Recently Shanker and Shukla have detailed and critical study about the modeling of lifetime data from various fields of knowledge using threeparameter GLD and GGD and concluded that in majority of data sets GGD gives better fit .
In the present paper, the moments and moments based expressions including expressions for coefficient of variation, skewness, kurtosis, and index of dispersion have been given.
In this paper moments and moments based characteristics including expressions for coefficient of variation, skewness, kurtosis and index of dispersion of the three-parameter generalized Lindley distribution (GLD) introduced by  have been derived and discussed.
The expressions for the hazard rate function and the mean residual life function of the distribution have been obtained.
The expressions for survival function, hazard rate function and mean residual life function have been obtained.
The goodness of fit of GLD has been compared with the goodness of fit obtained by GGD and found that GLD does not give satisfactory fit in all data sets.
It can be easily verified that the gamma distribution, the Lindley (1958) distribution and the exponential distribution are particular cases of (1.1) for (β = 0) , (α = β =1) and(α =1,β = 0) , respectively. have detailed study about various properties of Lindley distribution, estimation of parameter and application for modeling waiting time data in a bank.
Detailed and comparative study on modeling of lifetime data using one parameter Lindley and exponential distributions . (1.1) can be easily expressed as a twocomponent mixture of gamma (α ,θ ) and gamma (α 1,θ ) distributions.
Mean residual life function Using the mixture representation (1.2), the mean residual life function of the GLD can be obtained as: Where is the upper incomplete gamma function defined in (1.4).
The best distribution corresponds to lower values of −2ln L and K-S statistics and higher p- value.
It is obvious from the fitting of GLD and GGD that both are competing.
Finally, the goodness of fit of GLD with two- parameter gamma, Weibull and lognormal distributions and concluded that the GLD is competing with these two-parameter distributions .
In fact, GLD should have been compared with other three-parameter lifetime distributions to test its goodness of fit.