Standardized Residuals Plots

The standardized residuals plot for the Weibull and lognormal distributions can be obtained in ALTA. Each plot type is discussed next.

SR for the Weibull Distribution

Once the parameters have been estimated, the standardized residuals for the Weibull distribution can be calculated by:

Then, under the assumed model, these residuals should look like a sample from an extreme value distribution with a mean of 0. For the Weibull distribution the standardized residuals are plotted on a smallest extreme value probability paper. If the Weibull distribution adequately describes the data, then the standardized residuals should appear to follow a straight line on such a probability plot. Note that when an observation is censored (suspended), the corresponding residual is also censored.

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Fig. 10: Probability plot of standardized residuals for the Weibull distribution.

SR for the Lognormal Distribution

Once the parameters have been estimated using rank regression, the fitted or calculated responses can be calculated by:

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Then, under the assumed model, the standardized residuals should be normally distributed with a mean of 0 and a standard deviation of 1 (~N(0,1)). Consequently, the standardized residuals for the lognormal distribution are commonly displayed on a normal probability plot.

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Fig. 11: Probability plot of standardized residuals for the lognormal distribution.