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I'd like to test how well my data can be modeled by an Exponentially modified Gaussian distribution (Wikipedia) or Normal-exponential-gamma (NEG) Distribution. However, the parameter estimation (which involves Skewness) is not very robust when there are outliers in the data set.

I've good experiences with Median based parameter estimation on this data set (see the related question Estimating parameters of a normal distribution: median instead of mean? ).

Do you know a Median-based or similarly robust parameter estimation for the ExGaussian / NEG distributions? I've already tried trimming my data set, the results were clearly better afterwards. Yet, this obviously introduces a bias, that I would need to correct somehow.

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    $\begingroup$ If you have decided on a parametric family to model your data, why have you decided against maximum likelihood? $\endgroup$
    – AdamO
    Commented Mar 9, 2013 at 16:58
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    $\begingroup$ Because it is not pure. It's really dirty data. $\endgroup$
    – Erich Schubert
    Commented Mar 11, 2013 at 9:21
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    $\begingroup$ Then use a non-parametric approach. $\endgroup$
    – AdamO
    Commented Mar 11, 2013 at 19:19

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If it seems like most of the outliers are to the far right you could decide on a threshold including most of the datapoints to the left and censor all values to the right of that threshold. It would be akin to trimming but without introducing a bias. I don't know how you would run such an analysis in a classical statistics framework but it is "pretty easy" using Bayesian statistics

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