Master of Science / Department of Statistics / Paul I. Nelson / Quantiles are useful in describing distributions of component lifetimes. Data, consisting
of the lifetimes of sample units, used to estimate quantiles are often censored. Right censoring,
the setting investigated here, occurs, for example, when some test units may still be functioning
when the experiment is terminated. This study investigated and compared the performance of
parametric and nonparametric estimators of quantiles from right censored data generated from
Weibull and Lognormal distributions, models which are commonly used in analyzing lifetime
data. Parametric quantile estimators based on these assumed models were compared via
simulation to each other and to quantile estimators obtained from the nonparametric Kaplan-
Meier Estimator of the survival function. Various combinations of quantiles, censoring
proportion, sample size, and distributions were considered.
Our simulation show that the larger the sample size and the lower the censoring rate the
better the performance of the estimates of the 5th percentile of Weibull data. The lognormal data
are very sensitive to the censoring rate and we observed that for higher censoring rates the
incorrect parametric estimates perform the best.
If you do not know the underlying distribution of the data, it is risky to use parametric
estimates of quantiles close to one. A limitation in using the nonparametric estimator of large
quantiles is their instability when the censoring rate is high and the largest observations are
censored.
Key Words: Quantiles, Right Censoring, Kaplan-Meier estimator
| Identifer | oai:union.ndltd.org:KSU/oai:krex.k-state.edu:2097/4318 |
| Date | January 1900 |
| Creators | Serasinghe, Shyamalee Kumary |
| Publisher | Kansas State University |
| Source Sets | K-State Research Exchange |
| Language | en_US |
| Detected Language | English |
| Type | Report |
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