A Simple Minimum‐Bias Percentile Estimator of the Location Parameter for the Gamma, Weibull, and Log‐Normal Distributions

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Abstract
Estimating the unknown minimum (location) of a random variable has received some attention in the statistical literature, but not enough in the area of decision sciences. This is surprising, given that such estimation needs exist often in simulation and global optimization. This study explores the characteristics of two previously used simple percentile estimators of location. The study also identifies a new percentile estimator of the location parameter for the gamma, Weibull, and log‐normal distributions with a smaller bias than the other two estimators. The performance of the new estimator, the minimum‐bias percentile (MBP) estimator, and the other two percentile estimators are compared using Monte‐Carlo simulation. The results indicate that, of the three estimators, the MBP estimator developed in this study provides, in most cases, the estimate with the lowest bias and smallest mean square error of the location for populations drawn from log‐normal and gamma or Weibull (but not exponential) distributions. A decision diagram is provided for location estimator selection, based on the value of the coefficient of variation, when the statistical distribution is known or unknown.