Hi Wolfgang,
> testing hypotheses (e.g. of a binomial distributed X) and seeking for an unknown
> probability, one comes e.g. to inequatities of the form:
>
> F(50,1/6,k-1) >= 0.95
>
> 'solving' for k one should get 14,15,..
>
In the case of the normal distribution, by definition
quantile_normal(p,m,s)= x such that cdf_normal(x,m,s)=p
that is, the quantile function is the inverse of the distribution. Here
an example:
(%i1) load(distrib)$
(%i2) quantile_normal(0.975,0,1);
(%o2) 1.959963984540054
which is the value needed to construct 95% confidence intervals. Let's
apply now the inverse:
(%i3) cdf_normal(%,0,1);
1.959963984540054
erf(-----------------)
sqrt(2) 1
(%o3) ---------------------- + -
2 2
(%i4) float(%);
(%o4) 0.975
Take into account that some distribution and quantile functions don't
have closed forms and they must be computed numerically, which means
that you can't pass them symbolic parameters.
Thanks for your interest in this package.
--
Mario Rodriguez Riotorto
www.biomates.net