normal distribution, with means of 0 and 10 respectively and standard deviation 1. A fixed sample size of N=500 was used, of which different percentages (0-49% step 1%) were outliers drawn from G. Boxplot, median and MAD, IIR algorithm are compared, each simulation was replicated 1000 times and the average percentage of detected outliers was computed. Result is shown in Fig. 1a. In the second simulation, only mean of G distribution was changed to 5, result in Fig. 1b.

In Fig.1a, Boxplot and median and MAD perform well. But up to 25%, Boxplot breaks down; and up to 37%, median and MAD breaks down. IIR algorithm acts very steadily, always a little overestimates the outlier numbers. In Fig. 1b, Boxplot breaks down from 19% and median and MAD breaks down from 20%. IIR algorithm breaks down at 47%. In fact, the distance between distributions of means 0 and 5 is so close that separation of normal ones and outliers is no longer clear. Considering IIR algorithm can still detect 32.5% when contaminating percentage is up to 49%, it is indeed robust.

![0_image_0.png](0_image_0.png)

 (a) Distributions with mean 0 and 10 (b) Distributions with mean 0 and 5 

![0_image_1.png](0_image_1.png)

![0_image_2.png](0_image_2.png)

To see why IIR algorithm overestimates outliers, we gave another experiment. For simulated standard normal distributions with sample sizes 10, 50, 100, 500, 1000, 5000 and 10000, the percentages of detected outliers for three methods were computed. Each sample size was replicated 1000 times and average results were shown in Fig.1c. As sample size increases, Boxplot, median and MAD tend to detect outliers less than 1%, while IIR algorithm appears robust and keeps a little increasing. In theory, probability of the appearance of a deviant point increases with the increasing of sample size. But appearance doesn"t mean consistence, IIR algorithm can detect such kind of inconsistence, but other two seem to fail. The reason that IIR algorithm always a little 