Most methods that address missing data assume data is missing at random, NOT "missing" to remove "outliers".
One possible method to create a data set with missing values would be to start with a complete data set. Transcribe the data, drawing a Bernoulli random variable (rv) with probability p for each attribute of each observation. If rv==1 replace attribute value with a MISSING value/code. You could vary the Bernoulli parameter p and observe impact on your analysis / inference.