The mean of the inverse of a punctured normal distribution and its application

C. D. Lai; G. R. Wood; C. G. Qiao

doi:10.1002/bimj.200410033

The mean of the inverse of a punctured normal distribution and its application

C. D. Lai^*, G. R. Wood, C. G. Qiao

^*Corresponding author for this work

Research output: Contribution to journal › Article › peer-review

5 Citations (Scopus)

Abstract

The fundamental properties of a punctured normal distribution are studied. The results are applied to three issues concerning X/Y where X and Y are independent normal random variables with means μ_X and μ_Y respectively. First, estimation of μ_X/ μ_Y as a surrogate for E(X/Y) is justified, then the reason for preference of a weighted average, over an arithmetic average, as an estimator of μ_X/μ_Y is given. Finally, an approximate confidence interval for μ_X/μ_Y provided. A grain yield data set is used to illustrate the results.

Original language	English
Pages (from-to)	420-429
Number of pages	10
Journal	Biometrical Journal
Volume	46
Issue number	4
DOIs	https://doi.org/10.1002/bimj.200410033
Publication status	Published - 2004

Access to Document

10.1002/bimj.200410033

Cite this

@article{9be6e3ee25564e948c0e8f7d6d0e3ab0,

title = "The mean of the inverse of a punctured normal distribution and its application",

abstract = "The fundamental properties of a punctured normal distribution are studied. The results are applied to three issues concerning X/Y where X and Y are independent normal random variables with means μX and μY respectively. First, estimation of μX/ μY as a surrogate for E(X/Y) is justified, then the reason for preference of a weighted average, over an arithmetic average, as an estimator of μX/μY is given. Finally, an approximate confidence interval for μX/μY provided. A grain yield data set is used to illustrate the results.",

author = "Lai, {C. D.} and Wood, {G. R.} and Qiao, {C. G.}",

year = "2004",

doi = "10.1002/bimj.200410033",

language = "English",

volume = "46",

pages = "420--429",

journal = "Biometrical Journal",

issn = "0323-3847",

publisher = "Wiley-VCH, Wiley",

number = "4",

}

TY - JOUR

T1 - The mean of the inverse of a punctured normal distribution and its application

AU - Lai, C. D.

AU - Wood, G. R.

AU - Qiao, C. G.

PY - 2004

Y1 - 2004

N2 - The fundamental properties of a punctured normal distribution are studied. The results are applied to three issues concerning X/Y where X and Y are independent normal random variables with means μX and μY respectively. First, estimation of μX/ μY as a surrogate for E(X/Y) is justified, then the reason for preference of a weighted average, over an arithmetic average, as an estimator of μX/μY is given. Finally, an approximate confidence interval for μX/μY provided. A grain yield data set is used to illustrate the results.

AB - The fundamental properties of a punctured normal distribution are studied. The results are applied to three issues concerning X/Y where X and Y are independent normal random variables with means μX and μY respectively. First, estimation of μX/ μY as a surrogate for E(X/Y) is justified, then the reason for preference of a weighted average, over an arithmetic average, as an estimator of μX/μY is given. Finally, an approximate confidence interval for μX/μY provided. A grain yield data set is used to illustrate the results.

UR - http://www.scopus.com/inward/record.url?scp=26844578760&partnerID=8YFLogxK

U2 - 10.1002/bimj.200410033

DO - 10.1002/bimj.200410033

M3 - Article

AN - SCOPUS:26844578760

SN - 0323-3847

VL - 46

SP - 420

EP - 429

JO - Biometrical Journal

JF - Biometrical Journal

IS - 4

ER -

The mean of the inverse of a punctured normal distribution and its application

Abstract

Access to Document

Other files and links

Fingerprint

Cite this