Hi Vitaliy,

this is really nice. I had noticed before that FindDistribution suggests different distributions in different places. Here is an example for the UK.

citiesUK = CountryData["UnitedKingdom", "LargestCities"];
data = {#, #["Coordinates"], 
     FindDistribution[
      Select[QuantityMagnitude[
        WeatherData[#, "WindSpeed", {{2004, 1, 1}, Date[], "Day"}][
         "Values"]], NumberQ]]} & /@ citiesUK;
Plot[PDF[#, x] & /@ 
  DeleteCases[data[[All, -1]], _FindDistribution], {x, 0, 50}, 
 AxesLabel -> {"Windspeed", "Probability"}]

It is relatively easy to see what distribution are found with which frequency:

Tally[Head /@ (DeleteCases[data[[All, -1]], _FindDistribution])]
(*{{MixtureDistribution, 15}, {ExtremeValueDistribution, 61}, {GammaDistribution, 20}, {InverseGaussianDistribution, 1}, {WeibullDistribution, 1}, {MaxwellDistribution, 1}}*)

Or

BarChart[Apply[Labeled, Reverse[Reverse@SortBy[{{MixtureDistribution, 15}, {ExtremeValueDistribution, 61}, {GammaDistribution, 20}, {InverseGaussianDistribution, 1}, {WeibullDistribution, 1}, {MaxwellDistribution, 1}}, Last],2], {1}]]

I'd like to study the MixtureDistributions in more detail and read out the constituent parts:

If[Head[#] === MixtureDistribution, Head /@ #[[2]], Head[#]] & /@ DeleteCases[data[[All, -1]], _FindDistribution]

I can tally that now:

Reverse@SortBy[Tally[If[Head[#] === MixtureDistribution, Head /@ #[[2]], Head[#]] & /@ DeleteCases[data[[All, -1]], _FindDistribution]],Last]

BarChart[Apply[Labeled, 
  Reverse[{Rotate[#[[1]], Pi/2], #[[2]]} & /@ 
    Reverse@SortBy[
      Tally[If[Head[#] === MixtureDistribution, Head /@ #[[2]], 
          Head[#]] & /@ 
        DeleteCases[data[[All, -1]], _FindDistribution]], Last], 2], {1}]]

gives

We can now attach values to the different distributions:

rules = MapThread[
  Rule, {Reverse@
    SortBy[Tally[
       If[Head[#] === MixtureDistribution, Head /@ #[[2]], 
          Head[#]] & /@ 
        DeleteCases[data[[All, -1]], _FindDistribution]], Last][[All, 
      1]], Range[
    Length[Reverse@
      SortBy[Tally[
        If[Head[#] === MixtureDistribution, Head /@ #[[2]], 
           Head[#]] & /@ 
         DeleteCases[data[[All, -1]], _FindDistribution]], Last]]]}]

and then plot

GeoRegionValuePlot[#[[1]] -> #[[2]] & /@ 
  Transpose[{Delete[citiesUK, 12], 
    If[Head[#] === MixtureDistribution, Head /@ #[[2]], Head[#]] & /@ 
      DeleteCases[data[[All, -1]], _FindDistribution] /. rules}], 
 GeoRange -> Entity["Country", "UnitedKingdom"], 
 PlotRange -> {-0.5, 11, 0.5}, ColorFunction -> ColorData["Rainbow"]]

These are too few cities to make any general statement, but there might be a pattern to it, i.e. there are three green dots close to Liverpool an Manchester.

I am trying to do this for Europe now, but there are

citiesEurope = Flatten[CountryData[#, "LargestCities"] & /@ EntityList[EntityClass["Country", "Europe"]]];
citiesEurope // Length

3844 cities, so it takes a bit longer.

Cheers,

M.

Interesting, but I can't duplicate your answer on my version 10.4:

In[59]:= mags = QuantityMagnitude[windBOSTON["Values"]];
dis = FindDistribution[mags, 2]

Out[60]= {ExtremeValueDistribution[12.6967, 5.66123], 
 MixtureDistribution[{0.680313, 
   0.319687}, {NormalDistribution[13.118, 4.54959], 
   GammaDistribution[7.80677, 2.78237]}]}

or

In[65]:= mags = QuantityMagnitude[windBOSTON["Values"]];
dis = FindDistribution[mags]

Out[66]= ExtremeValueDistribution[12.6967, 5.66123]

on the same data.

I actually was wondering whether the mixture distribution is a consequence of different weather patterns. Like here in Boston we typically have either warm weather coming out the S to SW or the jet stream dipping down from the W to NW. If so, then one distribution would be more prevalent in the winter and another in the summer.

This is amazing idea, @Marco, it makes more sense now. Thanks for sharing! I find it curious, that the Weibull distribution, a popular model for wind, is quite rare and never enters MixtureDistribution. Perhaps because it works better for hourly/ten-minute wind speeds sampling, or at least this is what I understood.