Estimation of past extropy in the presence of measurement error

In scientific research, datasets commonly include measurement errors. Failing to account for these errors can lead to biased estimates and undermine the reliability of the findings. In this context, we concentrate on estimating the past extropy function while accounting for measurement errors. We proposed an estimator for the past extropy function and derived its asymptotic properties. To evaluate the accuracy, we conducted a simulation study and made a comparison with empirical estimator of past extropy based on the contaminated sample. Additionally, the precision of the estimator is validated through an analysis of real data.