Methods and formulas for goodness-of-fit measures in Parametric Distribution Analysis (Right 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.

Formula

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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