The Marshall-Olkin Topp-Leone Half-Logistic-G Family of Distributions with Applications
AbstractA new family of distributions called the Marshall-Olkin Topp-Leone Half-Logistic-G (MO-TLHL-G) family of distributions is proposed and studied. Structural properties of the new family of distributions including moments, incomplete moments, distribution of the order statistics, and Renyi entropy are derived. The maximum likelihood estimation technique is used to estimate the model parameters. A simulation study to examine the bias and mean square error of the maximum likelihood estimators and applications to real data sets to illustrates the usefulness of the generalized distribution are given.
A. Z. Afify, M. Alizadeh, M. Zayed, T. G. Ramires, and F. Louzada, The Odd Log-Logistic Exponentiated Weibull Distribution: Regression Modelling, Properties and Applications, Iranian Journal of Science and Technology, vol. 42, pp. 2273–2288, 2018.
C. Alexander, G. M. Cordeiro, E. M. M. Ortega, and J. M. Sarabia, Generalized Beta-generated Distributions, Computational Statistics and Data Analysis, vol. 56, pp.1880–1897, 2012.
M. Alizadeh, M. Emadi, M. Doostparast, G. M. Cordeiro, E. M. M. Ortega, and R. R. Pescim, A New Family of Distributions: the Kumaraswamy Odd Log-Logistic, Properties and Applications, Hacettepe Journal of Mathematics and Statistics, vol. 44, pp. 1491–1512, 2015.
M. Alizadeh, M. H. Tahir, G. M. Cordeiro, M. Mansoor, M. Zubair, and G. G. Hamedani, The Kumaraswamy Marshall-Olkin Family of Distributions, Journal of Egypt Mathematical Society, vol. 23, pp. 546–557, 2015.
A. Alzaghal, F. Famoye, and C. Lee, Exponentiated T-X Family of Distributions with Some Applications, International Journal of Probability and Statistics, vol. 2, pp. 31–49, 2013.
D. F. Andrews, and A. M. Herzberg, Data: A Collection of Problems From Many Fields for the Student and Research Worker, Springer Science & Business Media, 2012.
R. E. Barlow, R. H. Toland, and T. Freeman, A Bayesian Analysis of Stress-Rupture Life of Kevlar/Epoxy Spherical Pressure Vessels, Proceedings of the Canadian Conference in Applied Statistics, Edited by: Dwivedi, T. D. New York: Marcel Dekker, 1984.
W. Barreto-Souza, A. Lemonte, and G. M. Cordeiro, General Results for the Marshall and Olkins Family of Distributions, Annals of the Brazilian Academy of Sciences, vol. 85, 3–21, 2013.
M. Bourguignon, R. B. Silva, and G. M. Cordeiro, The Weibull-G Family of Probability Distributions, Journal of Data Science, vol. 12, pp. 53–68, 2014.
S. Chakraborty, and L. Handique, The Generalized Marshall-Olkin-Kumaraswamy-G Family of Distributions, Journal of Data Science, vol. 15, no. 3, pp. 391–422, 2017.
J. Chambers, W. Cleveland, B. Kleiner, and J. Tukey, Graphical Methods for Data Analysis, Chapman and Hall, London, 1983.
G. Chen, and N. Balakrishnan, A General Purpose Approximate Goodness-of-fit Test, Journal of Quality Technology, vol. 27, pp. 154–161, 1995.
G. M. Cordeiro, E. M. M. Ortega, and T. G. Ramires, A New Generalized Weibull Family of Distributions: Mathematical Properties and Applications, Journal of Statistical Distributions and Applications, vol. 13, 2015.
G. M.Cordeiro, E. M. M. Ortega, and S. Nadarajah, The Kumaraswamy Weibull Distribution with Application to Failure Data, Journal of the Franklin Institute, vol. 347, pp. 1399–1429, 2010.
G. M.Cordeiro, E. M. M. Ortega, and D. C. C. da Cunha, The Exponentiated Generalized Class of Distributions, Journal of Data science, vol. 11, pp. 1–27, 2013.
G. M. Cordeiro, and A. J. Lemonte, On the Marshall-Olkin Extended Weibull Distribution, Statistics Papers, vol. 54, pp. 333–353, 2011.
G. M. Corderio, A. Z. Afify, H. M. Yousof, R. R. Pescim, and G. R. Aryal, The Exponentiated Weibull-H Family of Distributions: Theory and Applications, Mediterranean Journal of Mathematics, vol. 14, no. 155, 2017.
G. M. Cordeiro, E. M. M. Ortega, B. V. Popovi´c, and R. R. Pescim, The Lomax Generator of Distributions: Properties, Minification Process and Regression Model, Applied Mathematics and Computation, vol. 247, pp. 465–486, 2014.
M. E. Ghitany, E. K. AL-Hussaini, and R. AL-Jarallah, Marshall-Olkin Extended Weibull Distribution and Its Application to Censored Data, Journal of Applied Statistics, vol. 32, no. 10, pp.1025-1034, 2005.
D. Kumar, Ratio and Inverse Moments of Marshall-Olkin Extended Burr Type III Distribution Based on Lower Generalized Order Statistics, Journal of Data Science, vol. 14, no. 1, pp. 53–66, 2016.
B. Lazhar, Marshall-Olkin Extended Generalized Gompertz Distribution, Journal of Data Science, vol. 15, no. 2, pp. 239–266, 2017.
L. Lepetu, B. O. Oluyede, B. Makubate, S. Foya, P. Mdlongwa, Marshall-Olkin Log-Logistic Extended Weibull Distribution: Theory, Properties and Applications, Journal of Data Science, vol.15, pp. 691–722, 2017.
A.N. Marshall, and I. Olkin, A New Method for Adding a Parameter to a Family of Distributions with Applications to the Exponential and Weibull Families, Biometrika, vol. 84, pp. 641–652, 1997.
D. P. Murthy, M. Xie, and R. Jiang, Weibull Models, NewYork: John Wiley & Sons, 2004.
B. O. Oluyede, and T. Yang, A New Class of Generalized Lindley Distributions with Applcations, Journal of Statistical Computation and Simulation, vol. 85, no. 10, pp. 2072–2100, 2015.
A. R´enyi, On Measures of Entropy and Information, Proceedings of the Fourth Berkeley Symposium on Mathematical Statistics and Probability, vol. 1, pp. 547–561, 1960.
M. Santos-Neo, M. Bourguignon, L. M. Zea, and A. D. C. Nascimento, The Marshall-Olkin Extended Weibull Family of
Distributions, Journal of Statistical Distributions and Applications, vol. 1, no. 9, 2014.
M. Shaked, and J. G. Shanthikumar, Stochastic Orders and Their Applications, Academic Press, University of Michigan, 1994.
M. H. Tahir, G. M. Cordeiro, M. Mansoor, and M. Zubair, The Weibull-Lomax Distribution: Properties and Applications, Hacettepe Journal of Mathematics and Statistics, vol. 44, no. 2, pp. 461–480, 2015.
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