Timeline for Does the density $g(y) \propto (1-y^2)^{(n-3)/2} e^{\delta y} \quad\text{for}\quad |y| \leqslant 1$ have a name?
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| Jul 24 at 20:32 | comment | added | whuber♦ | For integral $n$ the CDF does have a closed form, but it's a linear function of $\exp{\delta t}$ and $\exp{-\delta t}$ with coefficients that are polynomials of degree $n$ in $t.$ (The hypergeometric function hints at that.) | |
| Apr 16, 2022 at 0:34 | history | edited | Ben | CC BY-SA 4.0 |
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| Apr 15, 2022 at 13:37 | comment | added | Graham Bornholt | Thanks @Ben and@JimB. The only link I have to named distributions so far is that the n=3 case can be related to one case from the Von Mises-Fisher Distribution, and I think that is what you have found Ben. The connection with the sample correlation coefficient is interesting also. | |
| Apr 15, 2022 at 4:30 | comment | added | JimB | I wonder if $\tanh ^{-1}(y)$ might be a useful transformation as you describe because with n=5 and δ=0, the resulting density is that of the sample correlation coefficient from a bivariate normal with ρ=0 and sample size 6. | |
| Apr 15, 2022 at 2:54 | history | answered | Ben | CC BY-SA 4.0 |