Median larger than mean in a Weibull distribution in scipy.stats I am going a bit crazy here...
When I plot a Weibull function with shape = 6 and scale = 145 using exponweib.pdf(x, 1, 6, scale=145, loc=1), the results looks like this:

To my (rather limited) statistical knowledge this should be a right skewed PDF and therefore the median smaller than the mean.
However, scipy.stats tells me otherwise:
exponweib.median(1, 6, scale=145) returns 136.4 and exponweib.mean(1, 6, scale=145) returns 134.5. 
I am pretty sure I am overlooking something rather obvious here. Can anybody point me to it, please?
 A: I checked your results against those given by the Meta.Numerics library and got exactly the same values. A Weibull with shape parameter 6.0 has skewness -0.37.
If you look at the graphs of Weibull PDFs on Wikipedia for various shape parameters, you'll see that it's right-skewed for small values of the shape parameter, but left-skewed for large values of the shape parameter. The skewness crosses zero at a shape parameter of about 3.6. If you look at the skewness formula in the same article, you will see that it has terms with mixed signs, so it is certainly possible to get both positive and negative skewness depending on which terms predominate.
Finally, you can think in terms of hazard functions. A Weibull with shape parameter 1 is just an exponential, which has a constant hazard function and is strongly right-skewed (skewness 2). As you increase the shape parameter, you are making the hazard function rising, which is going to more heavily favor low values, even though the right tail still has to extend out to infinity. That must decrease the skewness relative to an exponential, and in fact, for high enough shape parameters, it eventually makes the skewness negative.
