Comparing Continuous Probability Distributions: Finding Significance

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SUMMARY

This discussion focuses on comparing continuous probability distributions using regression analysis. The method involves defining two variables, X(t) for the true distribution and Y(t) for the alternative distribution, and running the regression Y(t) = a + b X(t). The key question raised is how to assess the significance of the coefficients a and b, particularly when they are close to 0 and 1, respectively. A two-tailed hypothesis test is suggested as an effective approach to evaluate the significance of these coefficients.

PREREQUISITES
  • Understanding of regression analysis, specifically linear regression models.
  • Familiarity with hypothesis testing, particularly two-tailed tests.
  • Knowledge of continuous probability distributions and their properties.
  • Experience with statistical software or programming languages for simulation, such as R or Python.
NEXT STEPS
  • Research the implementation of two-tailed hypothesis tests in statistical software like R or Python.
  • Explore advanced regression techniques, including generalized linear models (GLMs).
  • Study the properties and applications of continuous probability distributions in statistical analysis.
  • Learn about simulation methods for validating statistical models and hypotheses.
USEFUL FOR

Statisticians, data analysts, researchers in quantitative fields, and anyone involved in comparing continuous probability distributions and conducting regression analysis.

jjstuart79
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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.
 
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I think I found the answer. A two-tailed hypothesis test should work.
 

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