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Sigma Magic Help Version 17

Distribution Identification

Overview

Distribution Identification is used to determine which distribution best fits the data points. For continuous distributions, the analysis that is considered for the curve fit is Beta, Cauchy, Erlang, Extreme Value, Exponential, Gamma, Laplace, Log-Normal, Logistic, Normal, Pareto, Power, Rayleigh, Triangular, Uniform, and Weibull. The available distributions for discrete distributions are Bernoulli, Binomial, Discrete Uniform, Geometric, Hyper Geometric, Negative Binomial, and Poisson. This analysis will fit the distribution and estimate the distribution parameters best.

This tool can be added to your active workbook by clicking on Stats and then selecting Distribution > Distribution Identification.

Inputs

Click on Analysis Setup to open the menu options for this tool.

Setup

A sample screenshot of the setup menu is shown below.
1
Data Type: Specify the data type for this analysis. The available options are:
OptionDescription
DiscreteDiscrete data is like count data that has only a finite set of values (like the number of defects in a product example 20, 30, 43).
ContinuousContinuous data can take any arbitrary value (like the temperature of the room example, 34.53 degrees centigrade).
2
Method: Specify the method to use to estimate the distribution parameters. The available options are:
OptionDescription
Method of MomentsEstimate the distribution parameters by matching the moments. For example, if you match the mean and standard deviation, the data and the fit will have the same mean and standard deviation. This is the default setting as it is robust and provides good estimates for the distribution parameters.
Maximum LikelihoodUsing this method, the distribution parameters are selected that maximize the maximum likelihood estimate of the selected distribution. Note that this method may not have a closed-form solution in all cases and may require some optimization algorithm to estimate the parameters.
3
Select Distributions: Specify the distributions to fit the data. Auto-fit for multiple distributions to identify the best distribution is only available for continuous data. For discrete data, you can only fit one distribution at a time. The available options if you want to select multiple distributions are:
OptionDescription
AllFit all possible distributions to your data.
BoundedFit all bounded distributions (both on the left side and right side) to your data. Example: Uniform distribution.
CustomSpecify the distributions that you would like to consider for determining the best fit.
Partially BoundedFit all distributions that are bounded on one side and unbounded on the other side. Example: Log-Normal distribution.
UnboundedFit all distributions that are unbounded on both the left and the right side of your data. Example: Normal distribution.
If you specify a single distribution, select the individual distribution that fits the data. The list of distributions shown under Available Distributions depends on the type of data you have. If your data type is continuous, only continuous distributions are shown, and if your data type is discrete, only discrete distributions are shown.
4
Goodness of Fit: Specify how you want to evaluate the goodness of fit. The available options are:
OptionDescription
Anderson-DarlingUse the AD values to estimate the best distribution. This is the default setting and focuses more on the distribution's tails.
Chi-SquareUse the Chi-Square values to estimate the best distribution. This method focuses on having a minimum difference between the data and the fit over the entire range.
5
Available Distributions: Lists all the distributions available for fit depending on the data type. If you have continuous data, you can fit about 22 different distributions; if you have discrete data, you can fit about seven different distributions.
6
Selected Distributions: You can drag and drop the distributions to fit into this list box. Note that for continuous data types, you can fit more than one distribution at a time, while for discrete data, you can only fit one distribution at a time. If you have made an incorrect selection and want to remove it from this list, select the item you wish to remove and double-click on it.
7
Help Button: Click on this button to open the help file for this topic.
8
Cancel Button: Click on this button to cancel all changes to the settings and exit this dialog box.
9
OK Button: Click on this button to save all changes and compute the outputs for this analysis.
Sigma Magic can also fit an individual distribution to your data and provide the estimated model parameters. The following screenshot shows an example of the dialog box for this study.
 1 Data Type: Ensure you have selected Discrete for this study to fit a discrete distribution to your data set. 2 Available Distribution: The list of available distributions is shown in this list. You can drag and drop any distribution you are interested in into the right under Selected distributions. 3 Selected Distribution: The distribution you have selected for the fit is shown on the right. Double-click on any item to remove it from this list. Since only one item can be selected, if you try to drop any distribution into this list, it will replace the existing distribution name. 4 Distribution Parameters: Note that some distribution parameters can be estimated from the data while others must be specified. Note that all the parameters will be estimated for continuous data type. However, for discrete data types, some distribution parameters may have to be provided by the user, and the software will estimate the rest.

