Algebraic Properties of Beta and Gamma Distributions, and Applications

✍ Scribed by Daniel Dufresne

• Publisher: Elsevier Science
• Year: 1998
• Tongue: English
• Weight: 197 KB
• Volume: 20
• Category: Article
• ISSN: 0196-8858
• DOI: 10.1006/aama.1997.0576

✦ Synopsis

Three new properties are derived. The first one relates to the distribution of UG q G X , where the three variables are independent, G, G X have gamma distributions and U is arbitrary; the second one concerns the case where U has a beta distribution, and the third one the case where 1rU has a beta distribution. These properties generalize the additivity of independent gamma distributions with the same scale parameter. Applications to Markov chains and to the stochastic equa-Ž . Ž . tion X s in law U X q C are given. The last section shows how non-negative relationships may be transformed into new ones on the whole line. In particular, the limit distribution of a time series with random coefficients and Gaussian error terms is found.