Moderate Deviations For Weighted Sample Quantiles

Quantile is a very important concept in statistics, it has very important applications inmany fields, especially in the finance and insurance. For example, in the insuranceindustry, insurance risk management tool is the most commonly used,and the uses ofsolvency limit. this series of problems can be classified as quantile topics in statistics.Recently, the study of quantile estimators are main about order statistics, kernel typequantile estimators. Some researchers have studied the order statistics,such as the largedeviations, the sample path large deviation made study deeply, kernel type quantileestimator is also favored by the researchers, not only to study the nature of its variousaspects but to be applied to all aspects of mathematics, physics, biology, etc. It can beseen that the research of quantile has important theoretical and practical significance.In this paper, the weighted sample quantile estimator extended usual quantileestimators to the general the weighted case, it is a more efficient estimate relative to thecurrent findings.On the assumption of that the sample is exponentially distributed, andaccording to the properties of order statistics with exponential distribution and mean1,using the classic Gartner-Ellis theorem, get the moderate deviation principle of weightedsample quantile and the speed of convergence of the weighted sample quantile.