Testing for bivariate gumbel against bivariate new better than used in expectation

Abstract

It is shown that a bivariate survival function is both New Better than Used in Expectation (NBUE) and New Worse than Used in Expectation (NWUE) if and only if it is a bivariate Gumbel distribution. Statistical procedures are then presented to test whether that, within the class of bi-variate NBUE survival functions, a survival function is a Gumbel's bivariate exponential.

Keywords:

• bivariate survival function
• NBUE
• NWUE
• Gum-
• bel bivariate exponential
• nonparametric test