Award Date

1-1-1997

Degree Type

Thesis

Degree Name

Master of Science (MS)

Department

Mathematics

Number of Pages

51

Abstract

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.

Keywords

Function; Generating; Inversion; Moment; Numerical

Controlled Subject

Mathematics; Finance

File Format

pdf

File Size

1218.56 KB

Degree Grantor

University of Nevada, Las Vegas

Language

English

Permissions

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Identifier

https://doi.org/10.25669/bys7-b05f processed, response: 201


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