Hence, the underlying leptokurtic distribution
of key monetary and financial variables seems to be in line with Minsky's financial fragility hypothesis (Minsky, 1982a, b), and Rindleberger's (1988, 2005) history of 'manias and crashes', and it is consistent with the origin and the course of the United States housing market implosion that initiated the 2007-2009 global financial crisis (Orlowski, 2008b).
Stocks with leptokurtic distributions
of returns are conventionally considered to be inherently more risky than stocks with normal pdfs.
The kurtosis coefficient (column 4) varies from 0.81 (implying platykurtic) to 80.54 which reflects a highly leptokurtic distribution
. Thus the underlying distributions do not appear to be normal.
(1996), Engle and Patton (2001), Hansen and Lunde (2005)) provides much empirical regularity associated with the volatility of returns on financial assets such as leptokurtic distributions
, volatility clustering, leverage effects, persistence and asymmetric volatility, among others.
Notable exceptions to this were the original Z-variance test and Fmax test for leptokurtic distributions
The values for kurtosis relate to leptokurtic distributions
, which exhibit fat tails and high peaks with respect to normal distributions.
Item 8, "I have trouble with constipation," and Item 19, "I feel that others would be better off if I were dead," were positively skewed (2.5 and 3.1, respectively) and had unusually leptokurtic distributions
(kurtosis = 6.1 and 10.3, respectively).
1996, Turchin 1998); a species following our population heterogeneity model, which is the weighted sum of normal distributions, would have ex ponentially bounded tails and should not exhibit the unbounded invasion speeds that some other leptokurtic distributions
can generate (Kot et al.
In fact, it is easy to demonstrate that the sample median is more efficient than the sample mean when the data are drawn from leptokurtic distributions
(i.e., distributions with fat tails relative to the norm).