Tests of Fit for Exponentiality based on the Empirical Laplace Transform

Statistics ◽  
2002 ◽  
Vol 36 (2) ◽  
pp. 147-161 ◽  
Author(s):  
Norbert Henze ◽  
Simos G. Meintanis
Keyword(s):  
Laplace Transform ◽  
Empirical Laplace Transform ◽  
Tests Of Fit

scholarly journals Empirical Laplace transform and approximation of compound distributions

1990 ◽  
Vol 27 (1) ◽  
pp. 88-101 ◽  
Author(s):  
Sándor Csörgő ◽  
Jef L. Teugels
Keyword(s):  
Laplace Transform ◽  
Asymptotic Behaviour ◽  
Random Variables ◽  
Compound Distributions ◽  
Empirical Laplace Transform ◽  
Image Position

Let be i.i.d. non-negative random variables with d.f. F and Laplace transform L. Let N be integer valued and independent of In many applications one knows that for y → ∞ and a function φ where in turn τ is the solution of an equation On the basis of a sample of size n we derive an estimator τ n for τ by solving ψ (τ n, Ln(τ n), L′n(τ n), · ··) = 0 where Ln is the empirical version of L. This estimator is then used to derive the asymptotic behaviour of φ (y, τ n, Ln(τ n), L′n(τ n), · ··). We include five examples, some of which are taken from insurance mathematics.

scholarly journals Empirical Laplace transform and approximation of compound distributions

1990 ◽  
Vol 27 (01) ◽  
pp. 88-101 ◽  
Author(s):  
Sándor Csörgő ◽  
Jef L. Teugels
Keyword(s):  
Laplace Transform ◽  
Asymptotic Behaviour ◽  
Random Variables ◽  
Compound Distributions ◽  
Empirical Laplace Transform ◽  
Image Position

Letbe i.i.d. non-negative random variables with d.f.Fand Laplace transformL.LetNbe integer valued and independent ofIn many applications one knows that fory→ ∞ and a functionφwhere in turnτis the solution of an equationOn the basis of a sample of sizenwe derive an estimatorτnfor τ by solvingψ(τn, Ln(τn),L′n(τn), · ··) = 0 whereLnis the empirical version ofL.This estimator is then used to derive the asymptotic behaviour ofφ(y, τn, Ln(τn),L′n(τn), · ··). We include five examples, some of which are taken from insurance mathematics.

New class of exponentiality tests based on U-empirical Laplace transform

2016 ◽  
Vol 57 (4) ◽  
pp. 977-990 ◽  
Author(s):  
Bojana Milošević ◽  
Marko Obradović
Keyword(s):  
Laplace Transform ◽  
New Class ◽  
Empirical Laplace Transform

The extinction time of a general birth and death process with catastrophes

1986 ◽  
Vol 23 (04) ◽  
pp. 851-858 ◽  
Author(s):  
P. J. Brockwell
Keyword(s):  
Laplace Transform ◽  
Size Distribution ◽  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
Death Process ◽  
Extinction Time ◽  
Birth And Death Process ◽  
Different Types ◽  
The Laplace Transform ◽  
Necessary And Sufficient

The Laplace transform of the extinction time is determined for a general birth and death process with arbitrary catastrophe rate and catastrophe size distribution. It is assumed only that the birth rates satisfyλ0= 0,λj> 0 for eachj> 0, and. Necessary and sufficient conditions for certain extinction of the population are derived. The results are applied to the linear birth and death process (λj=jλ, µj=jμ) with catastrophes of several different types.

Sign in / Sign up

Export Citation Format

Share Document