International Journal of Recent Technology and Engineering (IJRTE) ISSN: 2277-3878, Volume-9 Issue-5, January 2021 202 Published By: Blue Eyes Intelligence Engineering and Sciences Publication Retrieval Number: 100.1/ijrte.E5265019521 DOI:10.35940/ijrte.E5265.019521 Abstract: A novel distribution using Poisson-Generating family of distribution with parent distribution as shifted Gompertz distribution called Poisson shifted Gompertz distribution with relevant properties has been introduced. The estimation of unknown parameters is carried out via established methods including Maximum likelihood estimation (MLE). R software is applied for computational purposes. The application of the proposed model has been illustrated considering a real set of data and investigated the goodness-of-fit attained by the Poisson shifted Gompertz model through different graphical methods and test statistics where better fit was observed for the set of real data. Keywords: Estimation method, LSE, MLE, Poisson- Generating family, Shifted Gompertz distribution I. INTRODUCTION In the statistical literature it has been noticed that the many life-time distributions have been generated but the real data sets related to engineering, life sciences, biology, hydrology do not present a better fit in these models So, the generation of new modified models appears to be necessary to deal with the problems in these fields. For achieving a better fit for the data we encounter in survival analysis different distributions are created making changes to the baseline distribution.\ The extended family Poisson-Weibull distribution, introduced by (Bereta,at al., 2011) demonstrates failure rate functions with decreasing and increasing nature, also exponential-Poisson distribution, presented by (Kus, 2007) with zero truncated Poisson distribution and exponential distribution compounded together. Exponential Poisson distribution‟s CDF is,           1 ; , 1 exp 1 1 ; 0, , 0 t Gt e e t                     Cribari-Neto and Barreto-Souza (2009) have generated generalized exponential Poisson distribution as generalization of exponential-Poisson distribution (Kus, 2007) with insertion of power parameter to this model. Using the similar approach, Cancho (2011) presented Poisson exponential (PE) distribution based on exponential distribution. PE distribution‟s CDF is Manuscript received on January 16, 2021. Revised Manuscript received on January 20, 2021. Manuscript published on January 30, 2021. * Correspondence Author Arun Kumar Chaudhary*, Associate Professor, Department of Management Science(Statistics), Nepal Commerce Campus, Tribhuwan University, Nepal, Email: akchaudhary1@yahoo.com , chaudharyak111@gmail.com Vijay Kumar, Department of Mathematics and Statistics, DDU Gorakhpur University, Gorakhpur, India. Email: vijay.mathstat@ddugu.ac.in , vkgkp@rediffmail.com           exp 1 ; , 1 ; 0, , 0 t e e Gt e t                 Similarly Louzada-Neto et al., (2011) introduced Poisson-exponential having two parameters via Bayesian approach. Alkarni and Oraby (2012) have presented Poisson family class obtained via a lifetime distribution and truncated Poisson distribution compounded together The Poisson family‟s CDF is as follows,         1 exp 1 ; ; , ; 0 1 Gy W y e                (1.1) And its corresponding PDF can be expressed as           ; exp 1 ; ; , ; 0 1 gy Gy wy e                 (1.2) Where  the parameter is space and   ; gt  and   ; Gt  are the PDF and CDF. Employing same approach the Poisson Weibull power series class of distributions was given by (Morais & Barreto-Souza, 2011). Exponentiated Weibull–Poisson model with four parameters with increasing, decreasing, bathtub-shaped, and uni-modal failure rate has been presented by (Mahmoudi & Sepahdar, 2013) generated compounding exponentiated Weibull and Poisson distributions. Weibull–Poisson distribution is introduced by (Lu & Shi, 2012). Further Kaviayarasu and Fawaz (2017) made an extensive study on Weibull–Poisson distribution through a reliability sampling plan. Kyurkchiev et al. (2018) used the exponentiated exponential-Poisson as the software reliability model. Joshi & Kumar (2020) presented Poisson exponential power distribution and used different estimation methods to estimate the model parameter. Chaudhary & Kumar (2020) have introduced a new distribution using Poisson-G family called Poisson inverse NHE distribution. Chaudhary & Kumar(2020) introduced a new distribution generated by using the Poisson-G-family with parent distribution as NHE distribution named Poisson NHE distribution. Chaudhary & Kumar(2020) used Markov chain Monte Carlo (MCMC) method is used to estimate the parameters of the Gompertz extension distribution based on a complete sampleJoshi & Kumar (2020) have introduced a new model using Gompertz distribution called Poisson Shifted Gompertz Distribution: Properties and Applications Arun Kumar Chaudhary, Vijay Kumar