Publication date: 11/10/2021

## Fit Distributions

You can use the options in the Continuous Fit or Discrete Fit submenus to fit a distribution to a continuous variable. When you fit a distribution to a continuous variable, a curve is overlaid on the histogram and a Compare Distributions report and a Fitted Distribution report are added to the report window. A red triangle menu in the Fitted Distribution report contains additional options. See Fit Distribution Options. If a column contains a Distribution column property, the distribution in that column property is fit by default in the Distribution report.

Note: The Life Distribution platform also contains options for distribution fitting that might use different parameterizations and allow for censored observations. See Life Distribution in Reliability and Survival Methods.

### Continuous Fit

The Continuous Fit submenu contains options for fitting continuous distributions. For more information about the parameterization of these distributions, see Continuous Fit Distributions.

Fit Normal

Fits a normal distribution to the data. The normal distribution is often used to model symmetric data with most of the values falling in the middle of the curve.

Fit Cauchy

Fits a Cauchy distribution to the data. The Cauchy distribution has an undefined mean and standard deviation. Although most data do not inherently follow a Cauchy distribution, it can be useful for estimating a robust location and scale for data that contain a large proportion of outliers (up to 50%).

Fit Student’s t

Fits a Student’s t distribution to the data. The Student’s t distribution is a robust option that spans the space between a normal distribution and a Cauchy distribution. As the degrees of freedom in the Student’s t distribution approach infinity, the distribution is equivalent to the normal. When the degrees of freedom in the Student’s t distribution equals 1, the distribution is equivalent to the Cauchy. The Distribution platform estimates the degrees of freedom value.

Fit SHASH

Fits a sinh-arcsinh (SHASH) distribution to the data. The SHASH distribution is similar to Johnson distributions in that it is a transformation to normality, but the SHASH distribution includes the normal distribution as a special case. This distribution can be symmetric or asymmetric.

Fit Exponential

(Available only when all observations are nonnegative.) Fits an exponential distribution to the data. The exponential distribution is right-skewed and is often used to model lifetimes or the time between successive events.

Fit Gamma

(Available only when all observations are positive.) Fits a gamma distribution to the data. The gamma distribution is a flexible distribution for modeling positive values.

Fit Lognormal

(Available only when all observations are positive.) Fits a lognormal distribution to the data. The lognormal distribution is right-skewed and is often used to model lifetimes or the time until an event.

Fit Weibull

(Available only when all observations are positive.) Fits a Weibull distribution to the data. The Weibull distribution is a flexible distribution and is often used to model lifetimes or the time until an event.

Fit Normal 2 Mixture

Fits a mixture of two normal distributions. This flexible distribution is capable of fitting bimodal data.

Fit Normal 3 Mixture

Fits a mixture of three normal distributions. This flexible distribution is capable of fitting multi-modal data.

Fit Smooth Curve

Fits a smooth curve using nonparametric density estimation (Kernel Smoother). Control the amount of smoothing by changing the bandwidth with the slider that appears in the Nonparametric Density report.

Fit Johnson

Fits a Johnson distribution to the data. The most appropriate of the three types of Johnson distribution (Su, Sb, and Sl) is fit and reported. The Johnson family of distributions is useful for its data-fitting capabilities because it supports every possible combination of skewness and kurtosis. Information about selection procedures and parameter estimation for the Johnson distributions can be found in Slifker and Shapiro (1980).

Fit Beta

(Available only when all observations are between 0 and 1.) Fits a beta distribution to the data. The beta distribution is useful for modeling data that are between 0 and 1 (not inclusive) and is often used to model proportions or rates.

Fit All

Fits all available continuous distributions to a variable. The Compare Distributions report contains statistics about each fitted distribution. By default, the best fit distribution is selected and displayed on the histogram. Use the check boxes to show or hide a fit report and overlay curve for the selected distribution. Initially, the Compare Distributions list is sorted by AICc in ascending order.

Tip: You can quickly remove distributions from the Compare Distributions list by double-clicking the name of the distribution in the Distribution column. This action also removes the corresponding Fitted Distribution report.

Enable Legacy Fitters

Shows or hides the Legacy Fitters submenu. Some features of distribution fitting have been updated in JMP 15. This option enables you to use the older features from previous JMP releases that have been retained for compatibility purposes. See Details for the Legacy Distribution Fitters.

### Discrete Fit

The Discrete Fit submenu is available when all of the data values are integers. The Discrete Fit submenu contains options for fitting discrete distributions. For more information about the parameterization of these distributions, see Discrete Fit Distributions.

Fit Poisson

Fits a Poisson distribution to the data. The Poisson distribution is useful for modeling the number of events in a given interval and is often expressed as count data.

Fit Negative Binomial

Fits a negative binomial distribution to the data. The negative binomial distribution is useful for modeling the number of successes before a specified number of failures. The negative binomial distribution is also equivalent to the Gamma Poisson distribution.

