Doc

Arcsine Distribution

docs/tutorial:stats:continuous_arcsine

Defined over $x \in [0, 1]$ . To get the definition presented in Johnson, Kotz, and Balakrishnan, substitute $x = \frac{u + 1}{2} .$ i.e. $L = - 1$ and $S = 2.$

M (t) = 1 + k = 1 \sum \infty (r = 0 \prod k - 1 \frac{2 r + 1}{2 r + 2}) \frac{t ^{k}}{k !}

h [X] = lo g (\frac{π}{4}) \approx - 0.24156447527049044468

l_{x} (\cdot) = N lo g π + \frac{N}{2} \overline{lo g x} + \frac{N}{2} \overline{lo g (1 - x)}

References

Norman Johnson, Samuel Kotz, and N. Balakrishnan, Continuous Univariate Distributions, second edition, Volumes I and II, Wiley & Sons, 1994.
"Arcsine Distribution", Wikipedia, https://en.wikipedia.org/wiki/Arcsine_distribution

Implementation: scipy.stats.arcsine