A Two-Parameter Lindley Distribution for Modeling Waiting and Survival Times Data

Rama Shanker, Shambhu Sharma, Ravi Shanker

Department of Mathematics, Dayalbagh Educational Institute, Agra, India.
Department of Mathematics, G.L.A. College, N.P. University, Daltonganj, India.
Department of Statistics, Eritrea Institute of Technology, Mainefhi, Eritrea.

DOI: 10.4236/am.2013.42056                

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.

Keywords

Lindley Distribution; Moments; Failure Rate Function; Mean Residual Life Function; Stochastic Ordering; Estimation of Parameters; Goodness of Fit

Conflicts of Interest

The authors declare no conflicts of interest.

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