A new distribution with two parameters named discrete Marshall-Olkin extended Burr Type XII (DMOEBXII) distribution is introduced using the survival of discretizing approach. Some of the statistical properties are discussed for the new distribution such as survival, hazard rate, alternative hazard rate functions, moments, quantiles, and order statistics. Maximum likelihood method is applied under Type II censored samples for estimating the unknown parameters, survival and hazard rate function of the proposed model. A simulation study is carried out to illustrate the theoretical results of the maximum likelihood estimation. Finally, the DMOEBXII distribution is used to fit the number of day intervals between 109 consecutive coal-mining tragedies in the United Kingdom from 1875 to 1951, as well as 48 students' mathematics degrees at the Indian Institute of Technology in Kampur.
Keywords: Discrete Marshall-Olkin extended Burr Type XII distribution; Discrete lifetime models; Order statistics; Type II censored; Maximum likelihood estimation; Squared error loss function; A simulation study.