Main Article Content
Abstract
In this article, we introduce a new generalized family of Esscher transformed Laplace distribution, namely the Kumaraswamy Esscher transformed Laplace distribution. We study the various properties of the distribution including the survival function, hazard rate function, cumulative hazard rate function and reverse hazard rate function. The parameters of the distribution are estimated using the maximum likelihood method of estimation. A real application of this distribution on breaking stress of carbon fibres is also considered. Further, we introduce and study the exponentiated and transmuted exponentiated Kumaraswamy Esscher transformed Laplace distributions.
Keywords
Article Details
Copyright and licensing
Copyright © 2023 Pakistan Journal of Statistics and Operation Research
Creative Commons Attribution 4.0 International (CC BY 4.0)
Reuse is governed by the linked license.
How to Cite
References
Abdulkabir, M. and Ipinyomi, R. A. (2020). Type II half logistic exponentiated exponential distribution: properties
and applications. Pakistan Journal of Statistics, 36(1), 23-28.
Ahmad, Z., Ampadu, C.B., Hamedani, G.G., Jamal, F. and Nasir, M.A. (2019). The New Exponentiated T-X Class
of Distributions: Properties, Characterizations and Application. Pak.j.stat.oper.res., XV(IV), 941-962.
Ahmad, Z., Elgarhy, M., Hamedani, G.G. (2018). A new Weibull-X family of distributions: Properties, characterizations
and applications. J. Stat. Distrib. Appl., 5.
Akinsete, F. Famoye, C. Lee, (2008). The beta-Pareto distribution, Statistics, 42, 547-563.
Ali M., Khalil A., Ijaz M. and Saeed N. (2021). Alpha-Power Exponentiated Inverse Rayleigh distribution and its
applications to real and simulated data. PloS one, 16(1), e0245253. pmid:33444340.
Alizadeh M., Tahir M. H., Cordeiro G. M., Zubair M. and Hamedani G. G. (2015). The Kumaraswamy Marshal-
Olkin family of distributions. Journal of the Egyptian Mathematical Society, 23, 546557
Alzaghal, A., LEE, C. and Famoye, F. (2013). Exponentiated T-X family of distributions with some applications.
Int J Statist Probab, 2, 31-49.
Amer Ibrahim Al-Omari, Ahmed. M. H. Al-khazaleh and Moath Al-khazaleh (2019).Exponentiated new WEIBULLPARETO
distribution. Revista Investigation Operational, 40(2), 165-175.
Badr M. and Ijaz M. (2021). The Exponentiated Exponential Burr XII distribution: Theory and application to
lifetime and simulated data. PLoS ONE, 16(3), e0248873. https://doi.org/10.1371/journal.pone.0248873.
Cordeiro, G.M., Ortega, E.M.M., Nadarajah, S. (2010). The KumaraswamyWeibull distribution with application
to failure data. J. Frankl. Inst., 347, 13991429.
Dais George and Sebastian George (2011). Application of Esscher transformed Laplace distribution in Web
server data. Journal of Digital Information Management, 9(1), 19-26.
Dais George and Sebastian George (2013). Marshall-Olkin Esscher transformed Laplace distribution and processes.
Brazelian Journal of Probability and Statistics, 27(2), 162-184.
Dais George, Sebastian George and Rimsha, H. (2016). Esscher transformed and geometric Esscher transformed
Laplace processes. Far East Journal of Theoretical Statistics, 52(6), 455-483.
Dawlah Al-Sulami (2020). Exponentiated Exponential Weibull Distribution: Mathematical Properties and Application.
American Journal of Applied Sciences, 17, DOI: 10.3844/ajassp.2020, 188-195.
Elgarhy, M., Muhammad Ahsan ul Haq and Qurat Ain (2018). Exponentiated generalized Kumaraswamy distribution
with applications. Annals of Data Science, Springer, 5(2), 273-292.
Esscher, F. (1932). On the probability function in the collective theory of risk, Scandinavian Actuarial Journal,
, 175-195.
Francisco Louzada1, Vicente G. Cancho1 and Paulo H. Ferreira (2020). The exponentiated Poisson-exponential
distribution: a distribution with increasing, decreasing and bathtub failure rate. Journal of Statistical Theory
and Applications, 19(2), 274-285.
Gompertz, B. (1825). On the nature of the function expressive of the law of human mortality, and on a new mode
of determining the value of life contingencies. Philos Trans R Soc Lond, 115, 513-585.
