The Beta-Lindley Distribution: Properties and Applications

Abstract

We introduce the new continuous distribution, the so-called beta-Lindley distribution that extends the Lindley distribution. We provide a comprehensive mathematical treatment of this distribution. We derive the moment generating function and therth moment thus, generalizing some results in the literature. Expressions for the density, moment generating function, andrth moment of the order statistics also are obtained. Further, we also discuss estimation of the unknown model parameters in both classical and Bayesian setup. The usefulness of the new model is illustrated by means of two real data sets. We hope that the new distribution proposed here will serve as an alternative model to other models available in the literature for modelling positive real data in many areas.

Bivariate Beta Exponential Distributions

“…(27) Consistent estimators of these two moments can be expressed as (28) And (29) When the functions ρ and are one-to-one, consistent estimators of are given by , It can be called inversion of Kendall's (itau) and inversion of Spearman's rho (irho) respectively. For more information, see Kojadinovic and Yan (2010).…”

“…For more details, see, also, the beta-Pareto distribution by Akinsete, et al (2008), beta modified Weibull distribution by Silva et al(2010), beta generalized half-normal distribution by Pescim et al, (2010), And ,also, the beta Burr XII distribution by Paranaiba, et al, (2011), beta extended Weibull distribution by Cordeiro, et al(2012),beta exponentiated Weibull by Cordeiro et al(2013),beta-lindley distribution by Merovci and Sharma (2014), beta Burr type X distribution by Merovci et al,(2016). Eugene et al (2002) introduced the beta normal distribution by taking G(x) in (1) to be the cdf of the normal distribution.…”

The beta exponentiated Lindley distribution

“…(1) When α = 1, the BEL distribution is the beta Lindley (BL) distribution (see [13]), with the density given by:…”

Size Biased Lindley Distribution and Its Properties a Special Case of Weighted Distribution

“…Whereas Ghitany et al (2008) [8] examined the Poisson Lindley distribution to model count data, as well as Ghitany et al (2008) [9] aims their study for data does not include zero counts, since Zakerzadeh and Dolati (2009) [10] described generalized form of Lindley distribution with three parameters. Therefore Ghitany et al (2011) worked on modeling of survival data and introduced a Lindley distribution with two parameters called weighted Lindley distribution although Lord and Geedipally (2011) [11] proposed a new distribution called negative binomial Lindley, contains two parameter for crash count data.…”