Abstract
In this Paper, we have introduced a new version of new quasi lindley distribution known as the length-biased weighted new quasi lindley distribution (LBWNQLD). Length biased distribution is a special case of weighted distribution. The different structural properties of the newly proposed distribution are derived and the model parameters are estimated by using the method of maximum likelihood estimation and also the Fisher’s information matrix have been discussed. Finally, applications to real life two data sets are presented for illustration.
Highlights
The study of weighted distributions are useful in distribution theory because it provides a new understanding of the existing standard probability distributions and it provides methods for extending existing standard probability distributions for modeling lifetime data due to the introduction of additional parameter in the model which creates flexibility in their nature
In order to show that the length biased weighted new quasi Lindley distribution is better than the new quasi Lindley, quasi Lindley, Lindley and exponential distributions, the results obtained from the two real life data sets are used
We have introduced the length biased weighted new quasi Lindley distribution as a new generalization of new quasi Lindley distribution
Summary
The study of weighted distributions are useful in distribution theory because it provides a new understanding of the existing standard probability distributions and it provides methods for extending existing standard probability distributions for modeling lifetime data due to the introduction of additional parameter in the model which creates flexibility in their nature. Para and Jan (2018) introduced the Weighted Pareto type II Distribution as a new model for handling medical science data and studied its statistical properties and applications. Wani and Para (2018) discussed on the weighted three parameter quasi Lindley distribution with properties and applications. The probability density function of length biased weighted new quasi Lindley distribution is given by xf(x; θ, α) fl(x; θ, α) = E(x) , x > 0. Substitute the equations (1) and (4) in equation (3), we will obtain the probability density function of length biased weighted new quasi Lindley distribution fl (x ; xθ[3] (θ2 + 2α) αx)e−θx (5). The cumulative distribution function of length biased weighted new quasi Lindley distribution is given by x. After the simplification of equation (6), we obtain the cumulative distribution function of length biased weighted new quasi Lindley distribution
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