In this article, we investigate and compare a number of real inversion formulas for the Laplace transform. The focus is on the accuracy and applicability of the formulas for numerical inversion. In this contribution, we study the performance of the formulas for measures concentrated on a positive half-line to continue with measures on an arbitrary half-line. As our trial measure concentrated on a positive half-line, we take the broad Gamma probability distribution family.
Masol, V., & Teugels, J. L. (2010). Numerical accuracy of real inversion formulas for the Laplace transform. Journal of Computational and Applied Mathematics, 233(10), 2521-2533. https://doi.org/10.1016/j.cam.2009.10.033