分位數全距

Abstract

此論文中，我們介紹了一個新的全距，叫做「眾數型態分位數全距」。考慮到測量穩健性估計量時，breakdown point是一個重要的準則，且早期在建構的穩健性估計量中，breakdown points都在0.5以下(參見Hampel (1986))，我們將會說明這個新的分位數全距breakdown point可以提高到接近1。我們也利用模擬資料來比較此眾數型態及傳統分位數全距的MSE。更進一步地，我們會把此分位數全距延伸到建構製程能力指標上。

We introduce a new type of range, called the mode type interpercentile distance. With the fact that the breakdown point is one important criterion for measuring the robust type estimators and the fact that the proposed robust estimators are all with breakdown points less than or equal to 0.5)( see this point in Hampel et al. (1986)), we will show that this new interpercentile distance may have breakdown point as large as close to 1. Simulation for comparing this interpercentile distance and the traditional one will also be conducted through the mean square error (MSE). Moreover, an extension of this interpercentile distance to construct a process capability index will also be introduced.