On the Burr XII-Power Cauchy distribution: Properties and applications

We propose a new four-parameter lifetime model with flexible hazard rate called the Burr XII Power Cauchy (BXII-PC) distribution. derive BXII-PC distribution via (ⅰ) T-X family technique and (ⅱ) nexus between exponential gamma variables. The proposed is as it has famous sub-models such XII-half Cauchy, Lomax-power Lomax-half Log-logistic-power log-logistic-half Cauchy. failure function for can accommodate various shapes modified bathtub, inverted increasing, decreasing; increasing-decreasing decreasing-increasing-decreasing. Its density take exponential, J, reverse-J, left-skewed, right-skewed symmetrical. To illustrate importance of distribution, we establish mathematical properties random number generator, moments, inequality measures, reliability measures characterization. Six estimation methods are used to estimate unknown parameters perform simulation study on basis graphical results demonstrate performance maximum likelihood, product spacings, least squares, weighted Cramer-von Mises Anderson-Darling estimators consider an application real data set prove empirically potentiality model.