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In this research paper, a new life time family is introduced. Sadaf  proposed a moment exponential power series (MEPS) distribution. Generalized moment exponential power series (GMEPS) distribution is a general form of MEPS distribution. It is characterized by compounding GME distribution and power series (PS) distribution. This new family has some new sub models such as GME geometric distribution, GME Poisson (GMEP) distribution, GME logarithmic (GMEL) distribution and GME binomial (GMEB) distribution. We provide statistical properties of GMEPS family of distributions. We find here expression of quantile function based on Lambert W function, the density function of rth order statistic and moments of GMEPS distribution. Descriptive expressions of Shannon entropy and Rényi entropy of new general model are found. We provide special sub-models of the GMEPS family of distributions. The maximum likelihood (ML) estimation method is used to find estimates of the parameters of GMEPS distribution. Simulation study is carried out to check the convergence of new estimators. We apply GMEPS family of distributions on two sets of real data.
Marshall AW, Olkin I. A new method for adding a parameter to a family of distributions with application to the exponential and Weibull families. Biometrika. 1997;84(3):641-652.
Adamidis K, Loukas S. A lifetime distribution with decreasing failure rate. Statistics and Probability Letters. 1998;39(1):35-42.
Kus C. A new lifetime distribution. Computational Statistics and Data Analysis. 2007;51(9):4497-4509.
Tahmasbi R, Rezaei S. A two-parameter lifetime distribution with decreasing failure rate. Computational Statistics & Data Analysis. 2008;52(8):3889-3901.
Chahkandi M, Ganjali M. On some lifetime distributions with decreasing failure rate. Computational Statistics and Data Analysis. 2009;53(12):4433–4440.
Adamidis K, Dimitrakopoulou T, Loukas S. On an extension of the exponential-geometric distribution. Statistics & Probability Letters. 2005;73(3):259-269.
Barreto-Souza W, Morais AL, Cordeiro GM. The Weibull-geometric distribution. Journal of Statistical Computation and Simulation. 2011;81(5):645- 657.
Barreto-Souza W, Cribari-Neto F. A generalization of the exponential-Poisson distribution. Statistics & Probability Letters. 2009;79(24):2493-2500.
Silva RB, Bourguignon M, Dias CRB, Cordeiro GM. The compound class of extended Weibull power series distributions. Computational Statistics and Data Analysis. 2013;58:352–367.
Morais AL, Barreto-Souza W. A compound class of Weibull and power series distributions. Computational Statistics and Data Analysis. 2011;55(3):1410-1425.
Mahmoudi E, Jafari AA. Generalized exponential-power series distributions. Computational Statistics and Data Analysis. 2012;56(12):4047–4066.
Sandhya E, Prasanth CB. Marshall-Olkin discrete uniform distribution. Journal of Probability; 2014.
Silva RB, Corderio GM. The Burr XII power series distributions: A new compounding family. Brazilian Journal of Probability and Statistics. 2015;29(3):565-589.
Dara S. Reliability analysis of size biased distribution. Ph.D Thesis. National College of Business Administration and Economics, Lahore; 2012.
Iqbal Z, Wasim M, Riaz N. Exponentiated moment exponential distribution and power series distribution with applications: A new compound family. International Journal of Advance Research. 2017;5(7):1335-1355.
Noack A. A class of random variables with discrete distribution. Annals of Mathematical Statistics. 1950;21(1):127–132.
Murthy DNP, Xie M, Jiang R. Weibull models. Wiley; 2004.
Bjerkedal T. Acquisition of resistance in guinea pigs infected with different doses of virulent tubercle bacilli. American Journal of Epidemiol. 1960;72(1):130–148.
Corless RM, Gonnet GH, Hare DEG, Jeffrey DJ, Knuth DE. On the Lambert W function. Advances in Computational Mathematics. 1996;5(1):329-359.
Gradshteyn IS, Ryzhik IM. Table of integrals, series and products. San Diego: Academic Press; 2000.