StableDistribution[type, , , , ]
represents the stable distribution with index of stability , skewness parameter , location parameter , and scale parameter .
- A linear combination of independent identically distributed stable random variables is also stable.
- A stable distribution is defined in terms of its characteristic function , which satisfies a functional equation where for any and there exist and such that . The general solution to the functional equation has four parameters.
- StableDistribution allows 0<≤2, , to be any real number, and to be any positive real number.
- CharacteristicFunction[StableDistribution[0, , ...], t] is continuous in and given by .
- CharacteristicFunction[StableDistribution[1, , ...], t] is discontinuous in and given by .
- StableDistribution is equivalent to StableDistribution[1, , 0, 0, 1].
- StableDistribution[, ] is equivalent to StableDistribution[1, , , 0, 1].
- StableDistribution[, , , ] is equivalent to StableDistribution[1, , , , ].
- StableDistribution can be used with such functions as Mean, CDF, and RandomVariate.
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