Simultaneous Pitman closeness of progressively type-II right-censored order statistics to population quantiles |
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| Authors: | William Volterman Katherine F Davies N Balakrishnan |
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| Institution: | 1. Department of Mathematics and Statistics , McMaster University , Hamilton , Ontario , Canada , L8S 4K1 williamvolterman@gmail.com;3. Department of Statistics , University of Manitoba , Winnipeg , Canada , MB R3T 2N2;4. Department of Mathematics and Statistics , McMaster University , Hamilton , Ontario , Canada , L8S 4K1 |
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| Abstract: | In this work, we extend prior results concerning the simultaneous Pitman closeness of order statistics (OS) to population quantiles. By considering progressively type-II right-censored samples, we derive expressions for the simultaneous closeness probabilities of the progressively censored OS to population quantiles. Explicit expressions are deduced for the cases when the underlying distribution has bounded and unbounded supports. Illustrations are provided for the cases of exponential, uniform and normal distributions for various progressive type-II right-censoring schemes and different quantiles. Finally, an extension to the case of generalized OS is outlined. |
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| Keywords: | Pitman closeness order statistics progressive censoring quantiles generalized order statistics |
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