Omid KHARAZMİ, Ali SAADATİNİK, Mostafa TAMANDİ

A New Continuous Lifetime Distribution and its Application to the Indemnity and AircraftWindshield Datasets

Kharazmi and Saadatinik [21] introduced a new family of distribution called hyperbolic cosine – F (HCF)

Keywords:

Hyperbolic cosine function, Weibull distribution Hazard function, Mean residual life time, Maximum likelihood estimates,

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[1] Alexander, C., Cordeiro, G.M., Ortega, E.M. and Sarabia, J.M., Generalized beta-generated distributions. Computational Statistics & Data Analysis, 56 (2012) (6), 1880-1897.
[2] Alizadeh, M., Cordeiro, G.M., De Brito, E. and Demétrio, C.G.B., The beta Marshall-Olkin family of distributions. Journal of Statistical Distributions and Applications, 2 (2015) (1), 1.
[3] Alizadeh, M., Emadi, M., Doostparast, M., Cordeiro, G.M., Ortega, E.M. and Pescim, R.R., A new family of distributions: the Kumaraswamy odd log-logistic, properties and applications. Hacettepa Journal of Mathematics and Statistics, forthcomig (2015b).
[4] Alizadeh, M., Tahir, M.H., Cordeiro, G.M., Mansoor, M., Zubair, M. and Hamedani, G.G., The Kumaraswamy Marshal-Olkin family of distributions. Journal of the Egyptian Mathematical Society, 23 (2015c) (3), 546-557.
[5] Alzaatreh, A., Lee, C. and Famoye, F., A new method for generating families of continuous distributions. Metron, 71 (2013) (1), 63-79.
[6] Alzaghal, A., Famoye, F. and Lee, C., Exponentiated T - X Family of Distributions with Some Applications. International Journal of Statistics and Probability, 2 (2013) (3), 31.
[7] Amini, M., MirMostafaee, S.M.T.K. and Ahmadi, J., Log-gamma-generated families of distributions. Statistics, 48 (2014) (4), 913-932.
[8] Azzalini, A., A class of distributions which includes the normal ones. Scandinavian journal of statistics, (1985), 171-178.
[9] Azzalini, A., The skew-normal and related families (Vol. 3). Cambridge University Press (2013).
[10] Barreto-Souza, W., de Morais, A.L. and Cordeiro, G.M., The Weibull-geometric distribution. Journal of Statistical Computation and Simulation,81 (2011) (5), 645-657.
[11] Bourguignon, M., Silva, R.B. and Cordeiro, G.M., TheWeibull-G family of probability distributions. Journal of Data Science, 12 (2014) (1), 53-68.
[12] Cordeiro, G.M. and de Castro, M., A new family of generalized distributions. Journal of statistical computation and simulation, 81 (2011) (7), 883-898.
[13] Cordeiro, G.M., Alizadeh, M. and Diniz Marinho, P.R., The type I half-logistic family of distributions. Journal of Statistical Computation and Simulation, 86 (2016) (4), 707-728.
[14] Cordeiro, G.M., Alizadeh, M. and Ortega, E.M., The exponentiated half-logistic family of distributions: Properties and applications. Journal of Probability and Statistics, (2014).
[15] Cordeiro, G.M., Ortega, E.M. and da Cunha, D.C., The exponentiated generalized class of distributions. Journal of Data Science, 11 (2013) (1), 1-27.
[16] Eling, M., Fitting insurance claims to skewed distributions: Are the skew-normal and skew-student good models?. Insurance: Mathematics and Economics, 51 (2012) (2), 239-248.
[17] Eugene, N., Lee, C. and Famoye, F., Beta-normal distribution and its applications. Communications in Statistics- Theory and methods, 31 (2002) (4), 497-512.
[18] Frees, E. and Valdez, E., Understanding relationships using copulas. North American Actuarial Journal, 2 (1998), 1–25.
[19] Gupta, R.C., Gupta, P.L. and Gupta, R.D., Modeling failure time data by Lehman alternatives. Communications in Statistics-Theory and methods, 27 (1998) (4), 887-904.
[20] Jones, M.C., Families of distributions arising from distributions of order statistics. Test, 13 (2004) (1), 1-43.
[21] Kharazmi, O. and Saadatinik, A., Hyperbolic cosine-F families of distributions with an application to exponential distribution. Gazi Univ J Sci 29 (2016) (4):811–829.
[22] Marshall, A.W. and Olkin, I., A new method for adding a parameter to a family of distributions with application to the exponential andWeibull families. Biometrika, 84 (1997) (3), 641-652.
[23] Murthy, D.P., Xie, M. and Jiang, R., Weibull models (Vol. 505). JohnWiley & Sons (2004).
[24] Nadarajah, S., Cancho, V.G. and Ortega, E.M., The geometric exponential Poisson distribution. Statistical Methods & Applications, 22 (2013) (3), 355-380.
[25] Nadarajah, S., Nassiri, V. and Mohammadpour, A., Truncated-exponential skew-symmetric distributions. Statistics, 48 (2014) (4), 872-895.
[26] R Development, C.O.R.E. TEAM 2011: R: A Language and Environment for Statistical Computing. R Foundation for Statistical Computing, Vienna, Austria.
[27] Risti´c, M.M. and Balakrishnan, N., The gamma-exponentiated exponential distribution. Journal of Statistical Computation and Simulation, 82 (2012) (8), 1191-1206.
[28] Shannon, C.E., A mathematical theory of communication, bell System technical Journal, (1948) 27: 379-423 and 623–656. Mathematical Reviews (MathSciNet): MR10, 133e.
[29] Tahir, M.H., Cordeiro, G.M., Alzaatreh, A., Mansoor, M. and Zubair, M., The Logistic-X family of distributions and its applications. Communications in Statistics-Theory and Methods, (just-accepted) (2016).
[30] Tahir, M. H., Cordeiro, G.M., Alizadeh, M., Mansoor, M., Zubair, M. and Hamedani, G.G., The odd generalized exponential family of distributions with applications. Journal of Statistical Distributions and Applications, 2 (2015) (1), 1.
[31] Torabi, H. and Hedesh, N.M., The gamma-uniform distribution and its applications. Kybernetika, 48 (2012) (1), 16-30.
[32] Torabi, H. and Montazeri, N. H., The Logistic-Uniform Distribution and Its Applications. Communications in Statistics-Simulation and Computation, 43 (2014) (10), 2551-2569.
[33] Zografos, K. and Balakrishnan, N., On families of beta-and generalized gamma-generated distributions and associated inference. Statistical Methodology, 6 (2009) (4), 344-362.