Interpretation of Statistical Preference in Terms of Location Parameters

Abstract

Stochastic orders are methods that allow the comparison of random quantities. One of the most used stochastic orders is stochastic dominance. This method is based on the direct comparison of the cumulative distribution functions of the random variables, and it is characterized by comparing the expectations of the adequate transformation of the variables. Statistical preference is another alternative based on a probabilistic relation that provides preference degrees between the variables. This paper proves that statistical preference is connected to another location parameter different from the expectation: the median. Then, both stochastic orders have different interpretations, in the same way as mean and median are two different location parameters for describing random samples. Nevertheless, we prove that stochastic dominance and statistical preference are connected when the random variables are independent.

Keywords::

• Stochastic dominance
• statistical preference
• location parameter
• expectation
• median
• independent random variables

Acknowledgment

The research reported in this paper has been supported by Project TIN2014-59543-P of the Spanish Ministry of Economy.