A. V. Skorohod, “On a Theorem Concerning Stable Distributions,” In: Selected Translations in Mathematical Statistics and Probability, Vol. 1, Institute of Mathematical Statistics and American Mathematical Society, Providence, 1961, pp. 169-170.

has been cited by the following article:

• TITLE: Robust Linear Regression Models: Use of a Stable Distribution for the Response Data

  AUTHORS: Jorge A. Achcar, Angela Achcar, Edson Zangiacomi Martinez

  KEYWORDS: Stable Distribution; Bayesian Analysis; Linear Regression Models; MCMC Methods; OpenBugs Software

  JOURNAL NAME: Open Journal of Statistics, Vol.3 No.6, December 31, 2013

  ABSTRACT: In this paper, we study some robustness aspects of linear regression models of the presence of outliers or discordant observations considering the use of stable distributions for the response in place of the usual normality assumption. It is well known that, in general, there is no closed form for the probability density function of stable distributions. However, under a Bayesian approach, the use of a latent or auxiliary random variable gives some simplification to obtain any posterior distribution when related to stable distributions. To show the usefulness of the computational aspects, the methodology is applied to two examples: one is related to a standard linear regression model with an explanatory variable and the other is related to a simulated data set assuming a 23 factorial experiment. Posterior summaries of interest are obtained using MCMC (Markov Chain Monte Carlo) methods and the OpenBugs software.