Testing Multivariate Exponentiality Against MHNBUE Alternatives - A Laplace-Transform Statistic with Closed-Form Null Variance for Arbitrary Dimension
Keywords:
Asymptotic normality, Laplace transform, Makeham Weibull, MHNBUE, Multivariate exponentialityAbstract
This article develops a -dimensional Laplace-transform test of the hypothesis that a non-negative random vector has independent exponential margins, against the multivariate harmonic new better than used in expectation (MHNBUE) alternative. Setting , the practitioner standardizes to before applying the statistic. For the standardised observations, this paper constructs a test statistic from the -fold Laplace transform of the multivariate equilibrium function, derives a closed-form expression for its null variance valid for every dimension , prove a -dimensional Laplace-uniqueness characterisation of the null hypothesis, and establish its asymptotic normality. To the best of the authors’ knowledge, no previously published test for the MHNBUE alternative has been established for existing work covers only Monte Carlo upper and lower critical values, Pitman asymptotic efficacy, and empirical power are evaluated for against linear failure rate, Makeham, and Weibull alternatives. Numerical evidence shows that positive Clayton dependence pushes the statistic negative at a rate increasing with dimension; motivated by this, a pre-specified lower-tailed test is applied to the cross-validated American Football League scoring-times data, yielding rejection at the 5% significance level, interpreted as departure from bivariate exponentiality driven primarily by positive dependence rather than by marginal ageing.
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