(no subject)
In preparing figures for the book, I thought it would be an interesting idea to plot a likelihood ratio, showing how a fat tailed leptokurtic distribution differs from a normal bell-shaped distribution in relative terms. We tend to use leptokurtic distributions to assign extra probability to extreme events, like share market meltdowns and market meltdowns. So I did the maths.
What this graph shows is that, for this particular fat-tailed distribution relative to a normal distribution, a zero standard deviation move is 33% more likely than the reference normal distribution, but a +/- 2 standard deviation move is only 2/3 as likely to occur. Out beyond 3 standard deviations, though, the likelihoods are at least doubled. At least. Basically, we have more chance of either nothing much happening, or everything going completely ballistic.
But I sort of wonder if it's wise to include this graph in the book for some reason. What do you do when mathematical diagrams end up having completely unexpected resemblances to other structural forms in nature? Ignore it and presume maturity on the part of the readership? Um... Be sensitive to the readers and the potential for causing offence, and present the material differently? Maybe try to sample a different section of the function? I could just take the right hand side of the chart, I guess. That's probably the best idea so far.
I still like aardvark.
EDIT: I think we all agree this is more professional and has the same informational content:
What this graph shows is that, for this particular fat-tailed distribution relative to a normal distribution, a zero standard deviation move is 33% more likely than the reference normal distribution, but a +/- 2 standard deviation move is only 2/3 as likely to occur. Out beyond 3 standard deviations, though, the likelihoods are at least doubled. At least. Basically, we have more chance of either nothing much happening, or everything going completely ballistic.
But I sort of wonder if it's wise to include this graph in the book for some reason. What do you do when mathematical diagrams end up having completely unexpected resemblances to other structural forms in nature? Ignore it and presume maturity on the part of the readership? Um... Be sensitive to the readers and the potential for causing offence, and present the material differently? Maybe try to sample a different section of the function? I could just take the right hand side of the chart, I guess. That's probably the best idea so far.
I still like aardvark.
EDIT: I think we all agree this is more professional and has the same informational content: