Some inequalities in elementary special functions with applications to nonparametric statistical inference

Some inequalities are established in P₁(r, s) and P₁(r+1, s), where P₁(r, s) is the confidence coefficient of Wilks’ (1962) outer confidence interval (X_(r) X_(s)) for the quantile interval (ξ_p1, ξ_p2). An inequality concerning incomplete beta functions is also presented and it is shown to be an improved version of one of Koti's (1989) inequalities.