On generalized log-Moyal distribution: A new heavy tailed size distribution

A new class of distributions, the generalized log-Moyal, suitable for modelling heavy tailed data is proposed in this article. This class exhibits desirable properties relevant to actuarial science and inference. The proposed distribution can be related to some well known distributions like Moyal, folded-normal and chi-square. Statistical inference of the model parameters is discussed using the method of quantiles and the method of maximum likelihood estimation. Three celebrated data sets, namely, Norwegian fire insurance losses, Danish fire insurance losses and vehicle insurance losses, are used to show the applicability of the new class of distributions. Parametric regression modelling is discussed assuming that the response variable follows the generalized log-Moyal distribution.