Generalized modulus power transformations

Varghese T. George; Robert C. Elston

doi:10.1080/03610928808829781

Generalized modulus power transformations

Varghese T. George
, Robert C. Elston

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

34 Scopus citations

Abstract

Several power transformations proposed in the past are examined to find out the type of distributions that they can normalize, and a general family of transformations, “the Generalized Modulus Power Transformation” (GEMPT), is proposed. The GEMPT will remove skewness and kurtosis and induce normality from a broad class of distributions, which we investigate, implying certain limitations for all power transformations. The use of GEMPT is illustrated and shown to lead to a better approximation to a normal distribution in an example in which the response is expected to follow a rectangular hyperbola.

Original language	English (US)
Pages (from-to)	2933-2952
Number of pages	20
Journal	Communications in Statistics - Theory and Methods
Volume	17
Issue number	9
DOIs	https://doi.org/10.1080/03610928808829781
State	Published - Jan 1 1988
Externally published	Yes

Keywords

Michaelis-Menten equation
bimodality
kinky distributions
kurtosis
normality
skewness

ASJC Scopus subject areas

Statistics and Probability

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10.1080/03610928808829781

Cite this

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title = "Generalized modulus power transformations",

abstract = "Several power transformations proposed in the past are examined to find out the type of distributions that they can normalize, and a general family of transformations, “the Generalized Modulus Power Transformation” (GEMPT), is proposed. The GEMPT will remove skewness and kurtosis and induce normality from a broad class of distributions, which we investigate, implying certain limitations for all power transformations. The use of GEMPT is illustrated and shown to lead to a better approximation to a normal distribution in an example in which the response is expected to follow a rectangular hyperbola.",

keywords = "Michaelis-Menten equation, bimodality, kinky distributions, kurtosis, normality, skewness",

author = "George, \{Varghese T.\} and Elston, \{Robert C.\}",

note = "Funding Information: We thank Drs. J. A. Sp\textasciitilde{}izerand K. M. Neison for the data used in the example. We also thank one of the referees whose comments were heipfui in improving this paper. This work was supp\textasciitilde{}rted in part by U. S. Pub!ic Hea!th Service research grant GM28356 from the National Institute of General Medical Sciences and training grant 1 T32 HL07567 from the National Heart, Lung and Blood I n s t i t u t e .",

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doi = "10.1080/03610928808829781",

language = "English (US)",

volume = "17",

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journal = "Communications in Statistics - Theory and Methods",

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T1 - Generalized modulus power transformations

AU - George, Varghese T.

AU - Elston, Robert C.

N1 - Funding Information: We thank Drs. J. A. Sp~izerand K. M. Neison for the data used in the example. We also thank one of the referees whose comments were heipfui in improving this paper. This work was supp~rted in part by U. S. Pub!ic Hea!th Service research grant GM28356 from the National Institute of General Medical Sciences and training grant 1 T32 HL07567 from the National Heart, Lung and Blood I n s t i t u t e .

PY - 1988/1/1

Y1 - 1988/1/1

N2 - Several power transformations proposed in the past are examined to find out the type of distributions that they can normalize, and a general family of transformations, “the Generalized Modulus Power Transformation” (GEMPT), is proposed. The GEMPT will remove skewness and kurtosis and induce normality from a broad class of distributions, which we investigate, implying certain limitations for all power transformations. The use of GEMPT is illustrated and shown to lead to a better approximation to a normal distribution in an example in which the response is expected to follow a rectangular hyperbola.

AB - Several power transformations proposed in the past are examined to find out the type of distributions that they can normalize, and a general family of transformations, “the Generalized Modulus Power Transformation” (GEMPT), is proposed. The GEMPT will remove skewness and kurtosis and induce normality from a broad class of distributions, which we investigate, implying certain limitations for all power transformations. The use of GEMPT is illustrated and shown to lead to a better approximation to a normal distribution in an example in which the response is expected to follow a rectangular hyperbola.

KW - Michaelis-Menten equation

KW - bimodality

KW - kinky distributions

KW - kurtosis

KW - normality

KW - skewness

UR - https://www.scopus.com/pages/publications/0000688240

UR - https://www.scopus.com/pages/publications/0000688240#tab=citedBy

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DO - 10.1080/03610928808829781

M3 - Article

AN - SCOPUS:0000688240

SN - 0361-0926

VL - 17

SP - 2933

EP - 2952

JO - Communications in Statistics - Theory and Methods

JF - Communications in Statistics - Theory and Methods

IS - 9

ER -

Generalized modulus power transformations

Abstract

Keywords

ASJC Scopus subject areas

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