Risk Modeling – NYC Wind
I just posted my first Mathematica model today. It demonstrates modeling NYC Wind Speeds. Look for it under the new Model entry under the main menu. It is stored as both a notebook (.nb) and as a computable document (.cdf). To use the CDF, you will need to install the Wolfram Mathematica CDF Player.
I am currently using Mathematica 11.2 and the notebook and CDF are saved in Dropbox.
The workbook reads in the maximum wind speeds from NYC using the WeatherData Mathematica function. Those values are converted from km/hour to mph. From that converted data, Mathematica then fits several different statistical distributions and displays that fit. I chose these distributions because of their various properties, such as positive support including infinite support such as normal or log-normal. I also included the simplest distribution used within ERM, which is the triangular distribution. I also fit the extreme value distribution for modeling extreme winds. However, I find that these distributions don’t seem to get wind speeds in excess of 100mph, which is the certified wind speed protection that is required by NYC skyscrapers.
I also use the Mathematica function FindDistribution to find the best ten distribution to fit the data as well. Here we look at the maximum, mean and the 98% quantiles of these ten distributions and examine the Economic Capital metric. Even though Economic capital doesn’t make sense with a wind speed model, it is a means to determine what wind speed above the average wind speed would occur in a 1 in 50 year event. This is measured by the 98% percentile of a distribution less the mean of a distribution. Since, 98% = 100% – 1/50, the 98% percentile would tell you what the speed would be in a 1 in 50 year event. The excess of this over the mean, would be the excess wind speed above the mean, that you would need to address, if you wanted to cover a 1 in 50 events.
Wind Risk Links
Below are several useful wind risk links: