Abstract

This paper examines estimation and prediction problems based on current-record statistics derived from the Fréchet distribution (the inverse Weibull distribution). The Fréchet model is widely used in reliability engineering, extreme-value analysis, and environmental studies, particularly for modeling phenomena with heavy-tailed distributions and extreme events. Assuming that the observed data constitute current records from a two-parameter Fréchet distribution with shape parameter α and scale parameter s, we derive the corresponding probability density function (PDF) and cumulative distribution function (CDF) for both upper and lower current records. Closed-form expressions for the moments of these record values are then obtained. Subsequently, maximum-likelihood and Bayesian estimate of the model parameters are developed, along with procedures for predicting future current record values and constructing predictive intervals. A Monte Carlo simulation study is conducted to evaluate the performance of the proposed estimators under different sample sizes and parameter configurations. Finally, the proposed methodology is illustrated through an application to industrial data from Saudi Arabia, highlighting the practical importance of Fréchet record modeling in reliability and life-testing analyses.