Stochastic Dominance Without Tears

37 Pages Posted: 2 Feb 2021 Last revised: 10 Mar 2021

See all articles by Hrishikesh D. Vinod

Hrishikesh D. Vinod

Fordham University - Department of Economics

Date Written: January 26, 2021


When does an entire income distribution f(x2) dominate f(x1)? When can we comprehensively say that f(x2) is ``richer'' than f(x1)? Anderson (1996) proposed a nonparametric quantification for pair-wise welfare-ordering of two countries by their entire income distributions. His algorithm readily computes index values for stochastic dominance of orders 1 to 4, denoted as SD1 to SD4. This paper fills a gap in the literature by providing a simple ranking of n densities by suggesting two new SD-type algorithms, both avoiding pair-wise comparisons. The first new algorithm is exact because it replaces Anderson's trapezoidal approximations subject to truncation errors by exact areas under step-functions defined by empirical cumulative distribution functions, ECDF(xj). Our second new SD-type algorithm uses four orders of differencing of time series data. We use monthly return data on Apple, Microsoft, and Google stocks over the latest 14 years to illustrate. We provide intuitive derivations and include 95% bootstrap confidence intervals for inference on estimated SD-type indexes

Keywords: portfolio choice, poverty ranking, cumulative density, bootstrap, step-function

JEL Classification: C14, C58, G11

Suggested Citation

Vinod, Hrishikesh D., Stochastic Dominance Without Tears (January 26, 2021). Available at SSRN: or

Hrishikesh D. Vinod (Contact Author)

Fordham University - Department of Economics ( email )

Dealy Hall
Bronx, NY 10458
United States
718-817-4065 (Phone)
718-817-3518 (Fax)

Do you have a job opening that you would like to promote on SSRN?

Paper statistics

Abstract Views
PlumX Metrics