Burr type III分配可以對於峯度和偏度的調整，涵蓋較大的範圍區域。而且可以近似好幾個不同的分配，包括log-logistic分配，Weibull分配，Burr type XII分配等。由於異常值可能出現在檢測資料中，這會影響到統計推論。而以對稱影響函數之M估計量的穩健迴歸的方法，已被成功的應用在減少異常值對於統計推論的不良影響。然而當資料分配是非對稱時，上述方法會使估計量產生較大的誤差。我們欲發展一個數學模型，它可以減少異常值對於統計推論的不良影響。
傳統上，會建議採用一種簡易處理異常值的方式，就是從資料中把異常值刪除。刪除異常值的方法，有很多種類可供選擇。雖然直接把異常值刪除很容易，但這總比什麼都不做要好。不過這樣簡易的做法，還是存在著一些問題:何時刪除異常值是正當的? 而且要刪除異常值的條件是，資料異常的程度要夠大，對於是否夠大不容易客觀判斷。再者資料分析人員的主觀偏好，可能認為觀察值是正常的，而無法輕易做出移除它的決策。由於在大部份的實際案例中，大多無法確定觀察值是否為非典型資料，所以很容易會發生把正常資料刪除的風險，此舉會引起低估資料的變異性。在大部份已發表的論文中，都是用機率密度函數和分配函數來估計異常值，然而以skew logistic分配為例，它只有quantile函數。假如我們想要得到機率密度函數和分配函數的估計值，我們必須要應用數值方法的技巧去得到估計值。
本篇論文提出利用quantile函數，在具異常值檢測資料下以非對稱影響函數之AM估計量對Burr type III分配進行參數估計。對於Burr type III分配而言，模擬的結果驗證了，在以Bias 和 RMSE的評量標準下，對大部分的情況而言，非對稱影響函數之AM估計量比最大概似估計法和傳統的M估計量方法有更佳的表現。本研究亦提供了一組實例資料說明本篇論文所提出方法的效能。

The Burr type III distribution allows for a wider region for the skewness and kurtosis plane, which covers several distributions including: the log-logistic, and the Weibull and Burr type XII distributions. However, outliers may occur in the data set. The robust regression method such as M-estimator with symmetric influence function has been successfully used to diminish the effect of outliers on statistical inference. However, when the data distribution is asymmetric, these methods yield biased estimators. We want to develop a mathematical model which can diminish the effect of outliers on statistical inference.
The traditional method suggests that a simple way to handle outliers is to detect them and remove them from the data set. There are many methods for detecting outliers. Deleting an outlier, although better than doing nothing, still poses a number of problems. When is deletion justified? Deletion requires a subjective decision. When is an observation “outlying enough” to be deleted? The user of the data may think that “an observation is an observation” and hence feel uneasy about deleting them. Since there is generally some uncertainty as to whether an observation is really atypical, there is a risk of deleting “good” observations, which results in underestimating data variability. Most published papers presented the outlier estimation based on the CDF or PDF functions. However, the skew logistic distribution has only quantile function. If we wanted to compute the values of the CDF or PDF for these distributions, we would have to be made of numerical techniques to obtain specific approximate value.
We present an M-estimator with asymmetric influence function (AM-estimator) based on the quantile function of the Burr type III distribution to estimate the parameters for complete data with outliers. The simulation results show that the M-estimator with asymmetric influence function generally outperforms the maximum likelihood and traditional M-estimator methods in terms of bias and root mean square errors. One real example is used to demonstrate the performance of our proposed method.

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