scholarly journals A Histogram Estimator of the Hazard Rate with Censored Data

1985 ◽  
Vol 13 (2) ◽  
pp. 592-605 ◽  
Author(s):  
Regina Y. C. Liu ◽  
John Van Ryzin
Keyword(s):  
Censored Data ◽  
Hazard Rate ◽  
Histogram Estimator

scholarly journals Gamma Kernel Estimators for Density and Hazard Rate of Right-Censored Data

2011 ◽  
Vol 2011 ◽  
pp. 1-16 ◽  
Author(s):  
T. Bouezmarni ◽  
A. El Ghouch ◽  
M. Mesfioui
Keyword(s):  
Censored Data ◽  
Hazard Rate ◽  
Kernel Smoothing ◽  
Mean Squared Error ◽  
Boundary Region ◽  
Law Of Iterated Logarithm ◽  
Linear Estimator ◽  
Right Censored Data ◽  
Squared Error ◽  
Rate Functions

The nonparametric estimation for the density and hazard rate functions for right-censored data using the kernel smoothing techniques is considered. The “classical” fixed symmetric kernel type estimator of these functions performs well in the interior region, but it suffers from the problem of bias in the boundary region. Here, we propose new estimators based on the gamma kernels for the density and the hazard rate functions. The estimators are free of bias and achieve the optimal rate of convergence in terms of integrated mean squared error. The mean integrated squared error, the asymptotic normality, and the law of iterated logarithm are studied. A comparison of gamma estimators with the local linear estimator for the density function and with hazard rate estimator proposed by Müller and Wang (1994), which are free from boundary bias, is investigated by simulations.

NONPARAMETRIC ESTIMATION OF THE REVERSED HAZARD RATE FUNCTION FOR UNCENSORED AND CENSORED DATA

2011 ◽  
Vol 18 (05) ◽  
pp. 417-429 ◽  
Author(s):  
CHATHURI L. JAYASINGHE ◽  
PANLOP ZEEPHONGSEKUL
Keyword(s):  
Censored Data ◽  
Hazard Rate ◽  
Real Data ◽  
Reliability Function ◽  
Rate Function ◽  
Nonparametric Estimator ◽  
Selection Methods ◽  
Actuarial Science ◽  
Lifetime Distributions ◽  
Reversed Hazard Rate

Reversed hazard rate (RHR) function is an important reliability function that is applicable to various fields. Applications can be found in portfolio selection problems in finance, analysis of left-censored data, problems in actuarial science and forensic science involving estimation of exact time of occurrence of a particular event, etc. In this paper, we propose a new nonparametric estimator based on binning techniques for this reliability function for an uncensored sample and then provide an extension for RHR estimation under left censorship. The performance of the proposed estimators were then evaluated using simulations and real data from reliability and related disciplines. The results indicate that the proposed estimator does well for common lifetime distributions with the bin-width selection methods considered.

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