Some simple robust estimators of normal distribution tail percentiles and their properties

Abstract

Applications often require estimation of extreme percentile of a distribution. For example, in high temperature low cycle fatigue testing one wishes to estimate the cycles to failure associated with a low failure probability. Frequently, the available data suggest a normal distribution as a reasonable model for that part of the distribution that contains the percentile of interest, even though it may be inadequate as an overall representation. For such situations we seek estimators that are simple to apply by non-statisticians, robust to deviations from normality, and resistant to contamination by outliers in the right tail. We are especially concerned with situations that involve small sample sizes and extrapolation beyond the data.

Keywords:

• BLUE
• MLE
• trimmed samples/ censored samples
• selected order statistics