Modeling Samples

Abstract

We will assume the mechanism shown in Fig. 2.1 as the mother of all samples. You may see the contrivance in its center as a spring generating standard random numbers for free which are transmuted into numbers following a given distribution law after having passed through the gears of the mechanism. By default, we assume that the standard numbers are uniform in [0,1] like in this figure. Thus, we have an universal sampling mechanism $\mathcal M^*_X(U,g_\theta)$, and you are ensured that, like from a cornucopia, you may draw any kind of random variable X, provided you may device the gears in order to compute the related $\widetilde F_X^{-1}$ defined in Fact 1.4. Two considerations are in order to remove the wrong idea that we are univocally, hence a priori, describing the world.