How to use RMSE to evaluate a different type of fitted distributions?

Original question: If I fitted data to different types of distribution, how could I calculate the RMSE to decide which one is the best!! I just have one data so how I can find the difference between the true value and the predicted value??

The RMSE index or other efficiency criteria is not a good(or doable) index for distribution fitting. I think you should check the Kolmogorov Smirnov test, Anderson Darling test, and Chi-square test. You can review the below pages:

  1. Which statistical methods should be used to test the distribution of a small or large sample?
  2. Ranking the best fit of statistical distributions
  3. Anderson-Darling Test
  4. Kolmogorov-Smirnov Test
Name: Mohammed