Abstract

In this paper, a two-parameter Lindley distribution, of which the one parameter Lindley distribution (LD) is a particular case, for modeling waiting and survival times data has been introduced. Its moments, failure rate function, mean residual life function, and stochastic orderings have been discussed. It is found that the expressions for failure rate function mean residual life function and stochastic orderings of the two-parameter LD shows flexibility over one-parameter LD and exponential distribution. The maximum likelihood method and the method of moments have been discussed for estimating its parameters. The distribution has been fitted to some data-sets relating to waiting times and survival times to test its goodness of fit to which earlier the one parameter LD has been fitted by others and it is found that to almost all these data-sets the two parameter LD distribution provides closer fits than those by the one parameter LD.

Highlights

  • It is found that the expressions for failure rate function mean residual life function and stochastic orderings of the two-parameter Lindley distribution (LD) shows flexibility over one-parameter LD and exponential distribution

  • The distribution has been fitted to some data-sets relating to waiting times and survival times to test its goodness of fit to which earlier the one parameter LD has been fitted by others and it is found that to almost all these data-sets the two parameter LD distribution provides closer fits than those by the one parameter LD

  • The failure rate function and the mean residual life function of the distribution show its flexibility over one parameter LD and exponential distribution

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Summary

Introduction

Its cumulative distribution function has been obtained as. Nadarajah [3] have discussed various properties of this distribution and showed that in many ways (1.1) provides a better model for waiting times and survival times data than the exponential distribution. M. Sankaran [5] obtained the Lindley mixture of Poisson distribution. A two parameter Lindley distribution, of which the one-parameter LD (1.1) is a particular case, for modeling waiting and survival times data has been suggested. Its first four moments and some of the related measures have been obtained. Estimation of its parameters has been discussed and the distribution has been fitted to some of those data-sets where the one-parameter LD has earlier. Been fitted by others relating to waiting times and survival times data, to test its goodness of fit

Moments and Related Measures
Failure Rate and Mean Residual Life
Stochastic Orderings
Maximum Likelihood Estimates
Estimates from Moments
Goodness of Fit
Conclusion
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