52 Copyright © All rights are reserved by Obubu Maxwell. Current Trends on Biostatistics & Biometrics Research Article The Gompertz Length Biased Exponential Distribution and its application to Uncensored Data Obubu Maxwell 1 *, Oluwafemi Samuel Oyamakin 2 and Eghwerido Joseph Thomas 3 1 Department of Statistics, Nnamdi Azikiwe University, Awka, Nigeria 2 Department of Statistics, University of Ibadan, Ibadan, Nigeria 3 Department of Mathematics and Computer Science, Federal University of Petroleum Resources, Effurun, Nigeria *Corresponding author: Obubu Maxwell, Department of Statistics, Nnamdi Azikiwe University, Awka, Nigeria Received: February 22, 2019 Published: March 08, 2019 Introduction Length biased distributions are special case of the more general form known as weighted distribution [1], first introduced by [2] to model ascertainment bias and formalized in a unifying theory by [3]. Lifetime data may be modeled with several existing distributions, although the existing models are not adequate or are less representative of actual data in many situations. Therefore, the development of compound distributions that could better describe certain phenomena and make them more flexible than the baseline distribution is of great importance [4]. Thus, the choice of the model is also an important issue for reliable model parameter estimation. Some exponential distribution generalizations for modeling lifetime data due to some interesting advantages have been recently proposed [5]. In recent years many exponential distribution generalizations have been developed, such as the Marshall Olkin length biased exponential distribution [5], exponentiated exponential [6,7], generalized exponentiated moment exponential [8], extended exponentiated exponential [19], Marshall-Olkin exponential Weibull [10], Marshall-Olkin generalized exponential [5], and exponentiated moment exponential [11] distributions. A random variable X is said to have a length biased exponential distribution with parameter \beta if its probability density function (pdf) and cumulative distribution function (cdf) is given by equation (1) and (2) respectively [12]: 2 (, ) , 0, 0 x x gx e x β β β β − = > > (1) () 1 (1 ) , 0, 0 x x Gx e x β β β − = − + > > (2) Where is the scale parameter. The survival function is given by the equation () (1 ) , 0, 0 x x Sx e x β β β − = + > > (3) The hazard function is () , 0, 0 (1 ) x x x e Hx x x e β β β β β − − = > > + (4) Abstract This paper proposes a generalization of the length biased exponential distribution, called the Gompertz length biased exponential (GLBE) distribution. Some of the basic properties of the proposed model were derived in minute details and model parameters estimated by the maximum likelihood estimate method. The adequacy of the model is empirically validated with the use of real - life data. Keywords: Exponential Distribution; Length Biased; Gompertz Generalized Family Of Distribution; Quantile Function; Hazard Functions; Survival Function ISSN: 2644-1381 DOI: 10.32474/CTBB.2019.01.000111