Master of Science (MS)
Number of Pages
The main purpose of this thesis is to apply an algorithm for the numerical inversion of the Laplace transform that recovers the probability density function (PDF) of a sum of nonnegative continuous random variables. The Laplace transform is used in many disciplines. For example, in actuarial sciences, a common application is to study the distribution of the sum of nonnegative independent random variables. Because it is a popular method, numerical techniques have been developed to invert the Laplace transform. In the discrete case, by using a moment generating function (MGF) of a sum of independent discrete variables, the distribution can be analytically determined. In the continuous case, if the MGF fails to determine the distribution of a sum of nonnegative continuous independent variables analytically, then the PDF of the sum will be recovered by numerically inverting the Laplace transform.
Function; Generating; Inversion; Moment; Numerical
University of Nevada, Las Vegas
https://doi.org/10.25669/bys7-b05f processed, response: 201
Tsang, Andy M, "On numerical inversion of the moment generating function" (1997). UNLV Retrospective Theses & Dissertations. 3306.