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Castaño-Martínez, A.; López-Blázquez, F.; Salamanca-Miño, B.

Random translations, contractions and dilations of order statistics and records. (English) Zbl 1241.62075

Statistics 46, No. 1, 57-67 (2012).
Summary: We introduce a new tool to investigate some distributional properties of order statistics and records related by a random translation (contraction or dilation) scheme. This technique is based on the property of uniqueness of solutions of certain nonlinear integral equations of Volterra type. We show how this tool is used to obtain new characterizations of distributions.

Cited in 9 Documents

MSC:

62G30 Order statistics; empirical distribution functions
62G32 Statistics of extreme values; tail inference
62E10 Characterization and structure theory of statistical distributions
45D05 Volterra integral equations

Keywords:

contractions and dilations; non-linear integral Volterra equations
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References:

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