Journal of Statistical Theory and Applications

Volume 20, Issue 1, March 2021, Pages 33 - 45

Statistical Properties and Different Estimation Procedures of Poisson–Lindley Distribution

Authors
Mohammed Amine Meraou1, Mohammad Z. Raqab*, ORCID
1Department of Mathematics, The University of Jordan, Amman, 11942, Jordan
*Corresponding author. Email: mraqab@ju.edu.jo
Corresponding Author
Mohammad Z. Raqab
Received 21 October 2020, Accepted 28 October 2020, Available Online 11 January 2021.
DOI
10.2991/jsta.d.210105.001How to use a DOI?
Keywords
Anderson–Darling method; Cramer–von Mises; Least square estimators; Maximum likelihood estimators; Poisson–Lindley distribution
Abstract

In this paper, we propose a new class of distributions by compounding Lindley distributed random variates with the number of variates being zero-truncated Poisson distribution. This model is called a compound zero-truncated Poisson–Lindley distribution with two parameters. Different statistical properties of the proposed model are discussed. We describe different methods of estimation for the unknown parameters involved in the model. These methods include maximum likelihood, least squares, weighted least squares, Cramer–von Mises, maximum product of spacings, Anderson–Darling and right-tail Anderson–Darling methods. Numerical simulation experiments are conducted to assess the performance of the so obtained estimators developed from these methods. Finally, the potentiality of the model is studied using one real data set representing the monthly highest snowfall during February 2018, for a subset of stations in the Global Historical Climatological Network of USA.

Copyright
© 2021 The Authors. Published by Atlantis Press B.V.
Open Access
This is an open access article distributed under the CC BY-NC 4.0 license (http://creativecommons.org/licenses/by-nc/4.0/).

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Journal
Journal of Statistical Theory and Applications
Volume-Issue
20 - 1
Pages
33 - 45
Publication Date
2021/01/11
ISSN (Online)
2214-1766
ISSN (Print)
1538-7887
DOI
10.2991/jsta.d.210105.001How to use a DOI?
Copyright
© 2021 The Authors. Published by Atlantis Press B.V.
Open Access
This is an open access article distributed under the CC BY-NC 4.0 license (http://creativecommons.org/licenses/by-nc/4.0/).

Cite this article

TY  - JOUR
AU  - Mohammed Amine Meraou
AU  - Mohammad Z. Raqab
PY  - 2021
DA  - 2021/01/11
TI  - Statistical Properties and Different Estimation Procedures of Poisson–Lindley Distribution
JO  - Journal of Statistical Theory and Applications
SP  - 33
EP  - 45
VL  - 20
IS  - 1
SN  - 2214-1766
UR  - https://doi.org/10.2991/jsta.d.210105.001
DO  - 10.2991/jsta.d.210105.001
ID  - Meraou2021
ER  -