Use the Continuous or Discrete Fit options to fit a distribution to a continuous or discrete variable.
Use the Continuous Fit options to fit the following distributions to a continuous variable.
 • The Weibull, Weibull with threshold, and Extreme Value distributions often provide a good model for estimating the length of life, especially for mechanical devices and in biology.
 • The Gamma distribution is bound by zero and has a flexible shape.
 • The Beta distribution is useful for modeling the behavior of random variables that are constrained to fall in the interval 0,1. For example, proportions always fall between 0 and 1.
 • 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.
 • The Smooth Curve distribution... A smooth curve is fit 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 formed by summing the normal densities of the kernel standard deviation located at each data point.
 • The Johnson Su, Johnson Sb, and Johnson Sl Distributions are useful for its data-fitting capabilities because it supports every possible combination of skewness and kurtosis.
 • The Generalized Log (Glog) distribution is useful for fitting data that are rarely normally distributed and often have non-constant variance, like biological assay data.
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.
Related Information
 • Statistical Details for Continuous Fit Distributions
 • Statistical Details for Fitted Quantiles
 • Statistical Details for Fit Distribution Options
 • Poisson
 • Binomial
 • Gamma Poisson
 • Beta Binomial
Related Information
 • Statistical Details for Discrete Fit Distributions
 • Statistical Details for Fitted Quantiles
 • Statistical Details for Fit Distribution Options
 Diagnostic Plot Density Curve Uses the estimated parameters of the distribution to overlay a density curve on the histogram. Goodness of Fit Fix Parameters Enables you to fix parameters and re-estimate the non-fixed parameters. An Adequacy LR (likelihood ratio) Test report also appears, which tests your new parameters to determine whether they fit the data. Quantiles Returns the un-scaled and un-centered quantiles for the specific lower probability values that you specify. Set Spec Limits for K Sigma Use this option when you do not know the specification limits for a process and you want to use its distribution as a guideline for setting specification limits. Spec Limits Save Fitted Quantiles Save Density Formula Creates a new column in the current data table that contains fitted values that have been computed by the density formula. The density formula uses the estimated parameter values. Save Spec Limits Save Transformed Creates a new column and saves a formula. The formula can transform the column to normality using the fitted distribution. This option is available only when one of the Johnson distributions or the Glog distribution is fit. Remove Fit Removes the distribution fit from the report window.
The Diagnostic Plot option creates a quantile or a probability plot. Depending on the fitted distribution, the plot is one of four formats.
 • Weibull with threshold
 • Gamma
 • Beta
 • Poisson
 • GammaPoisson
 • Binomial
 • BetaBinomial
 • Normal
 • Normal Mixtures
 • Exponential
 • Weibull
 • LogNormal
 • Extreme Value
 • Johnson Sl
 • Johnson Sb
 • Johnson Su
 • Glog
Descriptions of the Diagnostic Plot Options describes the options in the red triangle menu next to Diagnostic Plot.
 Rotate Reverses the x- and y-axes. Confidence Limits 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)). Line of Fit Draws the straight diagonal reference line. If a variable fits the selected distribution, the values fall approximately on the reference line. Median Reference Line Draws a horizontal line at the median of the response.
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.
 • For Normal distributions, the Shapiro-Wilk test for normality is reported when the sample size is less than or equal to 2000, and the KSL test is computed for samples that are greater than 2000.
Related Information
 • Statistical Details for Fit Distribution Options
The Spec Limits option launches a window requesting specification limits and target, and then computes generalizations of the standard capability indices. This is done using the fact 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.
Related Information
 • Statistical Details for Fit Distribution Options