The computation of the probability density and distribution functions for some families of random variables by means of the Wynn-ρ accelerated Post-Widder formula

We propose the suitable use of the Post-Widder inversion formula for Laplace transforms–coupled with the Wynn’s ρ-algorithm for accelerating sequences–in order to evaluate (up to the desired accuracy) the probability density function and the distribution function of a large collection of random variables. The method is illustrated on the Tweedie law and the tempered positive Linnik law. In addition, a further application to some laws arising in the context of Brownian motion is considered. © 2018, © 2018 Taylor & Francis Group, LLC.