Truncated and Censored Samples from the Inverse Gaussian and the Gamma Distributions

1991 ◽  
pp. 106-127
Keyword(s):  
Inverse Gaussian ◽  
Censored Samples ◽  
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.

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