What does the Excel function TINV have to do with the T iCDF

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What does the Excel function TINV have to do with the T iCDF? William T. Shaw … formula for the quantiles of the Cauchy distribution, is rather worrying. …

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What does the Excel function TINV have to do with the T iCDF?
William T. Shaw
April 6, 2006
Abstract
This note is an on-line supplement to the paper New Methods for Managing “Student’s” T
Distribution and deals with the function TINV implemented in Microsoft Excel. TINV is not
the iCDF or quantile function, but can be remapped to supply the iCDF/quantile function.
Even then it produces wrong answers if you supply a non-integer for the degrees of freedom,
and has accuracy problems in the tails.
1 Microsoft’s implementation: TINV in Excel/VB
This implementation is particularly depressing as offers more than one way of returning complete
nonsense if you approach its use from a financial engineering perspective, where you expect TINV to
be, as its name suggests, the iCDF. The problem is that Microsoft have done things very confusingly
in that TINV (u, n) does not return what you think it should do, but have implemented a version
of the inverse that, in my view, confuses (a) the one- and two-tailed distributions, (b) the CDF
with the complementary CDF. This has created incredible confusion - do a search on TINV…