A smooth nonparametric quantile estimator for IFR distributions

Abstract

Assuming that the underlying distribution F has an increasing failure rate, a smooth quantile estimator is obtained based on the nonparametric maximum likelihood estimator of F. The quantile estimator is shown to be strongly consistent and asymptotically normal and does not require the selection of a smoothing parameter as do some other nonparametric quantile estimators. Some results of a small simulation and an illustrative example are also presented.

Keywords:

• Nonparametric maximum likelihood
• failure rate estimation
• consistency
• percentile estimation