Abstract
In this paper mathematical and statistical properties including moment generating function, mean deviations about mean and median, order statistics, Bonferroni and Lorenz curves, Renyi entropy and stress strength reliability of quasi Lindley distribution (QLD) introduced by Shanker and Mishra (2013 a) have been derived and discussed. The goodness of fit of QLD over exponential and Lindley distributions have been illustrated with five real lifetime data-sets and found that QLD provides better fit than exponential and Lindley distributions.
Highlights
Lindley distribution, introduced in the context of Bayesian analysis as a counter example of fiducial statistics, having probability density function (p.d.f) and cumulative distribution function (c.d.f) f ( x;θ ) = θ2 θ+ (1 + )x e−θ x ; x > 0, θ > 0 (1.1) F ( x;θ )
Its goodness of fit over exponential and Lindley distributions have been illustrated with some real lifetime data-sets and found that quasi Lindley distribution (QLD) gives better fit than exponential and Lindley distributions
If X is a continuous random variable having probability density function f (.), Renyi entropy is defined as component exceeds the strength (X < Y), the component fails instantly and the component will function satisfactorily till X > Y
Summary
Lindley distribution, introduced in the context of Bayesian analysis as a counter example of fiducial statistics, having probability density function (p.d.f) and cumulative distribution function (c.d.f). Shanker and Mishra (2013 a) have derived and discussed some of its mathematical properties including its shape, moments, coefficient of variation, coefficient of skewness and kurtosis, hazard rate function, mean residual life function and stochastic orderings. They have discussed the estimation of its parameters using maximum likelihood estimation and method of moments and its goodness of fit over Lindley and exponential distributions. In the present paper some of the important mathematical and statistical properties including moment generating function, mean deviations about mean and median, order statistics, Bonferroni and Lorenz curves, Renyi entropy measure and stress strength reliability of QLD of Shanker and Mishra (2013 a) have been derived and discussed. Its goodness of fit over exponential and Lindley distributions have been illustrated with some real lifetime data-sets and found that QLD gives better fit than exponential and Lindley distributions
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