Bonferroni Curve and the related statistical inference

Two measures of inequality, viz. the Bonferroni Curve and the Bonferroni index are studied. It is shown that these have some relationship with Lorenz Curve, Gini ratio and certain concepts used in reliability, life testing and renewal theory. The problem of testing of Bonferroni Curve and its ordinate(s) is discussed in the multivariate set-up. The variance-covariance structure of the vector of Bonferroni Curve ordinates is derived and a simulation exercise is done.