Analysis for the xgamma distribution based on record values and inter-record times with application to prediction of rainfall and COVID-19 records

Recently, Sen et al. (2016) introduced a new lifetime distribution, called "xgamma distribution", which can be used as an alternative to other lifetime distributions, like the exponential one. In this paper, we study the problem of classical and Bayesian estimation of the unknown parameter of the xgamma distribution based on record values and inter-record times. The problem of Bayesian prediction of future record values based on record values and interrecord times is also discussed. A small simulation study has been performed to compare the performance of the proposed estimators and the approximate Bayes predictors. Two real data sets related to rainfall and COVID-19 records have been analysed. We considered four one-parameter lifetime distributions as the base models for each data set and compared the goodness-of-fit results. Then, the numerical results of estimation of the parameter and prediction of future records based on the xgamma and exponential records and inter-record times were presented. We observed that the record values and inter-record times from the xgamma distribution could predict future records in a relatively satisfactory way.