Geometric Tweedie regression models for continuous and semicontinuous data with variation phenomenon

We introduce a new class of regression models based on the geometric Tweedie models (GTMs) for analyzing both continuous and semicontinuous data, similar to the recent and standard Tweedie regression models. We also present a phenomenon of variation with respect to the equi-varied exponential distribution, where variance is equal to the squared mean. The corresponding power v-functions which characterize the GTMs, obtained in turn by exponential-Tweedie mixture, are transformed into variance to use the conventional generalized linear models. The real power parameter of GTMs works as an automatic distribution selection such for asymmetric Laplace, geometric-compound-Poisson-gamma and geometric-Mittag-Leffler. The classification of all power v-functions reveals only two border count distributions, namely geometric and geometric-Poisson. We establish practical properties, into the GTMs, of zero-mass and variation phenomena, also in connection with some reliability measures. Simulation studies show that the proposed model highlights asymptotic unbiased and consistent estimators, despite the general over-variation. We illustrate two applications, under- and over-varied, on real datasets to a time to failure and time to repair in reliability; one of which has positive values with many achievements in zeros. We finally make concluding remarks, including future directions.