Convergence of the Gram-Charier expansion after the normalizing Box-Cox transformation

Ryuei Nishii

Research output: Contribution to journalArticle

2 Citations (Scopus)

Abstract

Consider an exponential family such that the variance function is given by the power of the mean function. This family is denoted by EDα if the variance function is given by μ(2-α)/(1-α), where μ is the mean function. When 0≤α<1, it is known that the transformation of ED(α) to normality is given by the power transformation X(1-2α)/(3-3α), and conversely, the power transformation characterizes ED(α). Our principal concern will be to show that this power transformation has an another merit, i.e., the density of the transformed variate has an absolutely convergent Gram-Charier expansion.

Original languageEnglish
Pages (from-to)173-186
Number of pages14
JournalAnnals of the Institute of Statistical Mathematics
Volume45
Issue number1
DOIs
Publication statusPublished - Mar 1 1993

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Normalizing Transformation
Box-Cox Transformation
Power Transformation
Variance Function
Exponential Family
Normality

All Science Journal Classification (ASJC) codes

  • Statistics and Probability

Cite this

Convergence of the Gram-Charier expansion after the normalizing Box-Cox transformation. / Nishii, Ryuei.

In: Annals of the Institute of Statistical Mathematics, Vol. 45, No. 1, 01.03.1993, p. 173-186.

Research output: Contribution to journalArticle

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