Probability Density Functions defined on R+ can be successfully modeled with the help of "second kind statistics". This new approach, proposed at Eusipco2000, is based on Mellin transform instead of Fourier transform so that classical probability density functions defined on R+ can be identified with the help of "second kind moments" and "second kind cumulants", the analytic expressions of which are oversimple. In this article, we propose to analyse $alpha$-stable positive distributions. Indeed we know that classical moments of such distributions are generally not defined. As it is possible to derive their "second kind moments" and their "second kind cumulants", the estimation of the parameters of such laws is avalaible with the help of very simple expressions.