TY - JOUR T1 - Estimation of Past Entropy in Length-Biased Data TT - برآورد آنتروپی گذشته در داده‌های طول-اریب JF - JSS JO - JSS VL - 15 IS - 2 UR - http://jss.irstat.ir/article-1-735-en.html Y1 - 2022 SP - 363 EP - 380 KW - Length-Biased Data KW - Kernel Density Estimation KW - Past Entropy KW - Simulation KW - Strong Consistency N2 - In this article, we propose two non-parametric estimators for the past entropy based on length-biased data, and the strong consistency of the proposed estimators is proved. In addition, some simulations are conducted to evaluate the performance of the proposed estimators. Based on the results, we show that they have better performance in a different region of the probability distribution for length-biased random variables. M3 10.52547/jss.15.2.363 ER -