Length biased Weighted New Quasi Lindley Distribution: Statistical Properties and Applications

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.

A Generalized Transmuted Moment Exponential Distribution: Properties and Application

This paper introduces a new generalization of moment exponential (or length biased) distribution. The new model is referred to as generalized transmuted moment exponential distribution. This model contains some new existing distributions. Structural properties of the suggested distribution including closed forms for ordinary and incomplete moments, quantile and generating functions and Rényi entropy are derived. Maximum likelihood estimation is employed to obtain the parameter estimators of the new distribution. We illustrate the importance of the new model by means of three applications to real data sets.

ON LIFETIME ESTIMATION IN THE PRESENCE OF LENGTH-BIASED SAMPLING PLAN

In the presence of length-biasedness, a lifetime measure of interest may be estimated in two ways: (i) by modeling the data correctly using a length-biased distribution and using the resulting estimators in the original model as an adjustment, or (ii) by modeling the data correctly using a length-biased distribution, and obtaining the original lifetime measure of interest via a transformation, if one exists. Here we examine sufficiency in information context under transformations.

ON INEQUALITIES AND SELECTION OF EXPERIMENTS FOR LENGTH BIASED DISTRIBUTIONS

The length biased distribution occurs naturally for some sampling plans in reliability, biometry, and survival analysis. In this note, inequalities for length biased distributions are proved for monotone hazard functions and mean residual life functions. The problem of sampling and selection of experiments from the length biased distribution as opposed to the original distribution is addressed. Certain modified cross-entropy measures are also investigated.

On Asymptotic Representations for Reduced Quantiles in Sampling from a Length-Biased Distribution*

Nonparametric estimation of the quantiles of a distribution based on a sample from the corresponding length-biased distribution is considered. Along with some representations of this estimator in terms of averages of independent random variables, some limiting results are established. The case of reduced quantile processes is also treated briefly.