Sadasivan Karuppusamy.* et al. Int. Journal of Engineering Research and Application www.ijera.com ISSN : 2248-9622, Vol. 8, Issue 1, ( Part -V) January 2018, pp.50-56 www.ijera.com DOI: 10.9790/9622-080105505650|Page Modified one-Parameter Lindley Distribution and Its Applications Sadasivan Karuppusamy 1 , Vinoth Balakrishnan 1 and Keerthana Sadasivan 2 1 Department of Statistics, Eritrea Institute of Technology, Eritrea 2 Department of Statistics, Minnesota State University, Mankato, USA * Corresponding Author:Sadasivan Karuppusamy ABSTRACT In this paper a new one-parameter lifetime distribution named “Modified One-Parameter Lindley Distribution” which is a modification of Lindley Distribution, with an increasing hazard rate for modeling lifetime data has been suggested. Its first four moments about origin and mean have been deduced and expressions for mean, variance, coefficient of variation, skewness, kurtosis and index of dispersion have been obtained. Various mathematical and statistical properties of the proposed distribution including its survival function, hazard rate function, mean deviations, and Bonferroni and Lorenz curves have been discussed. Estimation of its parameter has been obtained using the method of maximum likelihood and the method of moments. The applications and goodness of fit of the distribution have been discussed with two real lifetime data sets and the fit has been compared with other one-parameter lifetime distributions including Akash, Lindley and Exponential distributions. Key words: Lifetime distributions, Akash distribution, Lindley distribution, mathematical and statistical properties, estimation of parameter, goodness of fit. I. INTRODUCTION The analysis and modeling of lifetime data play a crucial role in all branches of applied sciences including engineering, medicine, economics and insurance. There are a number of continuous distributions for modeling lifetime data such as exponential, Lindley, gamma, log-normal and Weibull. Of these, exponential, Lindley and Weibull distributions gained popularity in modeling lifetime data as compared to gamma and log-normal distributions since their survival functions do not require numerical integration. Besides, in the recent past a number of new class of one parameter lifetime distributions have evolved in statistical literature, which are in general extensions or modifications or generalizations of Lindley distribution that was used in the context of fiducial and Bayesian statistics (Lindley 1958). The range of such distributions include Akash distribution (Shankar R, 2015a), Shankar distribution (Shankar R,2015b), Sujatha distribution (Shankar, 2015c), Amarendra distribution (Shankar R, 2016), Akshaya distribution (Shankar R, 2017) and Improved Second-Degree Lindley distribution (Karuppusamy S et al, 2017) and each of these distributions has its own advantages and disadvantages in modeling lifetime data. As a continuation of these models, in this paper, as an extension of Lindley distribution, we have proposed a new one parameter continuous distribution namely Modified One-Parameter Lindley Distribution (MOPLD) and it has been shown that it is better than exponential, Lindley, and Akash distributions for modeling life time data. We have also discussed various statistical properties including its shape, moment generating function, moments, skewness and kurtosis, hazard rate function, mean and variance, mean deviations, Bonferroni and Lorenzcurves, of this new distribution. Finally, the method of maximum likelihood and method of moments are discussed for estimating its parameter. We have also included the goodness of fit of the proposed distribution for two data sets using maximum likelihood estimation and the fit is compared with the ones that are obtained by other distributions. II. MODIFIED ONE- PARAMETERLINDLEY DISTRIBUTION The probability density function (p.d.f) and the cumulative density function (c.d.f) of Lindley distribution (1958) are given by 0 , 0 ; ) 1 ( 1 ) ; ( 2 1            x e x x f x (2.1) 0 , 0 ; 1 1 1 ) ; ( 1                   x e x x F x (2.2) A detailed discussion of Lindley distribution, its mathematical properties, estimation of parameter and application showing advantages of Lindley distribution over exponential distribution can be found in Ghitnay et al (2008). A modified version of Lindley distribution by the name Akash distribution was given by Shankar, R RESEARCH ARTICLE OPEN ACCESS