Length-Biased Weighted Lomax Distribution: Statistical Properties and Application

Abstract

The concept of length-biased distribution can be employed in development of proper models for lifetime data. Length-biased distribution is a special case of the more general form known as weighted distribution. In this paper we introduce a new class of length-biased weighted Lomax distribution, (LBWLD). The statistical properties of this distribution are derived and the model parameters are estimated by maximum likelihood estimation and the observed information matrix is determined. An application to real data set is finally presented for illustration.

Weighted Analogue of Inverse Gamma Distribution: Statistical Properties, Estimation and Simulation Study

“…Rao (1965) proposed the concept of weighted distribution, Patil and Rao (1978) discussed how, for example, truncated distributions and damaged observations can give rise to weighted distributions. Weighted distributions occur frequently in research related to bio-medicine, reliability, ecosystem and branching process can be seen in Patil and Rao (1986), Sharma et al (2017) studied on Length and Area biased Maxwell distribution, Ahmad et al (2016) studied length biased Weighted Lomax distribution with its applications, Das and Roy (2011) discussed the length-biased Weighted Generalized Rayleigh distribution with its properties, also they develop the length-biased Weighted Weibull distribution.…”

Estimation Parameter of R = P(Y < X) for Length-Biased Weighted Lomax Distributions in the Presence of Outliers

“…. It is easy to show that marginal distribution of X is expressed as [18] f (x; α, β, λ) = bα(α − 1)…”

The Theoretical Overview of Generalized Gumbel Type-Ⅱ Distribution

“…Gumbel distribution is a particular case of Generalized Extreme Value distribution also known as Fisher-Tippett Distribution is named after Emil Julius Gumbel (1891Gumbel ( -1966.It has received notable attention over the years, particularly in extreme value analysis of extreme events [1][2][3]. Going through Pinheiro and Ferrari,…”