 # Boost :

From: Deane Yang (deane_yang_at_[hidden])
Date: 2006-07-14 11:13:32

Paul A Bristow wrote:
> |
> | CDFz[mu, sigma](x) -> P
> |
> | becomes
> |
> | CDFz(x, mu, sigma) -> P
> |
> | The "standard" inverse CDF is then
> |
> | CDF'z(p, mu, sigma) -> x
>
> So how to we find out what is considered "standard" - ask you? consult
> Mathemetica's documentation?textbooks..? Is there agreement on standard? I
> suspect so, but

The standard inverse is just the quantile function, period. In other
words, if CDF[parameters..., x] = P, then inverseCDF[parameters..., P] = x.

All other possible inverse functions (where you are solving for one of
the parameters that specify the distribution) are ad hoc.

>
> If this is to be part of C++ Standard, there needs to be a clear
> statisticans standard.

The above is, as far as I know, the standard definition of the
inverseCDF or quantile function.

>
> | And one of the others is:
> |
> | CDF'z(x, mu, p) -> sigma
>
> What John called 'ad hoc'?

Yes. If you are specifying *both* the quantile level *and* the
probability, and solving for some other parameter that specifies the
distribution, then you are in the realm of ad hoc inverse functions,
because different families of distributions (normal versus students t
versus exponential....) have different parameterizations.

>