I need help with the following problem
I have a pdf of: f(s|k)=k*s^(k-1) where k is a constanct between 0<k<1 and s is between 0≤s≤1.
I am trying to take random draws from this distribution, ( i.e. I am looking for the inverse of the cdf of this function). I know that this is not a proper pdf, so does it need to be transformed first? What I am looking for, in case of a standard normal distribution, it would be the normsinv() function in excel.
Why does this need to be normalized exactly? It looks like a valid pdf to me.
This pdf is not "odd" at all; it is the pdf of a Beta(k, 1). The inverse cdf is given by betainv in excel, although you can invert this special case in closed form with no hassle.