Johnson quantile-parameterized distributions (J-QPDs) are parameterized by any symmetric percentile triplet (SPT) (e.g., the 10th–50th–90th) and support bounds. J-QPDs are smooth, highly flexible, ...and amenable to Monte Carlo simulation via inverse transform sampling. However, semibounded J-QPDs are limited to lognormal tails. In this paper we generalize the kernel distribution of J-QPD beyond the standard normal, generating new fat-tailed distribution systems that are more flexible than J-QPD. We also show how to augment the SPT/bound parameters with a tail parameter, lending separate control over the distribution body and tail. We then present advantages of our new generalized system over existing systems in the contexts of both expert elicitation and fitting to empirical data.
q
-Gaussian behavior is often encountered in quite distinct settings. A possible explanation is here given with reference to experimental scenarios in which data are gathered using a set-up that ...performs a normalization preprocessing. We show that the ensuing normalized input, as recorded by the measurement device, will
always be
q
-Gaussian distributed if the incoming data exhibit elliptical symmetry, a rather common feature. Moreover, we find that in these circumstances, the value of the associated parameter
q
can be deduced from
the normalization technique that characterizes the device. Finally, one concludes from the above remarks that great care should be exercised when empirically detecting
q
-Gaussian behavior. As an example, Gaussian data (the most common situation) will appear, after normalization, in the guise of
q
-Gaussian records.
