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The common approach for estimating the parameters of a normal distribution is to use the mean and the sample standard deviation / variance.

However, if there are some outliers, the median and the median deviation from the median should be much more robust, right?

On some data sets I tried, the normal distribution estimated by $\mathcal{N}(\text{median}(x), \text{median}|x - \text{median}(x)|)$ seems to produce a much better fit than the classic $\mathcal{N}(\hat\mu, \hat\sigma)$ using mean and RMS deviation.

Is there any reason to not use the median if you assume there are some outliers in the data set? Do you know some reference for this approach? A quick search on Google didn't find me useful results that discuss the benefits of using medians here (but obviously, "normal distribution parameter estimation median" is not a very specific set of search terms).

The median deviation, is it biased? Should I multiply it with $\frac{n-1}{n}$ to reduce bias?

Do you know similar robust parameter estimation approaches for other distributions such as Gamma distribution?

The common approach for estimating the parameters of a normal distribution is to use the mean and the sample standard deviation / variance.

However, if there are some outliers, the median and the median deviation from the median should be much more robust, right?

On some data sets I tried, the normal distribution estimated by $\mathcal{N}(\text{median}(x), \text{median}|x - \text{median}(x)|)$ seems to produce a much better fit than the classic $\mathcal{N}(\hat\mu, \hat\sigma)$ using mean and RMS deviation.

Is there any reason to not use the median if you assume there are some outliers in the data set? Do you know some reference for this approach? A quick search on Google didn't find me useful results that discuss the benefits of using medians here (but obviously, "normal distribution parameter estimation median" is not a very specific set of search terms).

The median deviation, is it biased? Should I multiply it with $\frac{n-1}{n}$ to reduce bias?

Do you know similar robust parameter estimation approaches for other distributions such as Gamma distribution or the Exponentially modified Gaussian distribution (which needs Skewness in parameter estimation, and outliers really mess up this value)?

The common approach for estimating the parameters of a normal distribution is to use the mean and the sample standard deviation / variance.

However, if the data is not pure but there are some outliers, the median and the median deviation from the median should be much more robust, right?

On some data sets I tried, the normal distribution estimated by $\mathcal{N}(\text{median}(x), \text{median}|x - \text{median}(x)|)$ seems to produce a much better fit than the classic $\mathcal{N}(\hat\mu, \hat\sigma)$ using mean and RMS deviation.

Is there any reason to not use the median if you assume there are some outliers in the data set? Do you know some reference for this approach? A quick search on Google didn't find me useful results that discuss the benefits of using medians here (but obviously, "normal distribution parameter estimation median" is not a very specific set of search terms).

The median deviation, is it biased? Should I multiply it with $\frac{n-1}{n}$ to reduce bias?

Do you know similar robust parameter estimation approaches for other distributions such as Gamma distribution?

The common approach for estimating the parameters of a normal distribution is to use the mean and the sample standard deviation / variance.

However, if there are some outliers, the median and the median deviation from the median should be much more robust, right?

On some data sets I tried, the normal distribution estimated by $\mathcal{N}(\text{median}(x), \text{median}|x - \text{median}(x)|)$ seems to produce a much better fit than the classic $\mathcal{N}(\hat\mu, \hat\sigma)$ using mean and RMS deviation.

Is there any reason to not use the median if you assume there are some outliers in the data set? Do you know some reference for this approach? A quick search on Google didn't find me useful results that discuss the benefits of using medians here (but obviously, "normal distribution parameter estimation median" is not a very specific set of search terms).

The median deviation, is it biased? Should I multiply it with $\frac{n-1}{n}$ to reduce bias?

Do you know similar robust parameter estimation approaches for other distributions such as Gamma distribution?

The common approach for estimating the parameters of a normal distribution is to use the mean and the sample standard deviation / variance.

However, if the data is not pure but there are some outliers, the median and the median deviation from the median should be much more robust, right?

On some data sets I tried, the normal distribution estimated by $\mathcal{N}(\text{median}(X), \text{median}(X - \text{median}(X))$ seems to produce a much better fit than the classic $\mathcal{N}(\hat\mu, \hat\sigma)$ using mean and RMS deviation.

Is there any reason to not use the median if you assume there are some outliers in the data set? Do you know some reference for this approach? A quick search on Google didn't find me useful results that discuss the benefits of using medians here (but obviously, "normal distribution parameter estimation median" is not a very specific set of search terms).

The median deviation, is it biased? Should I multiply it with $\frac{n-1}{n}$ to reduce bias?

Do you know similar robust parameter estimation approaches for other distributions such as Gamma distribution?

The common approach for estimating the parameters of a normal distribution is to use the mean and the sample standard deviation / variance.

However, if the data is not pure but there are some outliers, the median and the median deviation from the median should be much more robust, right?

On some data sets I tried, the normal distribution estimated by $\mathcal{N}(\text{median}(x), \text{median}|x - \text{median}(x)|)$ seems to produce a much better fit than the classic $\mathcal{N}(\hat\mu, \hat\sigma)$ using mean and RMS deviation.

Is there any reason to not use the median if you assume there are some outliers in the data set? Do you know some reference for this approach? A quick search on Google didn't find me useful results that discuss the benefits of using medians here (but obviously, "normal distribution parameter estimation median" is not a very specific set of search terms).

The median deviation, is it biased? Should I multiply it with $\frac{n-1}{n}$ to reduce bias?

Do you know similar robust parameter estimation approaches for other distributions such as Gamma distribution?