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Publication date: 11/10/2021

Distribution Options

Unless otherwise specified, all Y, Process variables are analyzed using the assumption that they follow a normal distribution. Use the Distribution Options outline to assign other distributions or calculation methods to variables in the Y, Process list and to specify options related to nonnormal calculations.

The available distributions are the Normal, Beta, Exponential, Gamma, Johnson, Lognormal, Mixture of 2 Normals, Mixture of 3 Normals, SHASH, and Weibull distributions. Except for Johnson distributions, maximum likelihood estimation is used to fit distributions. See Johnson Distribution Fit Method.

The Best Fit option determines the best fit among the available distributions and applies this fit.

The Nonparametric option fits a distribution using kernel density estimation.

For more options related to nonnormal fits, see Nonnormal Distribution Options.

Specify a Distribution

1. Select a variable or variables in the Y, Process list.

2. Select a distribution from the Distribution list.

3. Select Set Process Distribution to assign that distribution to the selected variables.

The specified distribution appears in parentheses in the expression “&Dist()” to the right of the variable names in the Y, Process list.

Note: If you select a distribution other than Normal, you cannot assign a Subgroup ID column or a Historical Sigma. These selections are not supported by the methods used to calculate nonnormal capability indices. See Capability Indices for Nonnormal Distributions: Percentile and Z-Score Methods.

Nonnormal Distribution Options

Nonnormal Capability Indices Method

Specifies the method used to compute capability indices for nonnormal distributions. See Capability Indices for Nonnormal Distributions: Percentile and Z-Score Methods.

Johnson Distribution Fit Method

Specifies the method used to find the best-fitting Johnson distribution. Before estimating the parameters, the best-fitting family of distributions is determined from among the Johnson Su, Sb, and Sl families. The procedure described in Slifker and Shapiro (1980) is used to find the best-fitting family.

Quantile Matching

The default method. It is more stable and faster than Maximum Likelihood. Quantile Matching Parameter estimates, assuming the best-fitting family, are obtained using a quantile-matching approach. See Slifker and Shapiro (1980).

Maximum Likelihood

Parameters for the best-fitting family are determined using maximum likelihood.

Distribution Comparison Criterion

(Available when a Best Fit Distribution is selected.) Specify the criterion that you want to use in determining a Best Fit. This criterion also determines the ordering of distributions in the Comparison Details report. See Order by Comparison Criterion.

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