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Alpha Distribution

docs/tutorial:stats:continuous_alpha

One shape parameter $α > 0$ (parameter $β$ in DATAPLOT is a scale-parameter). The support for the standard form is $x > 0$ .

M (t) = \frac{1}{Φ ( a ) 2 π} \int_{0}^{\infty} \frac{e ^{x t}}{x ^{2}} exp (- \frac{1}{2} (α - \frac{1}{x})^{2}) d x

The raw moment $E [X^{r}]$ exists if and only if $r < 1$ .

l_{x} (α) = N lo g [Φ (α) 2 π] + 2 N \overline{lo g x} + \frac{N}{2} α^{2} - α \overline{x^{- 1}} + \frac{1}{2} \overline{x^{- 2}}

Implementation: scipy.stats.alpha