions. In this paper, two characterisations of the X-Lindley distribution, introduced by Chouia and Zeghdoudi [5] have been studied. They are based on the failure, relation of the inverse failure rate functions with the left and right truncated moments, respectively. Section 2 gives some properties of X-Lindley distribution. Section 3 discusses the characterisation of general distribution by left truncated and failure rate function and then right truncated and reverse failure rate function. Section 4 studies the characterisation of X-Lindley distribution by using the relation between left/right truncated moment and failure/reverse failure rate function. Finally, an illustrative example of X-Lindley distribution with other one-parameter distributions is given to show the superiority and flexibility of this model.

3

Existence of periodic positive solutions to nonlinear Lotka-Volterra competition

Benhadri Mimia, Caraballo Tomas, Zeghdoudi Halim

Opuscula Mathematica

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2020

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Vol. 40, no. 3

341--360

EN

We investigate the existence of positive periodic solutions of a nonlinear Lotka-Volterra competition system with deviating arguments. The main tool we use to obtain our result is the Krasnoselskii fixed point theorem. In particular, this paper improves important and interesting work [X.H. Tang, X. Zhou, On positive periodic solution of Lotka-Volterra competition systems with deviating arguments, Proc. Amer. Math. Soc. 134 (2006), 2967-2974]. Moreover, as an application, we also exhibit some special cases of the system, which have been studied extensively in the literature.