Thread: Stochastic Orders

I am really desperate for this simple question:

Assume X and Y are random variables, such that:
X is "stochastically greater" than Y

Then by definition:
E[f(x)] >= E[f(y)] if f(.) is INCREASING

My question is:

What is f(.) is decreasing? Does the operator above change, or what?

Originally Posted by aelwany

I am really desperate for this simple question:

Assume X and Y are random variables, such that:
X is "stochastically greater" than Y

Then by definition:
E[f(x)] >= E[f(y)] if f(.) is INCREASING

My question is:

What is f(.) is decreasing? Does the operator above change, or what?

f is decreasing iff -f is increasing. This should answer your question.

Thank you very much Laurent. I appreciate your quick reply.