Random convex combinations of order statistics

Eric Beutner; Udo Kamps

doi:10.1016/j.spl.2007.02.005

Random convex combinations of order statistics

Eric Beutner^*, Udo Kamps

^*Corresponding author for this work

Research output: Contribution to Journal › Article › Academic › peer-review

Abstract

For order statistics X_{i, n}, X_{j, n}, X_{k, n} with 1 ≤ i < j < k ≤ n, and an independent beta distributed random variable C the distributional equation X_{j, n} over(=, d) (1 - C) · X_{i, n} + C · X_{k, n} is established for uniform distributions as well as seen to be characteristic.

Original language	English
Pages (from-to)	1133-1136
Number of pages	4
Journal	Statistics and Probability Letters
Volume	77
Issue number	11
DOIs	https://doi.org/10.1016/j.spl.2007.02.005
Publication status	Published - 15 Jun 2007
Externally published	Yes

Keywords

Beta distribution
Order statistics
Random convex combinations
Record values

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10.1016/j.spl.2007.02.005

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title = "Random convex combinations of order statistics",

abstract = "For order statistics Xi, n, Xj, n, Xk, n with 1 ≤ i < j < k ≤ n, and an independent beta distributed random variable C the distributional equation Xj, n over(=, d) (1 - C) · Xi, n + C · Xk, n is established for uniform distributions as well as seen to be characteristic.",

keywords = "Beta distribution, Order statistics, Random convex combinations, Record values",

author = "Eric Beutner and Udo Kamps",

year = "2007",

month = jun,

day = "15",

doi = "10.1016/j.spl.2007.02.005",

language = "English",

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journal = "Statistics and Probability Letters",

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AU - Kamps, Udo

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Y1 - 2007/6/15

N2 - For order statistics Xi, n, Xj, n, Xk, n with 1 ≤ i < j < k ≤ n, and an independent beta distributed random variable C the distributional equation Xj, n over(=, d) (1 - C) · Xi, n + C · Xk, n is established for uniform distributions as well as seen to be characteristic.

AB - For order statistics Xi, n, Xj, n, Xk, n with 1 ≤ i < j < k ≤ n, and an independent beta distributed random variable C the distributional equation Xj, n over(=, d) (1 - C) · Xi, n + C · Xk, n is established for uniform distributions as well as seen to be characteristic.

KW - Beta distribution

KW - Order statistics

KW - Random convex combinations

KW - Record values

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U2 - 10.1016/j.spl.2007.02.005

DO - 10.1016/j.spl.2007.02.005

M3 - Article

AN - SCOPUS:34248355588

SN - 0167-7152

VL - 77

SP - 1133

EP - 1136

JO - Statistics and Probability Letters

JF - Statistics and Probability Letters

IS - 11

ER -

Random convex combinations of order statistics

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Keywords

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