# Estimating a quantile of an exponential distribution

Andrew L. Rukhin, William Strawderman

Research output: Contribution to journalArticle

22 Citations (Scopus)

### Abstract

We consider the problem of estimating a quantile ξ + bσ of an exponential distribution on the basis of a random sample of size n ≥ 2. Here ξ and σ are unknown location and scale parameters and b is a given constant. For quadratic loss, it is established that the best equivariant estimator (Equation presented) is inadmissible if 0 ≤ b < n-1or b > 1 + n1. For b > 1 + n1the estimator (Equation presented) elsewhere, provides a noticeable improvement over δ0.

Original language English (US) 159-162 4 Journal of the American Statistical Association 77 377 https://doi.org/10.1080/01621459.1982.10477780 Published - Jan 1 1982

### Fingerprint

Quantile
Exponential distribution
Equivariant Estimator
Location Parameter
Scale Parameter
Unknown Parameters
Estimator

### All Science Journal Classification (ASJC) codes

• Statistics and Probability
• Statistics, Probability and Uncertainty

### Keywords

• Best equivariant estimator
• Location-scale parameter
• Minimaxness
• Quantile of the exponential distribution

### Cite this

@article{2d5308fcc1c54d9dbbd31fc2c681b504,
title = "Estimating a quantile of an exponential distribution",
abstract = "We consider the problem of estimating a quantile ξ + bσ of an exponential distribution on the basis of a random sample of size n ≥ 2. Here ξ and σ are unknown location and scale parameters and b is a given constant. For quadratic loss, it is established that the best equivariant estimator (Equation presented) is inadmissible if 0 ≤ b < n-1or b > 1 + n1. For b > 1 + n1the estimator (Equation presented) elsewhere, provides a noticeable improvement over δ0.",
keywords = "Best equivariant estimator, Inadmissibility, Location-scale parameter, Minimaxness, Quadratic loss, Quantile of the exponential distribution",
author = "Rukhin, {Andrew L.} and William Strawderman",
year = "1982",
month = "1",
day = "1",
doi = "10.1080/01621459.1982.10477780",
language = "English (US)",
volume = "77",
pages = "159--162",
journal = "Journal of the American Statistical Association",
issn = "0162-1459",
publisher = "Taylor and Francis Ltd.",
number = "377",

}

Estimating a quantile of an exponential distribution. / Rukhin, Andrew L.; Strawderman, William.

In: Journal of the American Statistical Association, Vol. 77, No. 377, 01.01.1982, p. 159-162.

Research output: Contribution to journalArticle

TY - JOUR

T1 - Estimating a quantile of an exponential distribution

AU - Rukhin, Andrew L.

AU - Strawderman, William

PY - 1982/1/1

Y1 - 1982/1/1

N2 - We consider the problem of estimating a quantile ξ + bσ of an exponential distribution on the basis of a random sample of size n ≥ 2. Here ξ and σ are unknown location and scale parameters and b is a given constant. For quadratic loss, it is established that the best equivariant estimator (Equation presented) is inadmissible if 0 ≤ b < n-1or b > 1 + n1. For b > 1 + n1the estimator (Equation presented) elsewhere, provides a noticeable improvement over δ0.

AB - We consider the problem of estimating a quantile ξ + bσ of an exponential distribution on the basis of a random sample of size n ≥ 2. Here ξ and σ are unknown location and scale parameters and b is a given constant. For quadratic loss, it is established that the best equivariant estimator (Equation presented) is inadmissible if 0 ≤ b < n-1or b > 1 + n1. For b > 1 + n1the estimator (Equation presented) elsewhere, provides a noticeable improvement over δ0.

KW - Best equivariant estimator

KW - Location-scale parameter

KW - Minimaxness

KW - Quantile of the exponential distribution

UR - http://www.scopus.com/inward/record.url?scp=0002551945&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0002551945&partnerID=8YFLogxK

U2 - 10.1080/01621459.1982.10477780

DO - 10.1080/01621459.1982.10477780

M3 - Article

AN - SCOPUS:0002551945

VL - 77

SP - 159

EP - 162

JO - Journal of the American Statistical Association

JF - Journal of the American Statistical Association

SN - 0162-1459

IS - 377

ER -