International Journal of Statistics and Probability; Vol. 8, No. 6; November 2019 ISSN 1927-7032 E-ISSN 1927-7040 Published by Canadian Center of Science and Education A New Generalized Family of Odd Lindley-G Distributions With Application Fastel Chipepa 1,3 , Broderick O. Oluyede 1,2 & Boikanyo Makubate 1 1 Department of Mathematical Statistics, Botswana International University of Science and Technology, P. Bag 16, Palapye, Botswana 2 Department of Mathematical Sciences, Georgia Southern University, GA 30460, USA 3 Department of Applied Mathematics and Statistics, Midlands State University, P. Bag 9055, Gweru, Zimbabwe Correspondence: Department of Mathematical Sciences Georgia Southern University GA 30460, USA. E-mail: boluyede@georgiasouthern.edu; Oluyedeo@biust.ac.bw Received: August 5, 2019 Accepted: September 9, 2019 Online Published: September 25, 2019 doi:10.5539/ijsp.v8n6p1 URL: https://doi.org/10.5539/ijsp.v8n6p1 Abstract A new family of distributions, namely the Kumaraswamy Odd Lindley-G distribution is developed. The new density function can be expressed as a linear combination of exponentiated-G densities. Statistical properties of the new family including hazard rate and quantile functions, moments and incomplete moments, Bonferroni and Lorenz curves, distribu- tion of order statistics and R´ enyi entropy are derived. Some special cases are presented. We conduct some Monte Carlo simulations to examine the consistency of the maximum likelihood estimates. We provide an application of KOL-LLo distribution to a real data set. Keywords: Kumaraswamy distribution, Lindley distribution, maximum likelihood estimation, Monte Carlo simulation, odd Lindley-G distribution 1. Introduction There are considerable amount of work in the literature on the modification of the beta distribution including work by (Eugene, Lee and Famoye 2002), (Nadarajah and Kotz, 2004), (Nadarajah and Kotz, 2006), (Cordeiro, Gomes, da Silva, and Ortega, 2013), (Oluyede and Yang, 2015), and (Makubate, Oluyede, Motobetso, Huang and Fagbamigbe, 2018), to mention a few. These extended models exhibited very interesting properties because of the two extra shape parameters that make it possible to explore skewness, kurtosis and tail properties inherent in some data. The core issue with beta generated distributions is lack of tractability and this is mainly caused by the involvement of the incomplete beta function in the cumulative distribution function (cdf). (Kumaraswamy, 1980) proposed a new distribution called the Kumaraswamy distribution. This new distribution has a wide application in hydrology. (Jones, 2009) studied the properties of the Kumaraswamy distribution and highlighted some of its similarities to the beta distribution and also its desirable tractability property over the beta distribution. Many generators for generating extended models have been studied and these includes beta-G (B-G) by (Eugene et al., 2002), by (Cordeiro and de Castro, 2011), McDonald-G (M-G) by (Alexander, Cordeiro, Ortega and Sarabia, 2012), gamma-G type 1 by (Zografos and Balakrishnan, 2009), gamma-G type 2 (Risti´ c and Balakrishnan, 2012), odd-gamma-G type 3 by (Torabi and Montazari, 2012), transformed-transformer (T-X) and Weibull-X by (Alzaatreh, Lee and Famoye, 2013), exponentiated T-X by (Alzaghal, Famoye and Lee, 2013), Weibull-G by (Bourguignon, Silva and Cordeiro, 2014), Lomax-G by (Cordeiro, Ortega, Popovi´ c and Pescim, 2014) and odd Lindley-G by (Gomes-Silva, Percontini, de Brito, Ramos, Ven´ ancio and Cordeiro, 2017), to mention a few. (Cordeiro et al, 2011) proposed a Kw-G distribution which states that given any baseline cdf G( x), a new family has its cdf and pdf given by F( x) = 1 − (1 − G( x) a ) b , (1) and f ( x) = abg( x)(G( x)) a−1 (1 − G( x) a ) b−1 , (2) respectively, for x > 0, a > 0 and b > 0. (Gomes-Silva et al., 2017) developed the odd Lindley-G (OL-G) distribution, whose cdf and probability density function 1