Entropy measures and record statistics play an important role in information theory, reliability testing and survival analysis to provide a meaningful framework for analyzing lifetime data. Recent studies by Kumar and Dangi [1] and Dangi and Kumar [2, 3] have introduced quantile-based Shannon, Rényi and Tsallis entropies for record values that possess desirable robustness and interpretability properties. The present paper introduces a quantile pseudo-likelihood estimation technique using the least squares method. A simulation study is performed to estimate the above-mentioned quantile entropies for the records using the Weibull distribution as the reference model. The simulation results indicate that the proposed method performs consistently well in terms of stability and efficiency. Overall, the results support the use of the QPLE as a reliable approach for quantile-based estimation in the context of record statistics.
