Compounded Bell-G class of statistical models with applications to COVID-19 and actuarial data

Abstract The compounded Bell generalized class of distributions is proposed in this article as an alternative to the Poisson family distributions. Some properties and actuarial measures are presented. a special model named Weibull (BellW) obtained such linear representation density, r th moment, incomplete moment generating function using Wright hypergeometric Meijer’s G function, p order statistics, reliability, stochastic ordering, residual reversed life. Moreover, some commonly used entropy measures, namely, Rényi, Havrda Charvat, Arimoto Tsallis for model. From inferential side, parameters estimated maximum likelihood estimation. simulation study performed highlight behavior estimates. including expected shortfall, value at risk, tail variance, variance premium BellW presented with numerical illustration. usefulness evaluated insurance claims COVID-19 datasets. Convincing results obtained.