Journal of Data Science

This article addresses the various mathematical and statistical properties of the Burr type XII distribution (such as quantiles, moments, moment generating function, hazard rate, conditional moments, mean residual lifetime, mean past lifetime, mean deviation about mean and median, stochasic ordering, stress-strength parameter, various entropies, Bonferroni and Lorenz curves and order statistics) are derived. We discuss some exact expressions and recurrence relations for the single and product moments of upper record values. Further, using relations of single moments, we have tabulated the means and variances of upper record values from samples of sizes up to 10 for various values of the α and β. Finally a characterization of this distribution based on conditional moments of record values and recurrence relation of kth record values is presented.