Popular methods for outlier detection (right skewed distribution) What are the popular methods for outlier detection in univariate data, which do not assume normal distribution?
 A: Generally, you should avoid trimming outliers in an ad hoc fashion and instead use nonparametric or robust alternatives.  A recent review with Monte Carlo studies can be found in Bakker and Wicherts (2014).  At least in psychology journals, Z-score cut-offs were most popular.  Of course, I wouldn't recommend that; the simulation studies in the same article demonstrate that Z-score cut-offs can inflate Type I error rates.
Although the review is focused on independent samples t-tests, most of their recommendations will apply more broadly. They concluded with the following recommendations:

• Correct or delete erroneous values.
• Based on prior research, it is not recommended to use Z scores
  to identify outliers. We recommend methods that suffer less from
  masking like the IQR or the MAD-median rule instead.
• Decide on outlier handling before seeing the results of the
  main analyses, and if possible, preregister the study at, for example,
  the Open Science Framework (http://openscienceframework.org/).
• If preregistration is not possible, report the outcomes both
  with and without outliers or on the basis of alternative methods.
• Report transparently about how outliers were handled.
• Do not carelessly remove outliers as this increases the probability
  of finding a false positive, especially when using a threshold
  value of Z lower than 3 or when the data are skewed.
• Use methods that are less influenced by outliers like nonparametric
  or robust methods such as the Mann-Whitney-Wilcoxon
  test and the Yuen-Welch test, or researchers may choose to conduct
  bootstrapping (all without removing outliers).

References:
Bakker, M., & Wicherts, J. M. (2014). Outlier removal, sum scores, and the inflation of the type I error rate in independent samples t tests: The power of alternatives and recommendations. Psychological Methods, 19(3), 409-427.
