Transmuted Lindley-Geometric Distribution and its Applications

Abstract

A functional composition of the cumulative distribution function of one probability distribution with the inverse cumulative distribution function of another is called the transmutation map. In this article, we will use the quadratic rank transmutation map (QRTM) in order to generate a flexible family of probability distributions taking Lindley geometric distribution as the base value distribution by introducing a new parameter that would offer more distributional flexibility. It will be shown that the analytical results are applicable to model real world data.

The Transmuted Generalized Lindley Distribution: Properties and an Application to a Data Set on Time-Up-to-Cure of Patients Treated With a Triazole Antifungal Drug in an Intensive Care Unit

“…For instance when α = 1 it reduces to transmuted Lindley as discussed in Merovci and Elbatal (2014). The generalized Lindley distribution is clearly a special case for λ = 0 (NADARAJAH; BAKOUCH; TAHMASBI, 2011).…”

“…Elbatal;Diab and Alim (2013)considered the transmuted modified inverse Weibull distribution. Merovci and Elbatal (2014) considered the transmuted generalized Linear Exponential Distribution. Merovci and Elbatal (2014) considered transmuted Lindley geometric distribution.…”

“…Merovci and Elbatal (2014) considered the transmuted generalized Linear Exponential Distribution. Merovci and Elbatal (2014) considered transmuted Lindley geometric distribution. Tian; Tian and Zhu (2013) considered the transmuted linear exponential distribution.…”

Statistical Study of Monthly Rainfall Trends by Using the Transmuted Power Lindley Distribution

“…This distribution uses a mixture of exponential and length biased exponential distributions to illustrate the different between fiducial and posterior distributions. Late years, different applications and modifications have been proposed for this model such as: Ghitany et al (2008) that argue that the Lindley distribution could be a better lifetime model than the exponential distribution through a numerical example; Nadarajah et al (2011) and Zakerzadeh and Dolati (2009) in the proposition of a generalization; Merovci and Elbatal (2014) introduced a new lifetime distribution; Warahena-Liyanage and Pararai (2014) proposed an exponentiated power Lindley distribution with applications.…”

An Extended Power Lindley Distribution and its Application

“…For example, the two-parameter weighted Li [Ghitany et al (2011)], generalized Li [Nadarajah et al (2011)], extended Li (Bakouch et al, 2012), beta Li (BLi) (Merovci and Sharma, 2014), Kumaraswamy Li (KLi) (Cakmakyapan and Kadilar, 2014), transmuted Li-geometric (Merovci and Elbatal , 2014), beta-exponentiated power Li (Pararai et al, 2015), gamma Li , beta transmuted Li (Afify et al, 2016b), odd log-logistic Li (Ozel et al, 2016), complementary generalized transmuted Poisson Li (CGTPLi) and pseudo Li distributions.…”