Advances and Applications in Statistics
Volume 1, Issue 1, Pages 1 - 26
(April 2001)
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A NOVEL MEANS OF ESTIMATING QUANTILES FOR 2-PARAMETER WEIBULL DISTRIBUTION UNDER THE RIGHT RANDOM CENSORING MODEL
Kuo-Ching Chiou (Taiwan) and Lee-Ing Tong (Taiwan)
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Abstract: Censoring models are frequently used in reliability
analysis to reduce experimental time. Three types of
censoring models are type-I, type-II and random
censoring. In this study, we focus on the right random
censoring model. In this model, if the failure time
exceeds its associated censoring time, then the
failure time becomes a censored observation. In this
case, many authors (see Lawless [Statistical Models
and Methods for Lifetime Data, John Wiley, New York,
1982], Lee [Statistical Methods for Survival Data
Analysis, 2nd ed., Wiley, New York, 1992], Miller
[Survival Analysis, John Wiley, New York, 1981], among
others) considered using the observed censoring time
to impute the censored observation which, however,
underestimates the true failure time. Herein, two
methods to impute the censored observations are
proposed in a right random censoring model for a
2-parameter Weibull distribution. By a Monte Carlo
simulation, the quantile estimates are calculated to
assess the performance of the proposed imputation
methods with respect to their relative mean square
error. Simulation results indicate that the two
imputation methods proposed herein are superior to the
available methods in [Statistical Models and Methods
for Lifetime Data, John Wiley, New York, 1982,
Statistical Methods for Survival Data Analysis, 2nd
ed., Wiley, New York, 1992, Survival Analysis, John
Wiley, New York, 1981] if the shape parameter of
Weibull distribution exceeds 1, except for the lower
quantiles. |
Keywords and phrases: random censoring model, failure time, censoring time, imputation, quantile, relative mean square error. |
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