The Kerridge [(1961). Inaccuracy and inference. Journal of the Royal Statistical Society: Series B 23(1): 184-194] inaccuracy measure is the mathematical expectation of the information content of the true distribution with respect to an assumed distribution, reflecting the inaccuracy introduced when the assumed distribution is used. Analyzing the dispersion of information around such measures helps us understand their consistency. The study of dispersion of information around the inaccuracy measure is termed varinaccuracy. Recently, Balakrishnan et al. [(2024). Dispersion indices based on Kerridge inaccuracy measure and Kullback–Leibler divergence. Communications in Statistics – Theory and Methods 53(15): 5574-5592] introduced varinaccuracy, to compare models where lower variance indicates greater precision. As interval inaccuracy is crucial for analyzing the evolution of system reliability over time, examining its variability strengthens the validity of the extracted information. This article introduces the varinaccuracy measure for doubly truncated random variables and demonstrates its significance. The measure has been studied under transformations, and bounds are also provided to broaden the applicability of the measure where direct evaluation is challenging. Additionally, an estimator for the measure is proposed, and its consistency is analyzed using simulated data through a kernel-smoothed nonparametric estimation technique. The estimator is validated on real data sets of COVID-19 mortality rates for Mexico and Italy. Furthermore, the article illustrates the practical value of the measure in selecting the best alternative to a given distribution within an interval, following the minimum information discrimination principle, thereby highlighting the effectiveness of the study.

Recently, there is a growing interest to study the variability of uncertainty measure in information theory. For the sake of analyzing such interest, varentropy has been introduced and examined for one-sided truncated random variables. As the interval entropy measure is instrumental in summarizing various system and its components properties when it fails between two time points, exploring variability of such measure pronounces the extracted information. In this article, we introduce the concept of varentropy for doubly truncated random variable. A detailed study of theoretical results taking into account transformations, monotonicity and other conditions is proposed. A simulation study has been carried out to investigate the behavior of varentropy in shrinking interval for simulated and real-life data sets. Furthermore, applications related to the choice of most acceptable system and the first-passage times of an Ornstein–Uhlenbeck jump-diffusion process are illustrated.