Open AccessOn The Burr XII-Gamma Distribution: Development, Properties, Characterizations and Applications
Author(s) -
Fiaz Ahmad Bhatti,
Gauss M. Cordeiro,
Mustafa Ç. Korkmaz,
G. G. Hamedani
Publication year - 2021
Publication title -
pakistan journal of statistics and operation research
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.354
H-Index - 15
eISSN - 2220-5810
pISSN - 1816-2711
DOI - 10.18187/pjsor.v17i4.3453
Subject(s) - mathematics , bathtub , moment generating function , estimator , gamma distribution , exponential family , exponential distribution , failure rate , exponential function , distribution (mathematics) , conditional probability distribution , probability density function , statistics , mathematical analysis , archaeology , history
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.