@article{Kayid2024, 
author = {Mohamed Kayid},
title = {Statistical inference of an        α  -quantile past lifetime function with applications},
year = {2024},
journal = {AIMS Mathematics},
volume = {9},
number = {6},
pages = {15346-15360},
keywords = {gaussian process, quantile past lifetime function, right censored data, survival analysis, Kaplan-Meier survival estimator},
url = {https://www.sciopen.com/article/10.3934/math.2024745},
doi = {10.3934/math.2024745},
abstract = {In reliability engineering and survival analysis, quantile functions are fundamental and often the most natural way to represent probability distributions and data samples. In this paper, the    α-quantile function of past lifetime was estimated for right-censored data by applying the Kaplan-Meier survival estimator. The weak convergence of the proposed estimator to a Gaussian process was investigated. A confidence interval for the    α-quantile of the past life function that does not depend on the density function was proposed. The strong convergence of the estimator to a Gaussian process was also discussed. The properties of the estimator and the confidence interval were investigated in a simulation study. Finally, two real datasets were analyzed.}
}