TEST OF FIT FOR THE INVERSE GAUSSIAN AND GAMMA DISTRIBUTIONS UNDER CENSORING

2001 ◽  
Vol 30 (4) ◽  
pp. 757-773
Author(s):  
K. Anaya ◽  
F. O'Reilly
Keyword(s):  
Inverse Gaussian ◽  
Gamma Distributions

scholarly journals Multifractality of products of geometric Ornstein-Uhlenbeck-type processes

2008 ◽  
Vol 40 (4) ◽  
pp. 1129-1156 ◽  
Author(s):  
V. V. Anh ◽  
Nikolai N. Leonenko ◽  
Narn-Rueih Shieh
Keyword(s):  
Dependence Structure ◽  
Inverse Gaussian ◽  
Infinitely Divisible ◽  
Covariance Functions ◽  
Lévy Motion ◽  
Gamma Distributions ◽  
Cumulative Processes ◽  
The Moment ◽  
Normal Inverse Gaussian ◽  
Mean Variance

We investigate the properties of multifractal products of geometric Ornstein-Uhlenbeck (OU) processes driven by Lévy motion. The conditions on the mean, variance, and covariance functions of the resulting cumulative processes are interpreted in terms of the moment generating functions. We consider five cases of infinitely divisible distributions for the background driving Lévy processes, namely, the gamma and variance gamma distributions, the inverse Gaussian and normal inverse Gaussian distributions, and the z-distributions. We establish the corresponding scenarios for the limiting processes, including their Rényi functions and dependence structure.

The Matsumoto–Yor independence property for GIG and Gamma laws, revisited

2002 ◽  
Vol 133 (1) ◽  
pp. 153-161 ◽  
Author(s):  
JACEK WESOŁOWSKI
Keyword(s):  
Functional Equation ◽  
Generalized Inverse ◽  
Independent Interest ◽  
Invariance Property ◽  
Complete Regression ◽  
Inverse Gaussian ◽  
Independence Property ◽  
Gamma Distributions ◽  
The Matrix ◽  
Generalized Inverse Gaussian

Matsumoto and Yor have recently discovered an interesting invariance property of a product of the generalized inverse Gaussian and gamma distributions. In this paper we obtain: (1) a complete regression version of its converse; (2) a converse to the matrix variate Matsumoto–Yor property which extends an earlier result. Of independent interest is a functional equation for matrix valued functions, which has been solved in the course of investigation of the second problem.

scholarly journals Multifractality of products of geometric Ornstein-Uhlenbeck-type processes

2008 ◽  
Vol 40 (04) ◽  
pp. 1129-1156 ◽  
Author(s):  
V. V. Anh ◽  
Nikolai N. Leonenko ◽  
Narn-Rueih Shieh
Keyword(s):  
Dependence Structure ◽  
Inverse Gaussian ◽  
Infinitely Divisible ◽  
Covariance Functions ◽  
Lévy Motion ◽  
Gamma Distributions ◽  
Cumulative Processes ◽  
The Moment ◽  
Normal Inverse Gaussian ◽  
Mean Variance

We investigate the properties of multifractal products of geometric Ornstein-Uhlenbeck (OU) processes driven by Lévy motion. The conditions on the mean, variance, and covariance functions of the resulting cumulative processes are interpreted in terms of the moment generating functions. We consider five cases of infinitely divisible distributions for the background driving Lévy processes, namely, the gamma and variance gamma distributions, the inverse Gaussian and normal inverse Gaussian distributions, and the z-distributions. We establish the corresponding scenarios for the limiting processes, including their Rényi functions and dependence structure.

Remaining useful life estimation: a review on stochastic process-based approaches

2020 ◽  
Vol 14 ◽  
Author(s):  
Dangbo Du ◽  
Jianxun Zhang ◽  
Xiaosheng Si ◽  
Changhua Hu
Keyword(s):  
Stochastic Process ◽  
Health Management ◽  
Remaining Useful Life ◽  
Future Trends ◽  
Prognostics And Health Management ◽  
Inverse Gaussian ◽  
Life Estimation ◽  
Inverse Gaussian Process ◽  
Pros And Cons ◽  
Useful Life

Background: Remaining useful life (RUL) estimation is the central mission to the complex systems’ prognostics and health management. During last decades, numbers of developments and applications of the RUL estimation have proliferated. Objective: As one of the most popular approaches, stochastic process-based approach has been widely used for characterizing the degradation trajectories and estimating RULs. This paper aimed at reviewing the latest methods and patents on this topic. Methods: The review is concentrated on four common stochastic processes for degradation modelling and RUL estimation, i.e., Gamma process, Wiener process, inverse Gaussian process and Markov chain. Results: After a briefly review of these four models, we pointed out the pros and cons of them, as well as the improvement direction of each method. Conclusion: For better implementation, the applications of these four approaches on maintenance and decision-making are systematically introduced. Finally, the possible future trends are concluded tentatively.

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