Alpha Power Lomax Distribution: Properties and Application

Authors

  • Y. Murat Bulut Department of Statistics, Eskisehir Osmangazi University, 26040 Eskisehir/Turkey
  • Fatma Zehra Doğru Department of Statistics, Giresun University, 28200 Giresun/Turkey
  • Olcay Arslan Department of Statistics, Ankara University, 06100 Ankara/Turkey

DOI:

https://doi.org/10.13052/jrss0974-8024.1412

Keywords:

Lomax distribution, alpha power transformation, maximum likelihood estimation

Abstract

This study offers a newly proposed distribution called alpha power Lomax (APL) distribution as a new extension of the Lomax distribution using the alpha power transformation (APT) method. Some distributional properties of newly defined distribution such as density function, moments, hazard and survival functions, orders statistics etc. are investigated. Parameters of the APL distribution are estimated with the help of the maximum likelihood (ML) estimation method. The applicability of the APL distribution is conducted through a simulation study and a real data example.

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Author Biographies

Y. Murat Bulut, Department of Statistics, Eskisehir Osmangazi University, 26040 Eskisehir/Turkey

Y. Murat Bulut received his B.Sc. in Mathematics from Çukurova University, Turkey, M.Sc., and Ph.D. degrees from Eskişehir Osmangazi University, Turkey. He is an assistant professor in the Department of Statistics at Eskişehir Osmangazi University, Turkey, since 2016. His research areas are robust statistics, distribution theory, and generalized linear models.

Fatma Zehra Doğru, Department of Statistics, Giresun University, 28200 Giresun/Turkey

Fatma Zehra Doğru received her B.Sc. and M.Sc. degrees in Statistics and Computer Sciences from the Karadeniz Technical University in 2009 and 2011; and a Ph.D. degree in Statistics from the Ankara University in 2015. She is currently working as an associate professor in the department of statistics at Giresun University, Turkey. Her research interests cover mixture models, mixture regression models, multivariate mixture models, robust statistics, statistical inference, and modeling.

Olcay Arslan, Department of Statistics, Ankara University, 06100 Ankara/Turkey

Olcay Arslan is a full Professor of Statistics at the Department of Statistics, Ankara University, Ankara, Turkey. She received her Ph.D. in Statistics from the University of Leeds, Leeds, UK, in 1993. Prior to joining Ankara University, she was working as a full professor at the department of Statistics, Cukurova University, Adana, Turkey. She was visiting scholar at Rutgers University and visiting professor at St. Cloud State University, St. Cloud, USA. Her principal research areas are robust statistical analysis, multivariate analysis, regression analysis, EM algorithm and distribution theory. She also works on model selection, scale mixtures, mean-variance (location-scatter) mixtures, finite mixtures and linear mixed models. She has published over 75 research papers in international refereed journals and also several book chapters in scientific books. She has been involved in organizing many scientific events devoted to statistics including ICORS 2008 (International conference on robust statistics, 2008) and IC-SMHD-2016 (International conference on information complexity and statistical modeling in high dimensions with application, 2016). She is an area editor of Hacettepe Journal of Mathematics and Statistics (HJMS) and members of the editorial board of several scientific journals on statistics and probability. She is also member of the ICORS steering committee.

References

K. S. Lomax, Business failures: Another example of the analysis of failure data, Journal of the American Statistical Association 49 (268) (1954) 847–852.

A. Hassan, A. Al-Ghamdi, Optimum step stress accelerated life testing for lomax distributions, Journal of Applied Sciences Research (5) (2009) 2153–2164.

C. M. Harris, The pareto distribution as a queue service descipline, Operations Research 16 (2) (1968) 307–313.

A. B. Atkinson, A. J. Harrison, Distribution of Personal Wealth in Britain, Cambridge University Press.

G. Campbell, M. V. Ratnaparkhi, An application of lomax distributions in receiver operating characteristic (roc) curve analysis, Communications in Statistics–Theory and Methods 22 (6) (1993) 1681–1697.

