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

Year 2019, Volume: 7 Issue: 1, 102 - 112, 30.04.2019

Omid Kharazmi , Ali Saadatinik Mostafa Tamandi

https://doi.org/10.36753/mathenot.559265

Cited By: 1

Abstract

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

distributions. They studied some properties of this model and obtained the estimates of its parameters by

different methods. In this paper, it is focused on a special case of HCF family withWeibull distribution

as a baseline model. Various properties of the proposed distribution including explicit expressions

for the moments, quantiles, moment generating function, failure rate function, mean residual lifetime,

order statistics and expression of the entropies are derived. Superiority of this model is proved in some

simulations and applications.

Keywords

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

References

• [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.