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.
In the present paper, a two-parameter quasi Shanker distribution (QSD) which includes one parameter Shanker distribution introduced by Shanker [1] as a special case has been proposed. Its statistical and mathematical properties including moments and moments based measures, hazard rate function, mean residual life function, stochastic ordering, mean deviations, Bonferroni and Lorenz curves and stress-strength reliability have also been discussed. The method of maximum likelihood estimation has been discussed for estimating the parameters of QSD. Finally, the goodness of fit of the QSD has been discussed with two real lifetime data and the fit is quite satisfactory over one parameter exponential, Lindley and Shanker distributions.
In this paper a simple and interesting method for finding moments of Poisson-Akash distribution (PAD) introduced by Shanker [1] has been suggested and hence the first two moments
In this paper a new one-parameter lifetime distribution named "Sujatha Distribution" with an increasing hazard rate for modelling lifetime data has been suggested. Its first four moments about origin and moments about mean have been obtained and expressions for coefficient of variation, skewness, kurtosis and index of dispersion have been given. Various mathematical and statistical properties of the proposed distribution including its hazard rate function, mean residual life function, stochastic ordering, mean deviations, Bonferroni and Lorenz curves, and stress-strength reliability have been discussed. Estimation of its parameter has been discussed using the method of maximum likelihood and the method of moments. The applications and goodness of fit of the distribution have been discussed with three real lifetime data sets and the fit has been compared with one-parameter lifetime distributions including Akash, Shanker, Lindley and exponential distributions.
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