×

zbMATH — the first resource for mathematics

Characterization of normal distribution related to two samples based on regression. (English) Zbl 1105.62015
Summary: Characterization of normal distributions related to two samples based on second conditional moments has been obtained. This characterization has been transformed to a characterization based on the UMVU estimators of the density function. These results are generalized to \(k\) samples from normal distributions. Finally, applications of these characterization results to goodness-of-fit test are discussed.
MSC:
62E10 Characterization and structure theory of statistical distributions
62F03 Parametric hypothesis testing
62G10 Nonparametric hypothesis testing
PDF BibTeX Cite
Full Text: DOI
References:
[1] D’Agostino RB, Stephens MA (1986) Goodness-of-fit techniques. Marcel Dekker, New York
[2] Gupta AK, Varga T (1990) Characterization of joint density by conditional densities. Commun. Statist. Theory Methods 19:4643–4652 · Zbl 0728.62016
[3] Gupta AK, Nguyen TT, Wang Y (1997) Characterizations of some continuous distributions. J Ital Statist Soc 1:59–65
[4] Lehmann EL, Casella G (1998) Theory of point estimation. Springer, Berlin Heidelberg New York · Zbl 0916.62017
[5] Nguyen TT, Dinh KT (1998) Characterizations of normal distributions supporting goodness-of-fit tests based on sample skewness and sample kurtosis. Metrika 48:21–30 · Zbl 0990.62008
[6] Nguyen TT, Dinh KT (2003) Characterizations of normal distributions and EDF goodness-of-fit tests. Metrika 58:149–157 · Zbl 1026.62010
[7] Rao CR (1967) On some characterizations of the normal law. Sankhya A 29:1–14 · Zbl 0158.37803
[8] Rosenblatt M (1952) Remarks on a multivariate transformation. Ann Math Statist 23:470–472 · Zbl 0047.13104
[9] Singh J, Oliker VI (1979) On minimum variance unbiased estimation and characterization of densities. In: Proceedings of the Conference in Optical Methods in Statistics Academic, New York pp. 435–442 · Zbl 0458.62020
[10] Wang Y, Gupta AK, Nguyen TT (1996) Characterization theorems for some discrete distributions based on conditional structure. Can J Stat 24:257–262 · Zbl 0858.62008
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.