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ENH: Compute the first partial moment of Student's t for large nu - #970
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bashtage merged 1 commit intoOct 20, 2026
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The first lower partial moment used gamma((nu + 1) / 2) / gamma(nu / 2), which overflows for nu above about 342, inside the bounds of the distribution, so partial_moment returned 0.0 or NaN for every odd order.
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Thanks. Makes sense to use SciPy's |
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…ounds partial_moment accepts -inf and inf, but the terms z**(n-1) * pdf(z) of the recursions are inf * 0 there, which is nan. Normal and StudentsT returned nan for n >= 2, and, since bashtage#970, StudentsT also for n = 1. The terms are 0 at -inf and inf, so the partial moment is 0 at -inf and the moment at inf.
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- Highlights and new features: NGARCH (bashtage#966), the VaR backtests (bashtage#965), the local block bootstrap (bashtage#967) and bandwidth_method (bashtage#964, and phillips_ouliaris here). - Changes that alter results: the automatic bandwidth entry of bashtage#983 now also describes the bandwidth of the kernels with bounded support, the fractional bandwidths and the Tukey-Parzen constant of bashtage#964, its S&P 500 bandwidths are those of the bandwidth attribute (30.96 and 34.50, where it said the 31.96 and 35.50 of opt_bandwidth), and it links phillips_ouliaris in arch.unitroot.cointegration. The ADF-Z tables of bashtage#972, bashtage#973 and bashtage#980. - Backward-incompatible changes: strings in object data. - Bug fixes: bashtage#954, bashtage#970, bashtage#974, bashtage#975, bashtage#977, bashtage#978, bashtage#982, and the constant data of the Newey-West bandwidth and mackinnonp at -inf and inf. - Maintenance: the CI changes and the version file. - Contributors: galafis, jackiectl2, mkzung and wavebyrd.
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Closes #969
The n=1 term is now
-(nu + z**2) / (nu - 1) * stats.t.pdf(z, nu), so it no longer divides two gamma functions that overflow. The n >= 2 branch already takes its constant from scipy the same way.Checked against an mpmath closed form for nu from 2.06 to 500, orders 0 to 4 and z from -30 to 8: largest relative error 2e-13. The new test covers nu = 342, 400 and 500.