期刊名称：Pakistan Journal of Statistics and Operation Research
印刷版ISSN：2220-5810
出版年度：2021
卷号：17
期号：4
页码：771-789
DOI：10.18187/pjsor.v17i4.3453
语种：English
出版社：College of Statistical and Actuarial Sciences
摘要：We introduce a four-parameter lifetime model with flexible hazard rate called the Burr XII gamma (BXIIG) distribution. We derive the BXIIG distribution from (i) the T-X family technique and (ii) nexus between the exponential and gamma variables. The failure rate function for the BXIIG distribution is flexible as it can accommodate various shapes such as increasing, decreasing, decreasing-increasing, increasing-decreasing-increasing, bathtub and modified bathtub. Its density function can take shapes such as exponential, J, reverse-J, left-skewed, right-skewed and symmetrical. To illustrate the importance of the BXIIG distribution, we establish various mathematical properties such as random number generator, ordinary moments, generating function, conditional moments, density functions of record values, reliability measures and characterizations. We address the maximum likelihood estimation for the parameters. We estimate the adequacy of the estimators via a simulation study. We consider applications to two real data sets to prove empirically the potentiality of the proposed model.
关键词：Characterizations;
Gamma distribution;
Maximum Likelihood Estimation;
Reliability
