Abstract
In the following work we model a random sample having support on the positive orthant using the power normal (PN) distribution. The PN distribution is unimodal, obtained from inverse Box-Cox (BC) transformation and there exists no close form expression for moment estimation. Hence, we simulate from the distribution to estimate its moments and also implement a naive bootstrap, on the random sample prior to the modelling, to account for the uncertainty in estimating the BC transformation parameters. In the real world examples we consider, we find the distribution efficient in modelling the tails of the underlying unknown process. Due to the minimalistic assumptions with PN distribution it can be used to model data observed both on the nominal scale and interval scale. In our simulation studies, wherein we consider samples from a known distribution with support defined on the positive orthant only, we observe that the PN distribution performs better than Kernel density estimation methods based on Gaussian assumptions for sampling and density estimation.
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