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 $ \alpha $-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 $ \alpha $-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.
Citation: Mohamed Kayid. Statistical inference of an $ \mathit{\alpha } $-quantile past lifetime function with applications[J]. AIMS Mathematics, 2024, 9(6): 15346-15360. doi: 10.3934/math.2024745
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 $ \alpha $-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 $ \alpha $-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.
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Mohamed Kayid. Statistical inference of an $ \mathit{\alpha } $-quantile past lifetime function with applications[J]. AIMS Mathematics, 2024, 9(6): 15346-15360. doi: 10.3934/math.2024745
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