International Journal of

ADVANCED AND APPLIED SCIENCES

EISSN: 2313-3724, Print ISSN: 2313-626X

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 Volume 8, Issue 4 (April 2021), Pages: 89-97

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 Original Research Paper

 Title: A new generalization of the inverse Lomax distribution with statistical properties and applications

 Author(s): Amal S. Hassan 1, *, Amer Ibrahim Al-Omar 2, Doaa M. Ismail 1, 3, Ayed Al-Anzi 4

 Affiliation(s):

 1Department of Mathematical Statistics, Faculty of Graduate Studies for Statistical Research, Cairo University, Giza, Egypt
 2Department of Mathematics, Faculty of Science, Al al-Bayt University, Mafraq, Jordan
 3Modern Academy for Engineering and Technology, Cairo, Egypt
 4Department of Mathematics, College of Science and Human Studies at Hotat Sudair, Majmaah University, Majmaah, Saudi Arabia

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 * Corresponding Author. 

  Corresponding author's ORCID profile: https://orcid.org/0000-0003-4442-8458

 Digital Object Identifier: 

 https://doi.org/10.21833/ijaas.2021.04.011

 Abstract:

In this paper, we introduce a new generalization of the inverse Lomax distribution with one extra shape parameter, the so-called power inverse Lomax (PIL) distribution, derived by using the power transformation method. We provide a more flexible density function with right-skewed, uni-modal, and reversed J-shapes. The new three-parameter lifetime distribution capable of modeling decreasing, Reversed-J and upside-down hazard rates shapes. Some statistical properties of the PIL distribution are explored, such as quantile measure, moments, moment generating function, incomplete moments, residual life function, and entropy measure. The estimation of the model parameters is discussed using maximum likelihood, least squares, and weighted least squares methods. A simulation study is carried out to compare the efficiencies of different methods of estimation. This study indicated that the maximum likelihood estimates are more efficient than the corresponding least squares and weighted least squares estimates in approximately most of the situations Also, the mean square errors for all estimates are decreasing as the sample size increases. Further, two real data applications are provided in order to examine the flexibility of the PIL model by comparing it with some known distributions. The PIL model offers a more flexible distribution for modeling lifetime data and provides better fits than other models such as inverse Lomax, inverse Weibull, and generalized inverse Weibull. 

 © 2021 The Authors. Published by IASE.

 This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/).

 Keywords: Inverse Lomax distribution, Moments, Order statistics, Maximum likelihood estimation, Power transformation

 Article History: Received 2 October 2020, Received in revised form 22 December 2020, Accepted 23 December 2020

 Acknowledgment:

No Acknowledgment.

 Compliance with ethical standards

 Conflict of interest: The author(s) declared no potential conflicts of interest with respect to the research, authorship, and/or publication of this article.

 Citation:

  Hassan AS, Al-Omar AI, and Ismail DM et al. (2021). A new generalization of the inverse Lomax distribution with statistical properties and applications. International Journal of Advanced and Applied Sciences, 8(4): 89-97

 Permanent Link to this page

 Figures

 Fig. 1 Fig. 2 Fig. 3 Fig. 4 Fig. 5 Fig. 6 

 Tables

 Table 1 Table 2 Table 3 Table 4 Table 5 Table 6 Table 7 Table 8 

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