This function gives a reliable approximation to the mode of a stable
distribution with location, dispersion, skewness and tail thickness
specified by the parameters
tail must be in (1,2).
vector of (real) location parameters.
vector of (positive) dispersion parameters.
vector of skewness parameters (in [-1,1]).
vector of parameters (in [1,2]) related to the tail thickness.
loc is a location parameter in the same way as the mean in the normal
distribution: it can take any real value.
disp is a dispersion parameter in the same way as the standard
deviation in the normal distribution: it can take any positive value.
skew is a skewness parameter: it can take any value in (-1,1).
The distribution is right-skewed, symmetric and left-skewed when
is negative, null or positive respectively.
tail is a tail parameter (often named the characteristic exponent):
it can take any value in (0,2) (with
yielding the Cauchy and the normal distributions respectively when symmetry
The simplest empirical formula found to give a satisfactory approximation to
the mode for values of
tail in (1,2) is
a = 1.7665114+1.8417675*tail-2.2954390*tail^2+0.4666749*tail^3
b = -0.003142967+632.4715*tail*exp(-7.106035*tail)
A list of size 3 giving the mode, a and b.
Philippe Lambert (Catholic University of Louvain, Belgium, firstname.lastname@example.org) and Jim Lindsey.
Lambert, P. and Lindsey, J.K. (1999) Analysing financial returns using regression models based on non-symmetric stable distributions. Applied Statistics, 48, 409-424.
stable for more details on the stable
stablereg to fit generalized linear models for the
stable distribution parameters.
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