Kumaraswamy Esscher Transformed Laplace Distribution: Properties, Application and Extensions

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.

Bimodal Power Laplace Distribution

“…Basically, all these existing asymmetric L distributions are either a percent mixture of the double exponential distribution or a split of it. These distributions in chronological order include: the skew-log-Laplace (Hartley and Revankar, 1974), asymmetric-Laplace (Hinkley and Revankar, 1977), log-Laplace (Inoue, 1978), skew-Laplace (Fieler et al, 1992, asymmetric-Laplace distribution (Koenker and Machado, 1999), asymmetric-Laplace (Kotz et al, 2001) called as the generalized asymmetric-Laplace by Yu and Zhang (2005), asymmetric-Laplace (Kotz et al, 2002), normal-Laplace (Reed and Jorgensen, 2004), skew-Laplace distribution (Aryal and Nadarajah, 2005), skew-Laplace-Laplace (Ali et al, 2009), beta-Laplace (Cordeiro and Lemonte, 2011), Esscher-transformed-Laplace (Sebastian and Dais, 2012), skew-Laplace-Normal and generalized skew-symmetric-Laplace-normal (Nekoukhou and Alamatsaz, (2012), alpha-skew-Laplace (Harandi and Alamatsaz, 2013), Kumaraswamy-Laplace (Nassar, 2016), transmuted Laplace (Hady and Shalaby, 2016) using the quadratic rank transmutation map studied by Shaw and Buckley (2009), flexible-skew-Laplace (Yilmaz, 2016), Laplace-exponential (Kiprotich, 2018), Balakrishnan-alpha-skew-Laplace (Shah et al 2019), reduced beta-skewed-Laplace (Arowolo et al, 2019), generalized-transmuted-Laplace (Radwan, 2020), alpha-beta-skew-Laplace (Shah and Hazarika, 2020), generalized skew-log-Laplace (Khandeparkar Dixit, 2021), beta-skew-Laplace, truncated beta-skew-Laplace, exponentiated beta-skew-Laplace and exponentiated Laplace (Tovar-Falon and Martinez-Florez, 2022), Balakrishnan-alpha-beta-skew-Laplace (Shah et al 2023) and Kumaraswamy-Esscher-transformed-Laplace (George and Rimsha, 2023). This paper is organized as follows.…”