Handique L. and Chakraborty S. (2015a). The Marshall-Olkin-Kumaraswamy-G family of distributions. arXiv:1509.08108
[math.ST].
Handique L. and Chakraborty S. (2015b). The generalized Marshall-Olkin-Kumaraswamy-G family of distributions.
arXiv:1510.08401 [math.ST].
Hassan, A.S. and Elgarhy, M. (2016). A new family of exponentiated Weibull-generated distributions. International
Journals of Mathematics and its Applications, 4(1), 135-148.
Krishnakumari, K. and Dais George (2020). Discrete Esscher transformed Laplace distribution and its applications,
Stochastic Modeling and Applications, 24(2), 149-159.
Kozubowski, T. J. and Podgorski, K. (2000). Asymmetric Laplace distributions. Math.Sci., 25, 37-46.
Kumaraswamy, P. (1980). Generalized probability density-function for double-bounded random processes. J
Hydrol, 46, 70-88.
Lehmann, E. L. (1953). The power of rank tests. Ann Math Statist, 24, 23-43.
Muhammad Shuaib Khan1, Robert King and Irene Lena Hudson, (2016). Transmuted Kumaraswamy distribution,
Statistics in Transition new series, 17(2), 183-210.
Nadarajah S and Kotz S. (2004). The beta Gumbel distribution. Math Probl Eng, 10, 323-332.
Nassar, M. M. and Elmasry, A. (2012). A study of generalized Logistic distributions. Journal of Egyptian
Mathematical Society, 20(2), 126-13.
Nassar M. M. and Nada N. K. (2011). The beta generalized Pareto distribution. J Statist Adv Theor Appl, 6, 1-17.
Nassar M. M. and Nada N. K. (2012). A study of generalized logistic distributions. Journal of Egyptian
Mathematical Society, 20(2), 126-133.
Nassar M. M. and Nada N. K. (2013). A new generalization of the Pareto geometric distribution. Journal of
Egyptian Mathematical Society, 21(2), 148-155.
Rimsha, H. and Dais George (2019). q-Esscher transformed Laplace distribution. Communication in Statistics-
Theory and Methods, 48(7), 1563-1578.
Rimsha, H. and Dais George (2020). Multivariate Esscher transformed Laplace distribution. Journal of Statistical
Theory and Applications, 19(2), 325-331.
Sebastian George and Dais George (2012). Esscher transformed Laplace distributions and its applications,
Journal of Probability and Statistical Sciences, 10(2), 135-152.
Sebastian George, Dais George and Ligi George (2016). Log-Esscher transformed Laplace distributions and its
applications, Journal of Probability and Statistical Sciences, 14(1), 29-44.
Sher B. Chhetri, Alfred A. Akinsete, Gokarna Aryal and Hongwei Long (2017). The Kumaraswamy transmuted
Pareto distribution. Journal of Statistical Distributions and Applications, 4(1), 1-24.
Suleman Nasirua, P., Peter N. Mwitab and Oscar Ngesa (2019). Exponentiated generalized exponential Dagum
distribution. Journal of King Saud University - Science, 31(3), 362-371.
Tahir, M. H. and Nadarajah, S. (2015). Parameter induction in continuous univariate distributions: Wellestablished
G families. Anais da Academia Brasileira de Cincias, 87(2), 539-568.
Tahir NawazSajid HussainTanvir, Ahmad Farah and Naz Muhammad Abid (2020). Kumaraswamy generalized
Kappa distribution with application to stream flow data. Journal of King Saud University - Science, 32(1),
-182.
Verhulst, P. F. (1838). Notice sur la loi la population suit dans son accroissement. Correspondence mathematique
et physique, 10, 113-121.
Verhulst, P. F. (1845). Recherches mathematiques sur la loi-accroissement de la population. Nou velles
Memoires de Academie Royale des Sciencs et Belles-Lettres de Bruxelles, 2, 18-38.
Verhulst, P. F. (1847). Deuxieme memoire sur la loi accroissement de la population. Memoires de Academie
Royale des Sciences, des Lettres et des Beaux-Arts de Belgique, 2, 20-32.
Zohdy M. Nofal, Emrah Altun, Ahmed Z. Afify, and Ahsanullah, M. (2019). The generalized Kumaraswamy-G
family of distributions. Journal of Statistical Theory and Applications, 18(4), 329-342.