A STUDY ON ALPHA POWER LOMAX DISTRIBUTION
DOI:
https://doi.org/10.29121/ijoest.v6.i5.2022.393Keywords:
Alpha Power Lomax Distribution, Maximum Likelihood Estimation, Renyi Entropies, Stress–Strength Reliability and Order StatisticsAbstract
In this paper, we refer to the new distribution an alpha power Lomax distribution. Various properties of the proposed distribution are obtained including mode, quantiles, entropies, and order statistics are obtained. Parameters of the proposed distribution are estimated using maximum likelihood, ordinary least squares and weighted least squares. Simulation study is conducted to compare between estimators.
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Abdo, N. F., El-bassiouny, A. H. and Shahen, H. S. (2015). Exponential Lomax Distribution. International Journal of Computer Applications, 121, 14-29. https://doi.org/10.5120/21602-4713.
Badr, M. M. (2019). Goodness of Fit Tests for the Compound Rayleigh Distribution with Application to Real Data. Heliyon, 5,1-6. https://doi.org/10.1016/j.heliyon.2019.e02225.
Balakrishnan, N. and Cohen, A. C. (2014). Order Statistics and Inference: Estimation Methods, Academic Press, San Diego, California.
Devi, B., Kumar, P. and Kour, K. (2017). Entropy of Lomax Probability Distribution And Its Order Statistic. International Journal of Statistics and Systems, 12(2), 175-181.
Dey, S., Nassar, M. and Kumar, D. (2019). Alpha Power Transformed Inverse Lindley Distribution : A Distribution With an Upside-Down Bathtub-Shaped Hazard Function. Journal of Computational and Applied Mathematics, 130-145. https://doi.org/10.1016/j.cam.2018.03.037.
El-Houssainy, A., Rady, W. and Elhaddad, T. (2016). The Power Lomax Distribution With an Application to Bladder Cancer Data. Springerplus, 1838,1-22. https://doi.org/10.1186/s40064-016-3464-y.
Hassan, A., and Mohamed, R. (2019). Weibull Inverse Lomax Distribution. Pakistan Journal of Statistical and Operation Research, 587-603. https://doi.org/10.18187/pjsor.v15i3.2378.
Ijaz, M., Asim, S. M. And Alamgir, M. (2019). Lomax Exponential Distribution With an Application to Real-Life Data. Plos One, 12-14. https://doi.org/10.1371/journal.pone.0225827.
Ihtisham, S., Khalil, A., Manzoor, S., Khan, S. A. and Ali, A. (2019). Alpha-Power Pareto Dis- Tribution its Properties and Applications. Plos One, 6-14. https://doi.org/10.1371/journal.pone.0218027.
Lomax, K, S. (1954). Business Failures: Another Example of the Analysis of Failure Data. Joumal of the American Statistical Association, 49, 847-852. https://doi.org/10.1080/01621459.1954.10501239.
Kriver, J. F. and Keeping, E. S. (1962). Mathematics of Statistics, 3rd edition, Part 1, Princeton, New Jersey.
Kotz, S. and Pensky, M. (2003). The Stress-Strength Model and its Generalizations : Theory and Applications, World Scientific, New Jersey. https://doi.org/10.1142/9789812564511.
Mahdavi, A. and Kundu, D. (2017). A New Method for Generating Distributions with an Application to Exponential Distribution. Communications in Statistics- Theory and Methods, 46(13), 6543-6557. https://doi.org/10.1080/03610926.2015.1130839.
Moors, J. (1988). A Quantile Alternative For Kurtosis, Journal of the Royal Statistical Society : Series D (The Statistician), 37, 25-32. https://doi.org/10.2307/2348376.
Nassar, M. Alzaatreh, A., Mead, M. and Abo-Kasem, O. (2017). Alpha Power Weibull Distribution : Properties and Applications. Communications in Statistics Theory and Methods, 20(46), 10236-10252. https://doi.org/10.1080/03610926.2016.1231816.
R'enyi, A. (1959). On The Dimension and Entropy of Probability Distributions. Acta Math. Hung. 10, 193-215. https://doi.org/10.1007/BF02063299.
Song, K.S. (2001). R'enyi Information, Loglikelihood and an Intrinsic Distribution Measure. J.Stat. Plan. Inference 93, 51-69. https://doi.org/10.1016/S0378-3758%2800%2900169-5.
Swain, J., Venkatraman, S. and Wilson, J. (1988). Least Squares Estimation of Distribution Function in Johnson's Translation System. Journal of Statistical Computation and Simulation, 29, 271-297. https://doi.org/10.1080/00949658808811068.
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Copyright (c) 2022 Rana A.Bakoban, E. A. Faraj, Najwa S. Alsulami
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