ما معنى Pseudo-random and counter-based generators, inverse transform sampling؟

A pseudo-random number generator is a deterministic recurrence $s_{k+1} = F(s_k)$, $u_k = G(s_k)$ whose outputs pass statistical tests of independent uniformity; the Mersenne Twister (Matsumoto and Nishimura, 1998) and PCG (O’Neill, 2014; NumPy’s default) are examples. A counter-based generator computes $u = G_k(c)$ directly from a counter $c$ and a key $k$ with a bijection $G_k$, so that any draw can be produced without its predecessors; Philox (Salmon, Moraes, Dror and Shaw, 2011) is one. Inverse transform sampling turns a uniform $U$ into a draw $F^{-1}(U)$ of the distribution function $F$.