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Variation diminishing property of densities of uniform generalized order statistics

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Abstract

Let f *,r , r  ≥  1, denote the density function of rth uniform generalized order statistics as defined by Kamps (1995) or Cramer and Kamps (2003). We prove the following variation diminishing property: the number of zeros in (0,1) of any linear combination \(\sum_{j=1}^{r}a_jf_{\ast,j}\) does not exceed the number of sign changes in the sequence (a 1, . . . ,a r ). This result is applied to study monotonicity and convexity properties of f *,r .

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Authors and Affiliations

  1. Institute of Mathematics, Polish Academy of Sciences, Śniadeckich 8, 00–956, Warsaw, Poland

    Mariusz Bieniek

  2. Institute of Mathematics, Maria Curie Skłodowska University, Pl. M. Curie Skłodowskiej 1, 20–031, Lublin, Poland

    Mariusz Bieniek

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  1. Mariusz Bieniek
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Correspondence to Mariusz Bieniek.

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Bieniek, M. Variation diminishing property of densities of uniform generalized order statistics. Metrika 65, 297–309 (2007). https://doi.org/10.1007/s00184-006-0077-4

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  • DOI: https://doi.org/10.1007/s00184-006-0077-4

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