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I need to characterize the mean, CV and skewness of my observed data (it is gamma-like distributed). This data is an artifact (outliers) enriched, so I decide to use robust statistics: median, interquartile range divided to median, and medcouple.

I have two questions:

1) Is it correct and commonly used robust statistics? (The biggest doubt I have about using IQR/median instead of CV).

2) Could you help me with references for my or your robust CV estimator?

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This question is very broad, and there are already many relevant posts on this site. Maybe you could add to your post some plot of your data, and explain us to what use you will put an estimated model? That could help us giving better answers.

First, you say data is sort-of gamma distributed, but with outliers. You could look into robust estimation of the gamma distribution parameters. In R the package robust has function gammaRob for robust estimation of gamma distribution parameters.

Apart from that:

  1. Robust estimation of CV: See A robust (non-parametric) measure like Coefficient of Variation -- IQR/median, or alternative?

  2. Robust estimation of mean: Crash course in robust mean estimation (and search this site)

  3. Robust estimation of skewness, see: Is there such a thing as a trimmed skewness estimator? and the wiki article on L-moments cited below.

  4. Maybe something based on L-moments? Look through https://stats.stackexchange.com/questions/tagged/l-moments and wikipedia.

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