Abstract
The generalized inverse Gaussian distribution converges in law to the inverse gamma or the gamma distribution under certain conditions on the parameters. It is the same for the Kummer’s distribution to the gamma or beta distribution. We provide explicit upper bounds for the total variation distance between such generalized inverse Gaussian distribution and its gamma or inverse gamma limit laws, on the one hand, and between Kummer’s distribution and its gamma or beta limit laws on the other hand
Highlights
The generalized inverse Gaussian distribution with parameters p ∈ R, a > 0, b > 0 has density g (x) = (a/b)p/2 √ x p e
In [1], the authors have established the rate of convergence of the GIG distribution to the gamma distribution by Stein’s method
In order to compare the rate of convergence obtained via Stein’s method with the rate obtained by using another distance, the authors have established an explicit upper bound of the total variation distance between the GIG random variable and the gamma random variable, which is of order n−1/4 for the case p = 12
Summary
The generalized inverse Gaussian (hereafter GIG) distribution with parameters p ∈ R, a > 0, b > 0 has density g. In [1], the authors have established the rate of convergence of the GIG distribution to the gamma distribution by Stein’s method. In order to compare the rate of convergence obtained via Stein’s method with the rate obtained by using another distance, the authors have established an explicit upper bound of the total variation distance between the GIG random variable and the gamma random variable, which is of order n−1/4 for the case p = 12. We generalize this result by providing the order of the rate of convergence in total variation of the GIG distribution to the gamma distribution for all p = k + 12 , k ∈ N.
Sign-in/Register to view highlights & summary Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
