Evaluations of expectations of order statistics and spacings based on IFR distributions

Agnieszka Goroncy () and Tomasz Rychlik ()
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Agnieszka Goroncy: Nicolaus Copernicus University
Tomasz Rychlik: Polish Academy of Sciences

Metrika: International Journal for Theoretical and Applied Statistics, 2016, vol. 79, issue 6, No 1, 635-657

Abstract: Abstract We consider i.i.d. random variables $$X_1,\ldots , X_n$$ X 1 , … , X n with a distribution function F preceding the exponential distribution function V in the convex transform order which means that F has an increasing failure rate. We determine sharp upper bounds on the expectations of order statistics and spacings based on $$X_1,\ldots , X_n$$ X 1 , … , X n , expressed in the population standard deviation units. We also specify the distributions for which all these bounds are attained. Finally, we indicate some reliability applications.

Keywords: Order statistics; Spacings; Optimal bound; Convex transform order; Increasing failure rate; Reliability system; 60E15; 62G32; 62N05 (search for similar items in EconPapers)
Date: 2016
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Citations: View citations in EconPapers (1)

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DOI: 10.1007/s00184-015-0570-8

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