Research Article
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Year 2019, , 102 - 112, 30.04.2019
https://doi.org/10.36753/mathenot.559265

Abstract

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.

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

Year 2019, , 102 - 112, 30.04.2019
https://doi.org/10.36753/mathenot.559265

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.

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.
There are 33 citations in total.

Details

Primary Language English
Journal Section Articles
Authors

Omid Kharazmi

Ali Saadatinik This is me

Mostafa Tamandi This is me

Publication Date April 30, 2019
Submission Date July 11, 2018
Published in Issue Year 2019

Cite

APA Kharazmi, O., Saadatinik, A., & Tamandi, M. (2019). A New Continuous Lifetime Distribution and its Application to the Indemnity and AircraftWindshield Datasets. Mathematical Sciences and Applications E-Notes, 7(1), 102-112. https://doi.org/10.36753/mathenot.559265
AMA Kharazmi O, Saadatinik A, Tamandi M. A New Continuous Lifetime Distribution and its Application to the Indemnity and AircraftWindshield Datasets. Math. Sci. Appl. E-Notes. April 2019;7(1):102-112. doi:10.36753/mathenot.559265
Chicago Kharazmi, Omid, Ali Saadatinik, and Mostafa Tamandi. “A New Continuous Lifetime Distribution and Its Application to the Indemnity and AircraftWindshield Datasets”. Mathematical Sciences and Applications E-Notes 7, no. 1 (April 2019): 102-12. https://doi.org/10.36753/mathenot.559265.
EndNote Kharazmi O, Saadatinik A, Tamandi M (April 1, 2019) A New Continuous Lifetime Distribution and its Application to the Indemnity and AircraftWindshield Datasets. Mathematical Sciences and Applications E-Notes 7 1 102–112.
IEEE O. Kharazmi, A. Saadatinik, and M. Tamandi, “A New Continuous Lifetime Distribution and its Application to the Indemnity and AircraftWindshield Datasets”, Math. Sci. Appl. E-Notes, vol. 7, no. 1, pp. 102–112, 2019, doi: 10.36753/mathenot.559265.
ISNAD Kharazmi, Omid et al. “A New Continuous Lifetime Distribution and Its Application to the Indemnity and AircraftWindshield Datasets”. Mathematical Sciences and Applications E-Notes 7/1 (April 2019), 102-112. https://doi.org/10.36753/mathenot.559265.
JAMA Kharazmi O, Saadatinik A, Tamandi M. A New Continuous Lifetime Distribution and its Application to the Indemnity and AircraftWindshield Datasets. Math. Sci. Appl. E-Notes. 2019;7:102–112.
MLA Kharazmi, Omid et al. “A New Continuous Lifetime Distribution and Its Application to the Indemnity and AircraftWindshield Datasets”. Mathematical Sciences and Applications E-Notes, vol. 7, no. 1, 2019, pp. 102-1, doi:10.36753/mathenot.559265.
Vancouver Kharazmi O, Saadatinik A, Tamandi M. A New Continuous Lifetime Distribution and its Application to the Indemnity and AircraftWindshield Datasets. Math. Sci. Appl. E-Notes. 2019;7(1):102-1.

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