eng Science and Education Publishing American Journal of Applied Mathematics and Statistics 2328-7292 2021-01-20 9 1 12 23 10.12691/ajams-9-1-3 AJAMS2021913 article Yasser M. Amer yasseramer4@yahoo.com 1 Dina H. Abdel Hady 2 Rania M. Shalabi 3 Cairo Higher Institutes in Mokattam, Cairo, Egypt Department of Statistics, Mathematics and Insurance, Faculty of Commerce, Tanta University, Egypt The Higher Institute of Managerial Science, 6th of October, Giza, Egypt In this paper two basic random variables constructed from Quasi Lindley distribution have been introduced. One of these variables is defined as the sum of two independent random variables following the Quasi-Lindley distribution with the same parameter (2SQLindley). The second one is defined as the difference of two independent random variables following the Quasi-Lindley distribution with also the same parameter (2DQLindley). For both cases, we provided some statistical properties such as moments, incomplete moments and characteristic function. The parameters are estimated by maximum likelihood method. From simulation studies, the performance of the maximum likelihood estimators has been assessed. The usefulness of the corresponding models is proved using goodness-of-fit tests based on different real datasets. The new models provide consistently better fit than some classical models used in this research. http://pubs.sciepub.com/ajams/9/1/3/ajams-9-1-3.pdf Quasi Lindley distribution mixed distribution maximum likelihood estimation incomplete moments characteristic function stochastic ordering and extreme order statistics