In the recent series of posts we have discussed estimation of the recovery time distribution from the empirical COVID-19 data (the confirmed cases time series). This was a quite easy task as we know both the confirmed cases time series and the recovered cases time series. In this post we will make an attempt to solve an inverse problem. Namely, I will try to recover the confirmed cases time series from the recovered cases time series.

There are many unsubstantiated claim about election fraud in the recent US presidential elections. Most of these claims provide no proofs or arguments, while there are few which are supposedly scientific. One of the example relies on the Benford's law, which specifies the expected frequency at which we should observe specific first digit of certain number. So if vote counts in polling stations do not follow Benford's law, it should be an indication of wide spread fraud!

Not so fast, as often in science, laws and models are applicable only when certain conditions (assumptions) are satisfied. In case of Benford's law, one main condition is that the original numbers (first digits of which we consider) should span multiple orders of magnitude. Also Benford's law is formulated as a rather general empirical observation. The law is supposedly observed in many naturally occurring data.

Vote counts is obviously an example of naturally occurring data. The issue is that vote counts do not span many order of magnitude. Also vote counts, especially in elections with two competitors, are not related to exponential growth (which is prevalent in many naturally occurring systems), which can actually be a driver for the Benford's law.

Watch the following video by Stand-up Maths for a video discussion on applicability of the Benford's law to the data from the recent presidential election in the US. The video below covers another simple method to check for the election fraud.

In the previous post we have shown that Weibull recovery model works well when trying to reconstruct the recovered cases time series from the confirmed cases time series. In that post we have used random simulation to generate fake recovered cases time series. In this post we will use convolution to get the expected recovered cases time series.

Today we celebrate 10 years since our English "Hello World" post! While it was not the first post on Physics of Risk, (we were writing posts in Lithuanian since 2006), nor it was the first post written in English (a post on Kirman's ants was published on April 11, 2010), it is still an important post, which marks our transition to writing in English.

Fig. 1:Stock image from pixabay.

It is interesting to see if we will survive another 10 years.

In the previous post we have estimated mean recovery time in COVID-19 Lithuanian data set. We have tried to generate fake recovery time series assuming that recovery times are exponentially distributed. We have failed. This time we will assume that recovery times are Weibull distributed.