A curve is overlaid on the histogram, and a Parameter Estimates report is added to the report window. A red triangle menu contains additional options. See Fit Distribution Options.
Note: The Life Distribution platform also contains options for distribution fitting that might use different parameterizations and allow for censoring. See Life Distribution in the Reliability and Survival Methods book.
Use the Continuous Fit options to fit the following distributions to a continuous variable.
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The Normal Mixtures distribution fits a mixture of normal distributions. This flexible distribution is capable of fitting multi-modal data. You can also fit two or more distributions by selecting the Normal 2 Mixture, Normal 3 Mixture, or Other options.
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The Smooth Curve distribution fits a smooth curve using nonparametric density estimation (kernel density estimation). The smooth curve is overlaid on the histogram and a slider appears beneath the plot. Control the amount of smoothing by changing the kernel standard deviation with the slider. The initial Kernel Std estimate is calculated from the standard deviation of the data.
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The All option fits all applicable continuous distributions to a variable. The Compare Distributions report contains statistics about each fitted distribution. Use the check boxes to show or hide a fit report and overlay curve for the selected distribution. By default, the best fit distribution is selected.
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Usually, specification limits are derived using engineering considerations. If there are no engineering considerations, and if the data represents a trusted benchmark (well behaved process), then quantiles from a fitted distribution are often used to help set specification limits. See Fit Distribution Options.
Computes generalizations of the standard capability indices, based on the specification limits and target you specify. See Spec Limits.
The Diagnostic Plot option creates a quantile or a probability plot. Depending on the fitted distribution, the plot is in one of the following four formats.
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Draws Lilliefors 95% confidence limits for the Normal Quantile plot, and 95% equal precision bands with a = 0.001 and b = 0.99 for all other quantile plots (Meeker and Escobar 1998).
The Goodness of Fit option computes the goodness of fit test for the fitted distribution. The goodness of fit tests are not Chi-square tests, but are EDF (Empirical Distribution Function) tests. EDF tests offer advantages over the Chi-square tests, including improved power and invariance with respect to histogram midpoints.
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For discrete distributions that have sample sizes less than or equal to 30, the Goodness of Fit test is formed using two one-sided exact Kolmogorov tests combined to form a near-exact test. See Conover (1972). For sample sizes greater than 30, a Pearson Chi-squared goodness of fit test is performed.
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The Spec Limits option opens a window that enables you to enter specification limits and a target. Then generalizations of the standard capability indices are computed. Note that for the normal distribution, 3σ is both the distance from the lower 0.135 percentile to median (or mean) and the distance from the median (or mean) to the upper 99.865 percentile. These percentiles are estimated from the fitted distribution, and the appropriate percentile-to-median distances are substituted for 3σ in the standard formulas.