(untitled) (Statistics, Optimization & Information Computing, 2025)
Two well-known distributions which are very helpful for modelling data in different areas, are the lognormal and inverse Weibull distributions. Choosing between the true or false distribution is substantial and of great importance. In order to determine the correct model, the ratios of biases and mean squared errors will have been computed by performing miss-specified analysis on the mean of these distributions and decision is made by comparing these ratios. To confirm the achieved theoretical results, a simulation study has been done. When the correct model is lognormal, then the miss-specification as the inverse Weibull (IW) model leads to larger values for ratios of biases and mean squared errors, so in this case miss-specification does not have a significant chance in practice. However, when the correct model is IW, there is a big chance for false specifying the lognormal model. Finally, this methodology is applied to determine the true distribution for a real data set of Covid-19 mortality rate in Germany.