Extreme Value Analysis

Cross Sectional Extreme Value Analysis

On March 20, Juan-Juan and I start tracking the development of the novel coronavirus in the Netherlands. On this page we provide a daily update of the cross-sectional analysis of the infected rates over Dutch municipalities. Read the description of our current and historical data sets here.

Our Method

Each day, we use the cross-sectional data of the infection rates over about 355 Dutch municipalities.

We select a set of the most infected municipalities and compare:

We report the daily and historical statistics:

  • Extreme Value Index. The higher index is, the larger heterogeneity among the most infected cities.
  • High quantiles at level 99.9%, 99.5% and 99%. The quantiles are estimated by the maximum likelihood method.
  • Fitted probability density function for the exceedances, for an expert/automatic choice of number of the most infected municipalities used in tail estimation.

Daily Statistics (update around 2:30 pm)

The number k = number of the most infected municipalities used in tail estimation
Infection rate = reported COVID-19 patients per 100,000 residents
  • Extreme value index today:

    EVI Today

  • High quantiles today:

    High quantiles Today

  • Fitted probability density function today:

    pdf Today

Historical Statistics (as of 10 March)

There were too little observations before 10 March for effective estimation.
  • Extreme value indexes: more results here

    EVI time series available soon

  • High quantiles: more results here

    High quantiles time series available soon

  • Fitted probability density functions: more results here

Update history

  • March 23: We have fixed a bug in the code, and made slight corrections to our statistics. There was one city missing in the tail estimation. We have added it back.
  • March 23: we are adding the moment estimates of high quantiles to our daily and historical statistics. The moment estimates tend to be more stable over the choice of k during the recent period.

Some references