Data

You will see the following dialog box if you click the Data button. Here, you can specify the data required for this analysis.
 1 Search Data: The available data displays all the columns of data that are available for analysis. You can use the search bar to filter this list and speed up the search for the right data for analysis. Enter a few characters in the search field, and the software will filter and display the filtered data in the Available Data box. 2 Available Data: The available data box contains the list of data available for analysis. If your workbook has no data in tabular format, this box will display "No Data Found." The information displayed in this box includes the row number, whether the data is Numeric (N) or Text (T), and the name of the column variable. Note that the software displays data from all the tables in the current workbook. Even though data within the same table have unique column names, columns across different tables can have similar names. Hence, it is crucial that you not only specify the column name but also the table name. 3 Add or View Data: Click on this button to add more data to your workbook for analysis or to view more details about the data listed in the available data box. When you click on this button, it opens the Data Editor dialog box, where you can import more data into your workbook. You can also switch from the list view to a table view to see the individual data values for each column. 4 Required Data: The code for the required data specifies what data can be specified for that box. An example code is N: 2-4. If the code starts with an N, you must select only numeric columns. You can choose numeric and text columns if the code begins with a T. The numbers to the right of the colon specify the min-max values. For example, if the min-max values are 2-4, you must select a minimum of 2 columns of data and a maximum of 4 columns in this box. If the minimum value is 0, then no data is required to be specified for this box. 5 Select Button: Click on this button to select the data for analysis. Any data you choose for the analysis is moved to the right. To select a column, click on the columns in the Available Databox to highlight them and then click on the Select Button. A second method to choose the data is to double-click on the columns in the list of Available Data. Finally, you can drag and drop the columns you are interested in by holding down the select columns using your left mouse key and dragging and dropping them in one of the boxes on the right. 6 Selected Data: The list box header will be displayed in black if the right number of data columns is specified. If sufficient data is not specified, the list box header will be displayed in red. Note that you can double-click on any of the columns in this box to remove them from the box. 6a Analysis Variable: You will need to specify the variable for which you want to identify the best distribution. This is a required field. 6b By Variable: If your data contains groups and you want to analyze the entire data set as one group, then you can leave this field blank. However, specify a column for the By Variable if you want to analyze the data by groups. The analysis variable will be split into groups depending on the By Variable's value, and each data group will be analyzed separately. 7 View Selection: Click on this button to view the data specified for this analysis. The data can be viewed in a tabular format or a graphical summary.

Charts

You will see the following dialog box if you click the Charts button.

Verify

If you click the Verify button, the software will perform some checks on the data you entered. A sample screenshot of the dialog box is shown in the figure below. The software checks if you have correctly specified the input options and entered the required data on the worksheet. The results of the analysis checks are listed on the right. If the checks are passed, they are shown as green checkmarks. If the verification checks fail, they are shown as a red cross. If the verification checks result in a warning, they are shown in the orange exclamation mark, and finally, any checks that are required to be performed by the user are shown as blue info icons.
 1 Item: The left-hand side shows the major tabs and the items checked within each section 2 Status: The right-hand side shows the status of the checks. 3 Overall Status: The overall status of all the checks for the given analysis is shown here. The overall status check shows a green thumps-up sign if everything is okay and a red thumps-down sign if any checks have not passed. Note that you cannot proceed with generating analysis results for some analyses if the overall status is not okay.

Outputs

Click on Compute Outputs to update the output calculations. A sample screenshot of the worksheet is shown below. For each distribution to fit the data, Sigma Magic will calculate the best possible values for the parameters and then report the Chi-Square and P-values for the fit. The distribution with the smallest chi-square value (or the largest P-value) is reported as the best-fit distribution. The distribution parameters of the selected distribution are also reported.

The software also allows you to estimate parameters for discrete distributions. If you were to estimate discrete distribution parameters, note that for some distributions, you may need to provide other parameters. For example, you must provide the number of trials for the binomial distribution, and the software will estimate the probability value. An example screenshot of distribution parameter identification for the discrete case is shown below.

Notes

Here are a few pointers regarding this analysis:
• If the analysis cannot calculate a valid parameter for the distribution, then the value is reported as a "*." For example, exponential distribution requires the data points to be positive. If negative values are entered, no parameters for this data set can be estimated.
• Note that distribution identification algorithms will be too sensitive and not report any specific distribution if you have too many data points. If you have many points, you want to sample within these data and then use that for distribution identification.

Examples

The following examples are in the Examples folder.
• For the data set in the file, find the best distribution and estimate the distribution parameters (Dist Identification 1.xlsx).