# Methods and formulas for goodness-of-fit measures in Distribution ID Plot (Arbitrary Censoring)

## Anderson-Darling statistic

The Anderson-Darling statistic is a measure of how far the plot points fall from the fitted line in a probability plot. The statistic is a weighted squared distance from the plot points to the fitted line with larger weights in the tails of the distribution. Minitab uses an adjusted Anderson-Darling statistic, because the statistic changes when a different plot point method is used.

Minitab provides an Anderson-Darling statistic for the maximum likelihood and least squares estimation methods.

### Notation

TermDescription
nnumber of plotted points
Ai
Bi
Ci
zifitted estimate of the cumulative distribution function for the ith point
Fn(zi)the point plotted for the ith data point
z0equals 0
Fn(z0)equals 0
lnn(z0)equals 0
zn+1

## Pearson correlation coefficient

For least squares estimation, Minitab calculates a Pearson correlation coefficient. If the distribution fits the data well, then the plot points on a probability plot will fall on a straight line. The correlation, usually signified by r (rho), measures the strength of the linear relationship between the X and Y variables on a probability plot.

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