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Non‐normal bivariate densities with normal marginals and linear regression functions *
Author(s) -
Ruymgaart F. H.
Publication year - 1973
Publication title -
statistica neerlandica
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.52
H-Index - 39
eISSN - 1467-9574
pISSN - 0039-0402
DOI - 10.1111/j.1467-9574.1973.tb00203.x
Subject(s) - mathematics , bivariate analysis , multivariate normal distribution , statistics , univariate , marginal distribution , bivariate data , joint probability distribution , normal distribution , econometrics , multivariate statistics , random variable
Summary It is well known that for a bivariate density in order to be bivariate normal, the possession of univariate normal marginal densities alone is not sufficient. In this paper it will be shown by means of some counterexamples that the additional requirement of linearity of the regression functions does not supply a sufficient condition either.