A Laplace transform method for order statistics from nonidentical random variables and its application in Phase-type distribution

2011 ◽  
Vol 81 (8) ◽  
pp. 1143-1149 ◽  
Author(s):  
Yousry H. Abdelkader
Keyword(s):  
Laplace Transform ◽  
Order Statistics ◽  
Random Variables ◽  
Phase Type Distribution ◽  
Laplace Transform Method ◽  
Transform Method ◽  
Type Distribution ◽  
Phase Type

scholarly journals A generalized class of correlated run shock models

2018 ◽  
Vol 6 (1) ◽  
pp. 131-138 ◽  
Author(s):  
Femin Yalcin ◽  
Serkan Eryilmaz ◽  
Ali Riza Bozbulut
Keyword(s):  
Stopping Time ◽  
Random Variables ◽  
Random Variable ◽  
Phase Type Distribution ◽  
Type Distribution ◽  
Shock Models ◽  
Phase Type ◽  
Over Time

AbstractIn this paper, a generalized class of run shock models associated with a bivariate sequence {(Xi, Yi)}i≥1 of correlated random variables is defined and studied. For a system that is subject to shocks of random magnitudes X1, X2, ... over time, let the random variables Y1, Y2, ... denote times between arrivals of successive shocks. The lifetime of the system under this class is defined through a compound random variable T = ∑Nt=1 Yt , where N is a stopping time for the sequence {Xi}i≤1 and represents the number of shocks that causes failure of the system. Another random variable of interest is the maximum shock size up to N, i.e. M = max {Xi, 1≤i≤ N}. Distributions of T and M are investigated when N has a phase-type distribution.

On the Upcrossing and Downcrossing Probabilities of a Dual Risk Model With Phase-Type Gains

2010 ◽  
Vol 40 (1) ◽  
pp. 281-306 ◽  
Author(s):  
Andrew C.Y. Ng
Keyword(s):  
Laplace Transform ◽  
Risk Model ◽  
Phase Type Distribution ◽  
Explicit Formulas ◽  
Type Distribution ◽  
Time Of Ruin ◽  
Dual Risk Model ◽  
Phase Type ◽  
The Laplace Transform ◽  
The Time Of Ruin

AbstractIn this paper, we consider the dual of the classical Cramér-Lundberg model when gains follow a phase-type distribution. By using the property of phase-type distribution, two pairs of upcrossing and downcrossing barrier probabilities are derived. Explicit formulas for the expected total discounted dividends until ruin and the Laplace transform of the time of ruin under a variety of dividend strategies can then be obtained without the use of Laplace transforms.

Bounds for Stopping Times with Application to the Approximation of Distribution Functions

1994 ◽  
Vol 8 (1) ◽  
pp. 21-31
Author(s):  
Rhonda Richter ◽  
J. George Shanthikumar
Keyword(s):  
Stochastic Systems ◽  
Sufficient Conditions ◽  
Random Variables ◽  
Distribution Functions ◽  
Poisson Processes ◽  
Stopping Times ◽  
Arbitrary Distribution ◽  
Phase Type Distribution ◽  
Type Distribution ◽  
Phase Type

We consider stopping times associated with sequences of non-negative random variables and Poisson processes. With sufficient conditions on the dependence property between the sequences of non-negative random variables (or the Poisson processes) and the stopping times, we develop easily computable stochastic bounds for the stopping times. We use these bounds to develop approximations within the class of generalized phase-type distribution functions for arbitrary distribution functions. The computational tractability of generalized phase-type distribution functions facilitate the computational analysis of complex stochastic systems using these approximate distribution functions. Applications of these approximations to renewal processes are illustrated.

scholarly journals Analytical solution to local fractional Landau-Ginzburg-Higgs equation on fractal media

2021 ◽  
Vol 25 (6 Part B) ◽  
pp. 4449-4455
Author(s):  
Shu-Xian Deng ◽  
Xin-Xin Ge
Keyword(s):  
Analytical Solution ◽  
Laplace Transform ◽  
Present Article ◽  
Iteration Method ◽  
Variational Iteration Method ◽  
Laplace Transform Method ◽  
Transform Method ◽  
Variational Iteration ◽  
Fractal Media

The main objective of the present article is to introduce a new analytical solution of the local fractional Landau-Ginzburg-Higgs equation on fractal media by means of the local fractional variational iteration transform method, which is coupling of the variational iteration method and Yang-Laplace transform method.

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