On Inferences of Parameters in the Bivariate Power-Normal Distribution

Abstract

Power-normal distribution is a parametric family of distributions including log-normal and normal distributions as special cases, based on the power-transformation proposed by Box & Cox (1964). In this paper, basic properties of the bivariate power-normal distribution, which is an extension of the power-normal distribution to a two-dimensional case, are considered through some numerical examples and a mid-sized simulation from a viewpoint of the precision of parameter estimates and normality of the bivariate power-transformed distribution. Thus, in order to consider the effect of magnitude of truncation of the bivariate power-transformed distribution on parameter estimates, the two algorithms are used to estimate the parameters; the first allows the truncation, the second, does not. The result shows that the shapes of the bivariate power-normal distribution have the effect on the parameter estimates, and that for practical usage, the difference between the two algorithms with/without the truncation could be ignored.