Where \ alpha is the shape parameter, or index of stability, \ mu is the location parameter, and " c " is the scale parameter.
2.
The Holtsmark distribution is a special case of a stable distribution with the index of stability or shape parameter \ alpha equal to 3 / 2 and skewness parameter \ beta of zero.
3.
\alpha, which must be greater than 0 and less than or equal to 2, is the shape parameter or index of stability, which determines how heavy the tails are.
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In more general usage, a "'central limit theorem "'is any of a set of i . i . d . random variables with power law tail distributions decreasing as " " ? " " 1 } } where ( and therefore having infinite variance ) will tend to an alpha-stable distribution with stability parameter ( or index of stability ) of as the number of variables grows.
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