Validating random variable generation from inverse transform sampling I'm building a simulator and I have to implement some probability distributions. What is the best (formal) way of validating this implementation? I took a look at KS-tests but it seems to me they are too easy to pass when setting $\alpha = 5\%$, for instance. Actually, it seems counterintuitive that decreasing $\alpha$ makes the test easier to pass, because, in this case, the objective is to actually accept the null hypothesis, not reject it. Also, chi-squared tests don't seem like the right choice because the distributions are continuous. Perhaps I'm missing something in my research, but is there a standard way to validate a (continuous) probability distribution implementation?

Rather than looking for a single (and therefore incomplete or insufficient) statistical test for one specific distribution $F$, one could call the whole collection of (Uniform) randomness tests constructed by the late Georges Marsaglia that he entitled DieHard. They cover several dozens of assessment of randomness. For instance, the corresponding (enlarged) R package is RDieHarder. The first step is to transform the simulated sample $X_1,\ldots,x_n$ by the targetted cdf $F(\cdot)$, assuming it is continuous, since the transformed random variable $F(X_i)$ is $\mathcal U(0,1)$.
