Lomax Weibull Distribution
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Published
Oct 17, 2019
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1-18
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Benjamin Apam
Department of Statistics, Bolgatanga Polytechnic, Bolgatanga, Ghana.
Nasiru Suleman
Department of Statistics, University for Development Studies, Ghana.
Emmanuel Adjei
Department of Statistics, Tamale Technical University, Tamale, Ghana.
Abstract
In this article, we introduce the Lomax-Weibull (LoW) distribution using the method of composition of CDFs from the Lomax and Weibull distributions. Expressions for the moment generating function, hazard and survival functions were derived. A plot of the probability distribution function and cumulative distributions were done using the Python software. We also used the maximum likelihood method of estimation to derive the score functions for estimating the parameters of the distribution.
Keywords:
Lomax-Weibull distribution, composition of CDFs, moments, maximum likelihood estimation, hazard rate function, survivor function.
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Original Research Article
References
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Cordeiro GM, Ortega EM, Nadarajah S. The Kumaraswamy Weibull distribution with application to failure data. Journal of the Franklin Institute. 2010;347(8):1399-1429.
Cordeiro GM, Ortega EM, Silva GO. The Kumaraswamy modified Weibull distribution: Theory and applications. Journal of Statistical Computation and Simulation. 2014;84(7):1387-1411.
Provost SB, Saboor A, Ahmad M. The Gamma-Weibull Distribution. Pak. J. Statist. 2011;27(2): 111-131.
Nasiru S. Another weighted Weibull distribution from Azzalini’s family. European Scientific Journal. ESJ. 2015;11(9):134-144.
Almalki SJ, Yuan J. A new modified Weibull distribution. Reliability Engineering & System Safety. 2013;111:164-170.
Akgül A. New reproducing kernel functions. Mathematical Problems in Engineering; 2015.
Akgül A, Kılıçman A. Numerical solutions of the second-order one-dimensional telegraph equation based on reproducing kernel Hilbert space method. In Abstract and Applied Analysis; 2013. Hindawi.
Akgül A, Khan Y, Akgül EK, Baleanu D, Al Qurashi MM. Solutions of nonlinear systems by reproducing kernel method. The Journal of Nonlinear Sciences and Applications. 2017;10:4408-4417.
Tchier F, Inc M, Kilic B, Akgül A. On soliton structures of generalized resonance equation with time dependent coefficients. Optik. 2017;128:218-223.
Hashemi MS, Inc M, Kilic B, Akgül A. On solitons and invariant solutions of the Magneto-electro-elastic circular rod. Waves in Random and Complex Media. 2016;26(3):259-271.
Almalki SJ, Nadarajah S. Modifications of the Weibull distribution: A review. Reliability Engineering & System Safety. 2014;124:32-55.
Ahsanullah M, Nevzorov VB, Shakil M. An introduction to order statistics; 2013.
Gupta V, Bhatt M, Gupta J. The Lomax-Frechet distribution. Journal of Rajasthan Academy of Physical Sciences. 2015;14 (1):25-43.
Gupta Jaya, Garg Mridula. The Lomax-Weibull distribution. Advanced Science Letters. 2018;24(11): 8126-8129.
Burch P. Application of the Weibull distribution. The British Institute of Radiodology. 1976;49(582): 564.
Justus C, Hargraves W, Mikhail A, Graber D. Methods for estimating wind speed frequency distributions. Journal of Applied Meteorology. 1978;17(3):350-353.
Famoye F, Lee C, Olumolade O. The beta-Weibull distribution. Journal of Statistical Theory and Applications. 2005;4(2):121-136.
Lai CD, Xie M, Murthy DNP. A modified Weibull distribution. IEEE Transactions on Reliability. 2003;52(1):33-37.
Cordeiro GM, Ortega EM, Nadarajah S. The Kumaraswamy Weibull distribution with application to failure data. Journal of the Franklin Institute. 2010;347(8):1399-1429.
Cordeiro GM, Ortega EM, Silva GO. The Kumaraswamy modified Weibull distribution: Theory and applications. Journal of Statistical Computation and Simulation. 2014;84(7):1387-1411.
Provost SB, Saboor A, Ahmad M. The Gamma-Weibull Distribution. Pak. J. Statist. 2011;27(2): 111-131.
Nasiru S. Another weighted Weibull distribution from Azzalini’s family. European Scientific Journal. ESJ. 2015;11(9):134-144.
Almalki SJ, Yuan J. A new modified Weibull distribution. Reliability Engineering & System Safety. 2013;111:164-170.
Akgül A. New reproducing kernel functions. Mathematical Problems in Engineering; 2015.
Akgül A, Kılıçman A. Numerical solutions of the second-order one-dimensional telegraph equation based on reproducing kernel Hilbert space method. In Abstract and Applied Analysis; 2013. Hindawi.
Akgül A, Khan Y, Akgül EK, Baleanu D, Al Qurashi MM. Solutions of nonlinear systems by reproducing kernel method. The Journal of Nonlinear Sciences and Applications. 2017;10:4408-4417.
Tchier F, Inc M, Kilic B, Akgül A. On soliton structures of generalized resonance equation with time dependent coefficients. Optik. 2017;128:218-223.
Hashemi MS, Inc M, Kilic B, Akgül A. On solitons and invariant solutions of the Magneto-electro-elastic circular rod. Waves in Random and Complex Media. 2016;26(3):259-271.
Almalki SJ, Nadarajah S. Modifications of the Weibull distribution: A review. Reliability Engineering & System Safety. 2014;124:32-55.
Ahsanullah M, Nevzorov VB, Shakil M. An introduction to order statistics; 2013.
Gupta V, Bhatt M, Gupta J. The Lomax-Frechet distribution. Journal of Rajasthan Academy of Physical Sciences. 2015;14 (1):25-43.
Gupta Jaya, Garg Mridula. The Lomax-Weibull distribution. Advanced Science Letters. 2018;24(11): 8126-8129.