On the Poisson XLindley process

• Autorzy: Sakri Amine , Seghier Fatma-Zohra , Vinoth Raman , Zeghdoudi Halim

Identyfikatory

DOI

10.14708/ma.v51i2.7200

Warianty tytułu

PL

Proces Poissona–XLindleya

• Języki publikacji: EN

Abstrakty

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.

Słowa kluczowe

EN

poisson process; poisson XLindley process; positive dependence; stochastic processes; stochastic properties

PL

proces Poissona; proces Poissona–XLindleya; dodatnia zależność; procesy stochastyczne; własności stochastyczne

• Wydawca: Polskie Towarzystwo Matematyczne
• Czasopismo: Mathematica Applicanda
• Rocznik: 2023
• Tom: Vol. 51, no. 2
• Strony: 273--289
• Opis fizyczny: Bibliogr. 22 poz.

Twórcy

autor

Sakri Amine

• Badji Mokhtar-Annaba University Numerical analysis, Optimization and Statistics Laboratory, 23000, Annaba- Algeria

• https://orcid.org/0000-0002-7635-2243+

autor

Seghier Fatma-Zohra

• Higher Normal School of Technological Education Skikda, Algeria

• https://orcid.org/0000-0003-0175-8430+

autor

Vinoth Raman

• Imam Abdulrahman Bin Faisal University Dammam, Eastern, Saudi Arabia

• https://orcid.org/0000-0002-3815-2312+

autor

Zeghdoudi Halim

• Badji Mokhtar-Annaba University Department of Mathematics, Science Faculty, 2300, Annaba-Algeria

• https://orcid.org/0000-0002-4759-5529

Bibliografia

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• [18] F. Z. Seghier, H. Zeghdoudi, and V. Raman. A Novel Discrete Distribution: Properties and Application Using Nipah Virus Infection Data Set. European Journal of Statistics, 3:3, 2022.
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Uwagi

PL

Opracowanie rekordu ze środków MNiSW, umowa nr SONP/SP/546092/2022 w ramach programu "Społeczna odpowiedzialność nauki" - moduł: Popularyzacja nauki i promocja sportu (2024).