
New consistent exponentiality tests based on Vempirical Laplace transforms with comparison of efficiencies
We present new consistent goodnessoffit tests for exponential distribu...
read it

Formalization of Lerch's Theorem using HOL Light
The Laplace transform is an algebraic method that is widely used for ana...
read it

Characterizations of the Cauchy distribution associated with integral transforms
We give two new simple characterizations of the Cauchy distribution by u...
read it

A new stochastic order based on discrete Laplace transform and some ordering results of the order statistics
This paper aims to study a new stochastic order based upon discrete Lapl...
read it

Note on approximating the Laplace transform of a Gaussian on a complex disk
In this short note we study how well a Gaussian distribution can be appr...
read it

Revisiting integral functionals of geometric Brownian motion
In this paper we revisit the integral functional of geometric Brownian m...
read it

On the Bernsteinvon Mises theorem for the Dirichlet process
We establish that Laplace transforms of the posterior Dirichlet process ...
read it
An Identity for Two Integral Transforms Applied to the Uniqueness of a Distribution via its LaplaceStieltjes Transform
It is well known that the LaplaceStieltjes transform of a nonnegative random variable (or random vector) uniquely determines its distribution function. We extend this uniqueness theorem by using the MuntzSzasz Theorem and the identity for the LaplaceStieltjes and the LaplaceCarson transforms of a distribution function. The latter appears for the first time to the best of our knowledge. In particular, if X and Y are two nonnegative random variables with joint distribution H, then H can be characterized by a suitable set of countably many values of its bivariate LaplaceStieltjes transform. The general highdimensional case is also investigated. Besides, Lerch's uniqueness theorem for conventional Laplace transforms is extended as well. The identity can be used to simplify the calculation of LaplaceStieltjes transforms when the underlying distributions have singular parts. Finally, some examples are given to illustrate the characterization results via the uniqueness theorem.
READ FULL TEXT
Comments
There are no comments yet.