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.