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Published in:
2019 | OriginalPaper | Chapter
Inverse Box-Cox and the Power Normal Distribution
Author : Rui Gonçalves
Published in: Innovation, Engineering and Entrepreneurship
Publisher: Springer International Publishing
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Abstract
In this paper we consider the power-normal (PN) family of distributions. This family is generated by inverting the Box-Cox [1] power transformation. If Y is a left truncated normal (TN) random variable then the variable \(X=(\lambda Y+1)^{1/\lambda }\) has a PN distribution with parameters \(\mu \) and \(\sigma \). We study the case where \(0<\lambda <1\). We obtain a formula for the rth ordinary moment of the power normal distribution. We examine the bivariate power normal distribution and we calculate the marginal and conditional distributions. We give a formula for the correlation curve and we provide a numerical illustration.