N. Balakrishnan, M. Ahsanullah, Relations for single and product moments of record values from lomax distribution, Sankhya: The Indian Journal of Statistics, Series B 56 (2) (1994) 140–146.

M. C. Bryson, Heavy-tailed distribution: properties and tests, Technometrics 16 (1) (1974) 61–68.

N. L. Johnson, S. Kotz, N. Balakrishnan, Contineous Univariate Distributions Vol. 1, 2nd Edition, Wiley, New York, 1994.

A. El-Bassiouny, N. Abdo, H. Shahen, Exponential lomax distribution, International Journal of Computer Applications 121 (13) (2015) 24–29.

G. M. Cordeiro, E. M. Ortega, B. V. Popović, The gamma-lomax distribution, Journal of Statistical Computation and Simulation 85 (2) (2015) 305–319.

M. E. Ghitany, F. A. Al-Awadhi, L. A. Alkhalfan, Marshall–olkin extended lomax distribution and its application to censored data, Communications in Statistics - Theory and Methods 36 (10) (2007) 1855–1866.

M. H. Tahir, G. M. Cordeiro, M. Mansoor, M. Zubair, The weibull-lomax distribution: properties and applications, Hacettepe Journal of Mathematics and Statistics 44 (2) (2015) 455–474.

A. Lemonte, G. Cordeiro, An extended lomax distribution, Statistics 47 (4) (2013) 800–816.

S. A. Al-Awadhi, M. E. Ghitany, Statistical properties of poisson–lomax distribution and its application to repeated accidents data, Journal of Applied Statistical Science 10 (4) (2001) 365–372.

E.-H. A. Rady, W. A. Hassanein, T. A. Elhaddad, The power lomax distribution with an application to bladder cancer data, SpringerPlus 5 (1) (2016) 1838.

S. Al-Marzouki, A new generalization of power lomax distribution, International Journal of MAthematics and its Applications 7 (1) (2018) 59–68.

A. Mahdavi, D. Kundu, A new method for generating distributions with an application to exponential distribution, Communications in Statistics-Theory and Methods 46 (13) (2017) 6543–6557.

M. Nassar, A. Alzaatreh, M. Mead, O. Abo-Kasem, Alpha power weibull distribution: Properties and applications, Communications in Statistics - Theory and Methods 46 (20) (2017) 10236–10252.

S. Dey, A. Alzaatreh, C. Zhang, D. Kumar, A new extension of generalized exponential distribution with application to ozone data, Ozone: Science & Engineering 39 (4) (2017) 273–285.

S. Dey, M. Nassar, D. Kumar, α

logarithmic transformed family of distributions with applications, Annals of Data Science 4 (4) (2017) 457–482.

S. Dey, M. Nassar, D. Kumar, Alpha power transformed inverse lindley distribution: A distribution with an upside-down bathtub-shaped hazard function, Journal of Computational and Applied Mathematics 348 (2019) 130–145.

M. Nassar, D. Kumar, S. Dey, G. M. Cordeiro, A. Z. Afify, The marshall–olkin alpha power family of distributions with applications, Journal of Computational and Applied Mathematics 351 (2019) 41–53.

E. T. Lee, J. W. Wang, Statistical Methods for Survival Data Analysis, 3rd Edition, Wiley, New York, 2003.

S. Ashour, M. Eltehiwy, Transmuted exponentiated lomax distribution, Australian Journal of Basic and Applied Sciences 7 (7) (2013) 658–667.

N. M. Kilany, Weighted lomax distribution, SpringerPlus 5 (1) (2016) 1862.

R Core Team, R: A language and environment for statistical computing (2016). URL https://www.R-project.org/

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Published

2021-03-08

How to Cite

Bulut, Y. M. ., Doğru, F. Z. ., & Arslan, O. . (2021). Alpha Power Lomax Distribution: Properties and Application. Journal of Reliability and Statistical Studies, 14(01), 17–32. https://doi.org/10.13052/jrss0974-8024.1412

Issue

2021: Vol 14 Iss 1

Section

Articles