5: Goodness of Fit

5.Goodness of Fit 5.1

• When the maximum likelihood method reduces to , it is relatively easy to judge goodness of fit.

  

  where depend on m theoretical parameters.

• Then the result of minimizing Equation (33) with respect to m theoretical parameters should be distributed according to distribution with n-m degrees of freedom.

• This function is plotted on p. 64 of EDJRS.

• If k is number of degrees of freedom.

  

• and Standard Deviation is .

• Distribution for One Degree of Freedom
• General Distribution
• Characteristic Function
• 5.2Confidence Level
• Typical Confidence Level Distributions
• Real World Confidence Levels
• Error Estimate from Value
• 5.3Bartlett's Function---Overview
• Bartlett's Function for
• 5.4Hypothesis Testing---I
• Hypothesis Testing---II
• Hypothesis Testing---III
• 5.5Student's t Distribution for Hypothesis Testing---I
• Student's t Distribution for Hypothesis Testing---II
• Student's t Distribution for Hypothesis Testing---III
• 5.6Robust Estimation--Motivation--I
• Robust Estimation---Motivation---II
• Robust Estimation---Motivation---III
• Robust Determination of Mean---I
• Robust Determination of Mean---II
• Robust Determination of Mean---III
• Robust Determination of Mean Trimmed Mean
• Likelihood Based Robust Estimation of Means---I
• Likelihood Based Robust Estimation of Means---II
• Particular Robust Estimates for Likelihood---Huber
• Particular Robust Estimates for Likelihood---Andrews
• Comparison of Methods---I
• Comparison of Methods---II