Conditions for finiteness and bounds on moments of generalized order statistics

Mariusz Bieniek () and Tomasz Rychlik ()
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Mariusz Bieniek: University of Maria Curie-Skłodowska
Tomasz Rychlik: Polish Academy of Sciences

Statistical Papers, 2024, vol. 65, issue 4, No 15, 2289-2312

Abstract: Abstract We present necessary and sufficient conditions for the finiteness of moments of a fixed order of generalized order statistics based on an arbitrary life baseline distribution with a finite expectation. The conditions depend on a relation between the moment order and the minimal parameter of the generalized order statistic and its multiplicity. Furthermore, under these conditions we determine sharp upper bounds on the moments of generalized order statistic expressed in the scale units being the respective powers of the mean of the baseline distribution.

Keywords: Generalized order statistic; Life distribution; Raw moment; Primary: 60E15; 62G32; Secondary: 62G30; 62N05 (search for similar items in EconPapers)
Date: 2024
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DOI: 10.1007/s00362-023-01482-5

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