J. Marcinkiewicz and A. Zygmund proved in 1936 that, for all functions f points x, the existence of nth Peano derivative f(n)(x) is equivalent to both f(n−1)(x) generalized Riemann $${{\tilde D}_n}f\left(x \right)$$ , based at x,x + h,x 2h,x 22{h,…,x} 2n−1h. For q ≠ 0, ±1, we introduce: two q-analogues n-th Dnf(x) Gaussian derivatives qDnf(x) $$_q{{\bar are h, x+qh, x+q2h,…, x qn−1h x+h,x qh, q...

Importance sampling (IS) and numerical integration methods are usually employed for approximating moments of complicated target distributions. In its basic procedure, the IS methodology randomly draws samples from a proposal distribution weights them accordingly, accounting mismatch between proposal. this work, we present general framework techniques inspired by methodology. The can also be see...