Characterizations using weighted distributions

Anthony Pakes; J. Navarro; J.M. Ruiz; Y.D. Aguila

doi:10.1016/S0378-3758(02)00357-9

Characterizations using weighted distributions

Anthony Pakes, J. Navarro, J.M. Ruiz, Y.D. Aguila

UWA Business School

Research output: Contribution to journal › Article

17 Citations (Scopus)

Abstract

For one-parameter natural exponential and power series families we give some general characterizations from an affine relation connecting the mean of member distributions and their length biased versions. Examples subsume many known cases. Other characterizations are explored using random variable relations involving the length biased version of partial sums. Finally, characterizations of the law of X admitting more general weights are obtained by equating the laws of a function H(X) and the weighted version of X. (C) 2002 Elsevier B.V. All rights reserved.

Original language	English
Pages (from-to)	389-420
Journal	Journal of Statistical Planning and Inference
Volume	116
Issue number	2
DOIs	https://doi.org/10.1016/S0378-3758(02)00357-9
Publication status	Published - 2003

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title = "Characterizations using weighted distributions",

abstract = "For one-parameter natural exponential and power series families we give some general characterizations from an affine relation connecting the mean of member distributions and their length biased versions. Examples subsume many known cases. Other characterizations are explored using random variable relations involving the length biased version of partial sums. Finally, characterizations of the law of X admitting more general weights are obtained by equating the laws of a function H(X) and the weighted version of X. (C) 2002 Elsevier B.V. All rights reserved.",

author = "Anthony Pakes and J. Navarro and J.M. Ruiz and Y.D. Aguila",

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AU - Navarro, J.

AU - Ruiz, J.M.

AU - Aguila, Y.D.

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N2 - For one-parameter natural exponential and power series families we give some general characterizations from an affine relation connecting the mean of member distributions and their length biased versions. Examples subsume many known cases. Other characterizations are explored using random variable relations involving the length biased version of partial sums. Finally, characterizations of the law of X admitting more general weights are obtained by equating the laws of a function H(X) and the weighted version of X. (C) 2002 Elsevier B.V. All rights reserved.

AB - For one-parameter natural exponential and power series families we give some general characterizations from an affine relation connecting the mean of member distributions and their length biased versions. Examples subsume many known cases. Other characterizations are explored using random variable relations involving the length biased version of partial sums. Finally, characterizations of the law of X admitting more general weights are obtained by equating the laws of a function H(X) and the weighted version of X. (C) 2002 Elsevier B.V. All rights reserved.

U2 - 10.1016/S0378-3758(02)00357-9

DO - 10.1016/S0378-3758(02)00357-9

M3 - Article

VL - 116

SP - 389

EP - 420

JO - Journal of Statistical Planning and Inference

JF - Journal of Statistical Planning and Inference

SN - 0378-3758

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