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## Main Question or Discussion Point

Hi,

I was searching the forum about comparing continuous probability distributions and came across this post back in 2005.

"You could make two variables X(t) = value of the "true" disrtibution (expensive simulation) at point t and Y(t) = value of the alternative dist. (practical simulation) at point t. Then run the regression Y(t) = a + b X(t) for as many t's as you can (or like), then show that the joint hypothesis "(a = 0) AND (b = 1)" is highly statistically significant."

My question is about the last sentence. What would be the best way to check to see if a = 0 and b =1? I know I could count how many times that is exactly true, but what if a = close to 0 and b = close to 1? I would like a way for that to count for some significance as well.

I appreciate any help.

I was searching the forum about comparing continuous probability distributions and came across this post back in 2005.

"You could make two variables X(t) = value of the "true" disrtibution (expensive simulation) at point t and Y(t) = value of the alternative dist. (practical simulation) at point t. Then run the regression Y(t) = a + b X(t) for as many t's as you can (or like), then show that the joint hypothesis "(a = 0) AND (b = 1)" is highly statistically significant."

My question is about the last sentence. What would be the best way to check to see if a = 0 and b =1? I know I could count how many times that is exactly true, but what if a = close to 0 and b = close to 1? I would like a way for that to count for some significance as well.

I appreciate any help.