Abstract
In this paper, a two-parameter Rama distribution is proposed. This is coined from Lindley distribution and Rama distribution. Its mathematical and statistical properties which include its shapes, moment, coefficient of variation, skewness, kurtosis, index of dispersion, hazard rate function, mean residual life function, stochastic ordering, mean deviation; Bonferroni and Lorenz curves are also discussed. The estimation of parameters has been X-rayed using methods of moment and maximum likelihood. Also AIC and BIC are used to test for the goodness of fit of the model which is applied to a real life data of hepatitis B patients. This new distribution is compared with Rama, 2-parameter Akash, 2-parameter Lindley, Akash, Shanker, Ishita, Lindley and Exponential distributions in order to determine the efficiency of the new model.
Highlights
Shanker [1] proposed a continuous lifetime distribution, known as Rama distribution defined by its probability density function and cumulative distribution function given below f (x; θ) = θ4 θ3 + (1 + x3 )e−θx ; x > 0, θ > 0, (1.1)Received: June 2, 2019; Accepted: July 30, 20192010 Mathematics Subject Classification: 97K80, 62Nxx.Keywords and phrases: Rama distribution, mathematical and statistical properties, estimation of parameters, goodness of fit.U
This new distribution is compared with Rama, 2-parameter Akash, 2-parameter Lindley, Akash, Shanker, Ishita, Lindley and Exponential distributions in order to determine the efficiency of the new model
A two-parameter Rama distribution (TPRD) with parameters θ and α is defined by its pdf and cdf f (x; θ, α) θ4 αθ3 +
Summary
Shanker [1] proposed a continuous lifetime distribution, known as Rama distribution defined by its probability density function (pdf) and cumulative distribution function (cdf) given below f (x; θ). Shanker [1] has discussed its important statistical properties including shapes of density function for varying values of parameters, hazard rate function; mean residual life function, stochastic ordering, mean deviations, Bonferroni and Lorenz curves and stressstrength reliability. He has discussed the maximum likelihood estimation of the parameter and showed the application of Rama distribution. The hazard rate function, mean residual life function, stochastic ordering, mean deviations, order statistics, Bonferroni and Lorenz curves of TPRD have been derived and discussed using method of moment and method of maximum likelihood. The goodness of fit of the proposed distribution has been discussed with a real life numerical data set and the fit has been compared with some well known lifetime distributions
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