Characterization of inverse-Gaussian and gamma distributions through their length-biased distributions

1989 ◽  
Vol 38 (5) ◽  
pp. 610-611 ◽  
Author(s):  
R. Khattree
Keyword(s):  
Inverse Gaussian ◽  
Gamma Distributions

On a characterization of gamma distributions via exponential mixtures

1980 ◽  
Vol 17 (02) ◽  
pp. 574-576
Author(s):  
Manish C. Bhattacharjee
Keyword(s):  
General Result ◽  
Residual Life ◽  
Infinite Divisibility ◽  
Mean Residual Life ◽  
Gamma Distributions ◽  
Mixing Distributions

A new and simpler proof of Morrison's result that within exponential mixtures only IFR gamma mixing produces linearly increasing mean residual life functions is given. A parallel and new characterization of the DFR gamma laws follows as a consequence. The method of proof used suggests a general result on the infinite divisibility of the mixing distributions in exponential mixtures.

On a characterization of gamma distributions via exponential mixtures

1980 ◽  
Vol 17 (2) ◽  
pp. 574-576 ◽  
Author(s):  
Manish C. Bhattacharjee
Keyword(s):  
General Result ◽  
Residual Life ◽  
Infinite Divisibility ◽  
Mean Residual Life ◽  
Gamma Distributions ◽  
Mixing Distributions

A new and simpler proof of Morrison's result that within exponential mixtures only IFR gamma mixing produces linearly increasing mean residual life functions is given. A parallel and new characterization of the DFR gamma laws follows as a consequence. The method of proof used suggests a general result on the infinite divisibility of the mixing distributions in exponential mixtures.

scholarly journals Lévy processes time-changed by the first-exit time of the inverse Gaussian subordinator

Filomat ◽  
2018 ◽  
Vol 32 (7) ◽  
pp. 2545-2552
Author(s):  
Farouk Mselmi
Keyword(s):  
Lévy Processes ◽  
Exponential Family ◽  
Exit Time ◽  
Levy Processes ◽  
Variance Function ◽  
Inverse Gaussian ◽  
Natural Exponential Family ◽  
First Exit Time

This paper deals with a characterization of the first-exit time of the inverse Gaussian subordinator in terms of natural exponential family. This leads us to characterize, by means its variance function, the class of L?vy processes time-changed by the first-exit time of the inverse Gaussian subordinator.

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.

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