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Document the exact trimmed L-moments of t(2) #352

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jorenham opened this issue Nov 20, 2024 · 0 comments
Open

Document the exact trimmed L-moments of t(2) #352

jorenham opened this issue Nov 20, 2024 · 0 comments
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documentation Improvements or additions to documentation

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@jorenham
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jorenham commented Nov 20, 2024

The L-scale in the general case:

$$\large \lambda_{2}^{(s, t)} = \sqrt{\pi / 2}\ L(t + \frac 1 2,\ t + 1)$$

where L is the analytical continuation of the Lah number (i.e. written in terms of gamma functions).

For the symmetric case:

$$\large \tau_{2k}^{(t, t)} = \frac{4^{k+t}}{k} \frac{ B(k + t + \frac 1 2,\ -\frac 1 2) B(1 + t,\ 2 + t) }{ B(k + t + \frac 3 2,\ \frac 1 2 - k) B(2k + t,\ \frac 3 2 - k) }$$

source: me

@jorenham jorenham added the documentation Improvements or additions to documentation label Nov 20, 2024
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