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GOD JUL

December 23, 2007

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God Jul allihopa!

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The COVID-19 testing delays in Sweden as a prime example of queueing theory

One branch of statistics is Queueing Theory . It is an attempt to predict the behaviour of a system as a function of the inflow and the outflow. As examples you typically have either bank tellers or buffered network routers, but now we have an excellent example in front of us in the Swedish news. One tool in the fight against the COVID-19 pandemic is testing. By tracking who is infected we can better prevent it from spreading to others, but for that to work, we need the test done and the test result returned before the person has already spread the virus. In Sweden we expanded the testing capactity slowly but steadily during May and June and all through this process the waiting time, if you were allowed to get a test, was short. As vacations ended and autumn colds came, that changed. Now people may have to wait for 4 days to get a test done and for another 4 days before the result is returned, despite labs working more efficiently and faster than ever before and returning 50% more ...

A better algorithm for paths with gradients

To code example → This article will present an algorithm, and code, to create the effect in the image below, where a gradient follows along a shape, a "path" in SVG parlance. This is not the first attempt at solving this problem, thus the "better" part of the title, but I found earlier available code to have some very specific flaws, especially with complex paths. By default, SVG provides for two ways to do gradients, linearGradient and radialGradient. As the names imply, the gradient for those either follows a straight line or a circular radius. In particular, there is no way in SVG to have a gradient evolve along a path. Linear Gradient Radial Gradient If you try to apply either gradient to a path, you will see that it is just applied along a line or along a ra...

Finding a beautiful model: The case for Johnson SU in stock market modelling

The world is a confusing place, and the only way we have to make sense of it is to create idealized models of it. In our mind the ball is spherical, the ground is flat, the sky is blue and humans have two arms, two legs, two eyes, and two kidneys. All necessary simplifications because the whole truth is too complicated. An interesting complicated place is the stock market, and how prices move there. If we, using Nobel Laurate Robert Schiller 's data , look at the real total return of the stock market the last 150 years, we get a striking image ( total returns means that it's including dividends, real , means that it compensates for inflation ): Maybe a bit too striking since the exponential growth means that everything before 1950 disappears into the x axis. When studying exponential growth, it's almost always better to look at it with a logarithmic scale , where a doubling looks the same regardless of whether it is 1 to 2, or 1 million to 2 million. Many...

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