Journal of Statistical Theory and Practice

, Volume 7, Issue 1, pp 133–145 | Cite as

Stable Paretian Versus Student’s t Stock Market Hypothesis

  • Artun Alparslan
  • Anthony Tessitore
  • Nilufer UsmenEmail author


This article investigates the types of probability distributions that can best represent equity returns using a large sample of daily S&P500 index returns. The competing models, Stable Paretian and Pearson families, are compared using Bayesian methods. The evidence against Stable Paretian as a model of S&P500 index returns is overwhelming. The distribution that best fits the data is Pearson Type IV, and Student’s t fits almost as well. One implication is that a Bayesian decision maker should strongly shift beliefs in favor of a Pearson distribution with finite means and variances as a model of daily changes in the S&P500 stock index.


Stable Paretian family Pearson family Student’s t Bayesian estimation 

AMS Subject Classification

62F15 91G10 91G60 


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Copyright information

© Grace Scientific Publishing 2013

Authors and Affiliations

  • Artun Alparslan
    • 1
  • Anthony Tessitore
    • 1
  • Nilufer Usmen
    • 2
    Email author
  1. 1.GramercyGreenwichUSA
  2. 2.Department of Economics and FinanceMontclair State University School of BusinessMontclairUSA

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