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> Lewis Lehe is a PhD student in Transportation Engineering at UC Berkeley, and Victor Powell is a freelance developer/teacher.js. Is this a typo, or is teacher.js a cute way of saying JavaScript teacher?
I did not quite get the example with the bets. It is not clear what kind of problem the fat tails bring compared to normal as long as the distribution is symmetrical. There is a term for dealing with actual distributions that differ from the one you put as basis in your theory. http://en.wikipedia.org/wiki/Robust_statistics Regression analysis and particulary ANOVA are sensitive to http://en.wikipedia.org/wiki/Hetero…
This is great, but I have a slight complaint. Sliding the kurtosis indicator changes the left distribution, which makes sense. However, it also changes the appearance of the right, normal distribution, which is misleading. Normal distributions have [EDIT: constant] kurtosis. I realize that the appearance is changing because the scale is changing so that the max is always pegged. However, it might be less confusing if…
Normal distributions have excess kurtosis equal to zero.
> Lewis Lehe is a PhD student in Transportation Engineering at UC Berkeley, and Victor Powell is a freelance developer/teacher.js. Is this a typo, or is teacher.js a cute way of saying JavaScript teacher?
I worked with an exponential distribution before at work. At first, it seemed like we could model them like gaussian because the part of the data we were interested in was "close enough" to a gaussian. We already wrote code that worked for our other data that was gaussian. As it turns out, I was wrong. The thing that can't be easily seen in pictures is that exponential distributions move differently than gaussian dis…
Also, it is important to note that Gaussian is symmetric about its mean, whereas an exponential distribution takes values between 0 and infinity.
Any chance you feel like sharing the d3 code? Would love to see how this was done.
Nice use of d3 that really adds value. I'll use this as an example next time I do time series training at work. Could I ask what you've used to make the animation repeat? From a quick search I noticed you aren't using setInterval() or d3.timer(). Are you just calling redraw as quickly as the CPU runs the code or am I missing something?
.transition()
.duration(dur)
.ease("linear")
.attr("transform", "translate(" + x2(-1) + ",0)")
.each('end', plot1Anim);
Actually, in practice, it's generally difficult to know with much accuracy what a distribution is. Then, for the OP, in practice it's much more difficult to know much about the tails or when they are fat or not or if fat how fat.
The OP wants to claim that the normal distribution applies to heights of people. I can believe that this is only roughly true!
Actually, the usual way we come to a normal distribution is from the central limit theorem (CLT); in practice we want something like the mechanism of the CLT to apply.
When do we get the CLT? Sure: If for some positive integer n our random variable Y is the sum, divided by the square root of n, of n independent, identically distributed (i.i.d.) samples of some distribution with, say, a mean and a finite variance.
If n is 12, then can start to entertain normality if don't want accuracy in the tails. If want high accuracy in the tails of the normal distribution from the CLT, then I'd recommend some careful work and otherwise not trust the accuracy.
A place where have a better shot at getting accuracy in a tail is the exponential distribution. The leading case is: Suppose we have a Geiger counter that goes "click" when it detects a radioactive decay. If the click rate is low so that the chances of two or more decays giving only one click are low, and real random variable T is the time until the next click, then under usual situations in practice T will have quite accurately exponential distribution.
More generally, the stochastic process of such clicks is a Poisson process and an example of an arrival process. Well with weak assumptions, for positive integer n, the sum of n independent arrival processes approaches a Poisson process as n approaches infinity. This result is the renewal theorem with a proof in W. Feller's volume II.
An example of a use of the renewal theorem is arrivals at a Web site. So, for each person on the planet there is an arrival process for that person at that site. If assume that the people are independent, then the Web site sees the sum of those arrivals and should see, over intervals of time much shorter than one day, a good approximation to a Poisson process.
So, that's some 'applied probability' where we might work with tails.
Mostly in applied probability, just f'get about accuracy in the tails!
Nice use of d3 that really adds value. I'll use this as an example next time I do time series training at work. Could I ask what you've used to make the animation repeat? From a quick search I noticed you aren't using setInterval() or d3.timer(). Are you just calling redraw as quickly as the CPU runs the code or am I missing something?
.transition() .duration(dur) .ease("linear") .attr("transform", "translate(" + x2(-1) + ",0)") .each('end', plot1Anim); the thing gets called when the transition ends.