Probability density function
![]() Symmetric α-stable distributions with unit scale factor; α=1.5 (blue line) represents the Holtsmark distribution |
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Cumulative distribution function
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Parameters |
c ∈ (0, ∞) — scale parameter |
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Support | x ∈ R |
expressible in terms of hypergeometric functions; see text | |
Mean | μ |
Median | μ |
Mode | μ |
Variance | infinite |
Skewness | undefined |
Ex. kurtosis | undefined |
MGF | undefined |
CF |
c ∈ (0, ∞) — scale parameter
The (one-dimensional) Holtsmark distribution is a continuous probability distribution. The Holtsmark distribution is a special case of a stable distribution with the index of stability or shape parameter equal to 3/2 and skewness parameter of zero. Since equals zero, the distribution is symmetric, and thus an example of a symmetric alpha-stable distribution. The Holtsmark distribution is one of the few examples of a stable distribution for which a closed form expression of the probability density function is known. However, its probability density function is not expressible in terms of elementary functions; rather, the probability density function is expressed in terms of hypergeometric functions.