Fit ZI Poisson

(Available only when there are values of zero in the data.) Fits a zero-inflated Poisson distribution to the data. The zero-inflated Poisson assumes a greater proportion of the data are zero values than would occur in a standard Poisson distribution.

Fit ZI Negative Binomial

(Available only when there are values of zero in the data.) Fits a zero-inflated negative binomial distribution to the data. The zero-inflated negative binomial assumes a greater proportion of the data are zero values than would occur in a standard negative binomial distribution.

Fit Binomial

Fits a binomial distribution to the data. The binomial distribution is useful for modeling the total number of successes in n independent trials that all have a fixed probability, p, of success. The sample size can be specified as a fixed sample size for all observations, or it can be specified as another column in the data table that contains sample sizes for each row.

Note: When a non-constant sample size is specified, density curves, diagnostic plots, and profilers are not available.

Fit Beta Binomial

Fits a beta binomial distribution to the data. The beta binomial distribution is an overdispersed version of the binomial distribution. It requires a sample size greater than one for each observation. The sample size can be specified as a fixed sample size for all observations, or it can be specified as another column in the data table that contains sample sizes for each row.

Note: When a non-constant sample size is specified, density curves, diagnostic plots, and profilers are not available.

### Fit Distribution Options

Each fitted distribution report has a red triangle menu that contains additional options.

Density Curve

Uses the estimated parameters of the distribution to overlay a density curve on the histogram.

Diagnostic Plots

Contains the following options:

QQ Plot

Shows or hides a quantile-quantile (QQ) plot. This plot shows the relationship between the observations and the quantiles obtained using the estimated parameters.

PP Plot

Shows or hides a percentile-percentile (PP) plot. This plot shows the relationship between the empirical cumulative distribution function (CDF) and the fitted CDF obtained using the estimated parameters.

Profilers

Contains the following options:

Distribution Profiler

Shows or hides a prediction profiler of the cumulative distribution function (CDF).

Quantile Profiler

Shows or hides a prediction profiler of the quantile function.

Save Columns

Contains the following options:

Save Density Formula

Saves a column to the data table that contains the density formula computed using the estimated parameter values.

Save Distribution Formula

Saves a column to the data table that contains the cumulative distribution function (CDF) formula computed using the estimated parameter values.

Save Simulation Formula

Saves a column to the data table that contains a formula that generates simulated values using the estimated parameters. This column can be used in the Simulate utility as a Column to Switch In. See Simulate.

Save Transformed

(Available only for Johnson and SHASH distribution fits.) Saves a column to the data table that contains a transform formula. The formula can be used to transform the analysis column to normality using the fitted distribution.

Goodness of Fit

(Not available for Johnson, Smooth Curve, Normal Mixture, Binomial, or Beta Binomial distributions.) Shows or hides a Goodness-of-Fit Test report that contains a goodness-of-fit test for the fitted distribution.

For continuous fits, the goodness-of-fit test is the Anderson-Darling test. The p-value for the test is simulated using a parametric bootstrap, similar to the procedure described in Section 4.1 of Stephens (1974). For Normal distributions, the Shapiro-Wilk test for normality is also reported when the sample size is less than or equal to 2000 and there are no fixed parameters.

For discrete fits, the goodness-of-fit test is a Pearson chi-squared test.

Fix Parameters

(Not available for Johnson distribution or smooth curve fits.) 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.

Process Capability

(Not available for Cauchy, Student’s t, or discrete distribution fits.) Enables you to create a Process Capability analysis using the fitted distribution, which is a measure of how well process performs with respect to the specification limits. When you select the Process Capability option from a Fitted Distribution red triangle menu, a window appears with the following options:

Enter Spec Limits

Enables you to manually enter specification limits. To use the fitted distribution to calculate specification limits, leave this section blank and use the options under Calculate Quantile Spec Limits Options.

Calculate Quantile Spec Limits Options

Enables you to calculate specification limits based on the fitted distribution. There are two methods available.

In the first method, you enter probabilities associated with the quantiles of the fitted distribution to calculate specification limits.

In the second method, you enter a K-Sigma Multiplier value that is used to calculate specification limits. This method has options for creating two-sided or one-sided limits.

After entering probabilities or a value for sigma multiplier, click Calculate Spec Limits to calculate the specification limits. These limits are entered into the Enter Spec Limits panel. Click OK to accept these limits and generate the Process Capability report.

Process Capability Options

Contains the following options:

The Moving Range Options outline contains options that enable you to select the type of moving range statistic. See Moving Range Options in Quality and Process Methods.

The Nonnormal Distribution Options outline contains options that enable you to select methods used for nonnormal process capability calculations. See Nonnormal Distribution Options in Quality and Process Methods.

For more information about the Process Capability options and report, see Process Capability in Quality and Process Methods.

Note: You can set preferences for many of the options in the Process Capability report in Distribution at File > Preferences > Platforms > Process Capability.

Remove Fit

Removes the distribution fit from the report window.