I have two sets of deterministic numbers, collected in the two

[PAHV]

I have two sets of deterministic numbers, collected in the two vectors: x=[x(1),...,x(n)] and y=[y(1),...,y(n)]. My (determinstic) theory says that x(i)=y(i) for all i=1,...,n. But instead, I want to assume that the numbers x and y are stochastic. If we let f(.) be a pdf, does this mean that I can test a stochastic version of my theory by setting up a hypothesis test H0: f(x)=f(y) vs. H1: Not H0? That is, is it true that x=y <=> f(x)=f(y) if f is a pdf?

 

[Stephen Tashi]

I want to assume that the numbers x and y are stochastic. If we let f(.) be a pdf

To do a hypothesis test, you must assume enough information in the hypothesis H0 to be able to compute the probability that the observed data happened. Your statements that "x and y are stochastic" and that we let "f(.) be a pdf" are not sufficient to describe a specific probability model for the data. Think of trying to write a stochastic simulation for the data. What you have said isn't sufficient information to give to a programmer who is supposed to write the simulation. Can you describe how you would simulate the data in a computer program?