Jan

3

I am reading Michael Panik’s Advanced Statistics from an Elementary Point of View, and I would recommend it as a second book on statistics for someone who would like to carry his statistical education a little bit further, and who is not partial to such things as measure theory, partial differential equations, and differential manifolds — topics taught beyond the usual first year advanced calculus class. I find that reading such books keeps my mind active, and leaves me with something tangible after I have read about abysmal subjects such as redistribution, egalitarianism, energy saving, organic foods, and the more stringent regulation of hedge funds to cure the coming depression cited in the papers. It also leaves me with that tangible feeling, especially after coming from a very amateur performance of PDQ Bach where half the show consists of corny anti-Bush jokes, bathroom humor, and slap stick of the kind that kindergarten children respond to.

In the second chapter, Panik discusses how to compare distributions. Let’s start with the quartiles, Q1, Q2, Q3, and Q4, which divide a distribution into four equal parts.

Q1 is the point below which 25% of the observations lie, Q3 - Q1 is a measure of dispersion where the middle 50% lie, etc.. (Q3-Q1)/2 = QD is called the quartile deviation, SK = (Q3 -Q2)/(Q2 -Q1)/ Q3 - Q1 is a measure of skewness with the more positive values being right skewed. QD / (P90 - P10) = K is a measure of kurtosis where p90 is the 90th percentile (which 90% of observations are below).

For a sharp peaked curve of the kind that the dooms-dayists feel we have, K = approximately 0.5, and for a normal curve k = 0.25, and for a flat curve K = 0. It would be interesting to compute the 3 statistics for each day (QD, SK, and K) for the distribution of % changes in a given index like the S&P 500 or Dow Jones. We could then see if there are any predictive properties that are over and above the normal negative serial correlation from day to day, (which great books on behavioral finance still claim is not a real regularity that disproves efficient markets).

What a topsy turvy world.


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