# Help Manual

### Contents

• Introduction
• Project
• Analytics Templates
• Change Templates
• Lean Templates
• Graph Templates
• Projects Templates
• Stats Templates
• Analysis
• Miscellaneous

Sigma Magic Help Version 15

# 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. For discrete distributions, the available distributions are Bernoulli, Binomial, Discrete Uniform, Geometric, Hyper Geometric, Negative Binomial, and Poisson. This analysis will fit the distribution and provide the best estimate for the distribution parameters.

This template 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 template.

### 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 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 deg centigrade).
2
Fit Type: Specify the type of fit. The available options are:
OptionDescription
AutoAutomatically determine the best distribution by fitting different distributions to the data.
IndividualFit a specific individual distribution to the data and estimate the best fit parameters.
3
Select Distributions: Specify the distributions to fit to the data (for the Auto fit case). Note that auto fit is currenly only available for continuous data. The available options 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 to your data. Example: Normal distribution.
4
Single Distribution: Specify the individual distribution to fit to the data (does not apply for the Auto fit case). The list of distributions shown in this dialog box depends on the type of data you have. If your data type is continuous, only continuous distributions are shown. If your data type is discrete, then only discrete distributions are shown.
7
Select Distributions: The checkbox next to each distribution name signifies those distributions
8
Help Button: Click on this button to open the help file for this topic.
9
Cancel Button: Click on this button to cancel all changes to the settings and exit this dialog box.
10
OK Button: Click on this button to save all changes and compute the outputs for this analysis.
Sigma Magic can also be used to fit an individual distribution to your data and provide you with the estimated model parameters. The following screenshot shows an example of the dialog box for this study.
 1 Fit Type: Ensure that you have selected Individual for this study to fit a specific distribution to your data. You can use both the continuous and discrete data for this analysis. 2 Distribution Name: Select the distribution you would like to fit to your data. 3 Distribution Parameters: Note that some distribution parameters can be estimated from the data while others have to be specified. Note that for continuous data type, all the parameters will be estimated. However, for discrete data type, some distribution parameters may have to be provided by the user and the rest will be estimated by the software.

### Data

If you click on the Data button, you will see the following dialog box. 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 to speed up finding the right data to use 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 does not have any 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 important that you not only specify the column name but also the table name. 3 Add or View Data: Click on this button either to add more data into 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 up the Data Editor dialog box where you can import more data into your workbook, or you can 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, then you will need to select only numeric columns. If the code starts with a T, then you can select both numeric and text columns. The numbers to the right of the colon specify the min-max values. For example, if the min-max values are 2-4, then you need to select a minimum of 2 columns of data and a maximum of 4 columns of data 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 select 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 select the data is to double click on the columns in the list of Available Data. Finally, you can also 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: If the right amount of data columns has been specified, the list box header will be displayed in the black color. If sufficient data has not been specified, then the list box header will be displayed in the red color. Note that you can double-click on any of the columns in this box to remove them from the box.

### Charts

If you click on the Charts button, you will see the following dialog box.

### Verify

If you click on the Verify button, the software will perform some checks on the data you have entered. A sample screenshot of the dialog box is shown in the figure below. The objective of this analysis as well as any checks that are performed is listed in this dialog box. For example, the software may check 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, then they are shown as a green-colored checkmark. If the verification checks fail, then they are shown as a red-colored cross. If the verification checks result in a warning, they are shown in the orange color exclamation mark and finally, any checks that are required to be performed by the user are shown as blue info icons.

## Outputs

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

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, for binomial distribution you need to provide the number of trials 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, then no parameters can be estimated for this data set.
• 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 a large number of points, you want to sample within these data and then use that for distribution identification.

## Examples

Following examples can be found in the Examples folder.
• For the data set given in the file, find the best distribution and estimate the distribution parameters (Dist Identification 1.xlsm).