Lower k-record values from unit-Gompertz distribution and associated inference

TL;DR

This paper studies the statistical properties and inference methods for lower k-record values from the unit-Gompertz distribution, providing explicit formulas, estimators, predictors, and a real data application.

Contribution

It derives explicit moments, develops estimators and predictors, and evaluates their performance for lower k-records from the unit-Gompertz distribution, including a COVID-19 data analysis.

Findings

BLIE and BLIP outperform BLUE and BLIP in mean squared error

Derived explicit formulas for moments and covariances

Applied methods to COVID-19 data

Abstract

Mazucheli et al. (2019) introduced the unit-Gompertz (UG) distribution and studied some of its properties. More specifically, they considered the random variable X =exp(-Y), where Y has the Gompertz distribution. In this paper, we consider the lower k-record values from this distribution. We obtain exact explicit expressions as well as several recurrence relations for the single and product moments of lower k-record values and then we use these results to compute the means, variances and the covariances of the lower k-record values. We make use of these calculated moments to find the best linear unbiased estimators (BLUEs) of the location and scale parameters of the UG distribution. Applying the relation between the BLUE and the best linear invariant estimator (BLIE), we obtain the BLIEs of the location and scale parameters, as well. In addition, based on the observed k-records, we investigate how to obtain the best linear unbiased predictor (BLUP) and best linear invariant predictor (BLIP) for a future k-record value. Confidence intervals for the unknown parameters and prediction intervals for future k-records are also discussed. A simulation study is performed to assess the point and interval estimators and predictors proposed in the paper. The results show that the BLIE and BLIP outperform the BLUE and BLIP, in the sense of mean squared error criterion, respectively. Finally, a real data set pertaining to COVID-19 2-records is analyzed.