The distribution of the sample correlation coefficient under variance-truncated normality

The non-null distribution of the sample correlation coefficient under bivariate normality is derived when each of the associated two sample variances is subject to stripe truncation including usual single and double truncation as special cases. The probability density function is obtained using seri...

Full description

Saved in:
Bibliographic Details
Published inMetrika Vol. 87; no. 5; pp. 471 - 497
Main Author Ogasawara, Haruhiko
Format Journal Article
LanguageEnglish
Published Berlin/Heidelberg Springer Berlin Heidelberg 01.07.2024
Springer Nature B.V
Subjects
Bivariate analysis
Correlation coefficients
Economic Theory/Quantitative Economics/Mathematical Methods
Hypergeometric functions
Mathematics and Statistics
Normality
Probability density functions
Probability Theory and Stochastic Processes
Statistics
Variance
Stripe truncation
Multivariate normality
Sample variances and covariances
Multivariate gamma function
Weighted hypergeometric functions
Wishart distribution
Online AccessGet full text

Cover

More Information
Summary:The non-null distribution of the sample correlation coefficient under bivariate normality is derived when each of the associated two sample variances is subject to stripe truncation including usual single and double truncation as special cases. The probability density function is obtained using series expressions as in the untruncated case with new definitions of weighted hypergeometric functions. Formulas of the moments of arbitrary orders are given using the weighted hypergeometric functions. It is shown that the null joint distribution of the sample correlation coefficients under multivariate untruncated normality holds also in the variance-truncated cases. Some numerical illustrations are shown.
Bibliography:ObjectType-Article-1
SourceType-Scholarly Journals-1
ObjectType-Feature-2
content type line 14
ISSN:0026-1335
1435-926X
DOI:10.1007/s00184-023-00918-0