Inference for the Unit-Gompertz distribution based on record data

Abstract

Practically record values are applied in situations concerning meteorology, hydrology, and sports events. A keen interest of a sports statistician may be to predict the future record value for a specific event. There are practical situations in which the record values from the available data are lost due to specific reasons. This need for record values stimulates us to construct the probability model that predicts the future record value and provides an estimation procedure in case of censored data. In the present study, the mechanism of sample moments of lower record values using the Type-II censoring is developed by assuming that the record characteristics follow the Unit Gompertz distribution. Utilizing this mechanism, the moments of lower record values are evaluated and tabulated for the specific values of the parameters. These tabulated values are applied to estimate the location and scale parameters of the underlying distribution by the method of ordered least squares. Furthermore, the point prediction and prediction interval for future record values are produced. Finally, the methodology is applied to real-life data to explain the procedure as well as show the effectiveness of forecasting out-of-sample data through the samplemoments of the lower record values, depending on the characteristicparameters of the Unit Gompertz distribution