Multivariate dependence of spacings of generalized order statistics

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Abstract

Multivariate dependence of spacings of generalized order statistics is studied. It is shown that spacings of generalized order statistics from DFR (IFR) distributions have the CIS (CDS) property. By restricting the choice of the model parameters and strengthening the assumptions on the underlying distribution, stronger dependence relations are established. For instance, if the model parameters are decreasingly ordered and the underlying distribution has a log-convex decreasing (log-concave) hazard rate, then the spacings satisfy the MTP2 (S- MRR2) property. Some consequences of the results are given. In particular, conditions for non-negativity of the best linear unbiased estimator of the scale parameter in a location-scale family are obtained. By applying a result for dual generalized order statistics, we show that in the particular situation of usual order statistics the assumptions can be weakened.

AMS subject classifications

primary
60E15
secondary
62G30
62H05
62N02

Keywords

Spacings of generalized order statistics
Multivariate total positivity
Strongly multivariate reverse regular rule
Conditionally increasing in sequence
Negative and positive orthant dependence
Right tail increasing in sequence
Increasing failure rate
Reversed hazard rate
Non-negativity of BLUE
Dual generalized order statistics

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