IBM Business Analytics Proven Practices: Design Measures of Distribution Skewness and Kurtosis in IBM Cognos Report Studio

Product(s): IBM Cognos 10.2.x; Area of Interest: Reporting

This document will have all the steps to dynamically calculate kurtosis and skewness of a distribution (or data set) that report authors can use in Report Studio along with charts as part of descriptive statistics.

Kalyani Raut, Cognos BI Developer, IBM

Kalyani is a Cognos BI developer in the Predictive Maintenance and Quality team (BA). She has worked on Cognos FM modeling and designed various types of Report Studio reports. She has 8 years of experience.



Mohit Sewak, Solution Architect, IBM

Mohit Sewak is a Predictive and Advanced Analytics Solution Architect and SME at IBM, India Software Labs. He holds several patents and publications in his field of expertise and has rich experience helping some of the most valuable clients worldwide with using advanced analytics and BI solutions to make better business strategy, improve operations, and optimally serve their customers. In his current role he is involved in envisioning and implementation of advanced analytics capability into IBM’s Predictive Maintenance and Quality offering. Mohit is academically an MBA and is pursuing MS. He holds several professional certifications like Certified Supply Chain Professional (CSCP), Certified Project Management Professional (PMP), and certified into methodologies and tools like Lean Six Sigma, SPSS, SAS, R, Hadoop, etc.



04 June 2014

Introduction

Purpose of Document

This document will have all the steps to dynamically calculate kurtosis and skewness of a distribution (or data set) that report authors can use in Report Studio along with charts as part of descriptive statistics. Computations which are generally shown in descriptive statistics table such as mean, median, standard deviation, min and max have readily available functions/operators in Report Studio and hence can be created easily. But kurtosis and skewness which were part of the summary descriptive statistics in Cognos Statistics are not available in Report Studio. So if a report author wants to show this information along with others in a descriptive statistics table similar to the ones which were readily available in Cognos Statistics then they are left with Report Studio to work with and design these query calculations manually.

Applicability

This document applies to IBM Cognos BI 10.2 and higher.

Assumptions

Target readers should be an IBM Cognos BI report author and have good knowledge on IBM Cognos Report Studio 10.2.1.1. In addition, this document makes use of the IBM Cognos BI samples, in particular the GO Data Warehouse (analysis) package.


Creating kurtosis and skewness measures

Descriptive statistics quantitatively summarizes the main features of a data set. Measures of distribution, such as kurtosis and skewness, characterize the shape and symmetry of the distribution.

Kurtosis characterizes the relative peakedness or flatness of a distribution. Positive kurtosis indicates a relatively peaked distribution. Negative kurtosis indicates a relatively flat distribution.

Skewness is a measure of the asymmetry of a distribution. A distribution with a significant positive skewness has a long right tail. A distribution with a significant negative skewness has a long left tail.

In this example, we used the Returned Items namespace under the Sales and marketing (analysis) folder of GO Data Warehouse (analysis) package. The Return quantity fact against calendar date is used in the report. The remainder of this document lists the steps to be used for creating kurtosis and skewness calculated data items.

  1. Open IBM Cognos Report Studio and create a new Column Chart report using the GO Date Warehouse (analysis) package.
  2. Drag Date from the following location to the x-axis of the chart (Figure 1),
    [go_data_warehouse].[Sales and Marketing (analysis)].[Returned items].Time].[Time].[Day].[Date]
  3. Add Return quantity from the following location to the Series of the chart (Figure 1),
    [go_data_warehouse].[Sales and Marketing (analysis)].[Returned items].[Returned items].[Return
     quantity]
    Figure 1 - Returned items namespace showing the Return quantity and Date query items
    Figure 1 - Returned items namespace showing the Return quantity and Date query items
  4. From Toolbox tab, add a Data Item to Query1 in Query Explorer for each of the 13 items listed in Table 1.
    Table 1 - The 13 Data Items to add to the Query1 query
    Data Item NameExpression
    Meanaverage([Return quantity] for report)
    SDstandard-deviation-pop ([Return quantity] for report)
    Obs-mean[Return quantity]-[Mean]
    Power(Obs-mean,4)power ([Obs-mean],4)
    Power(Obs-mean,3)power([Obs-mean],3)
    Power(Obs-mean,2)power([Obs-mean],2)
    Avg(Power(Obs-mean,3))average([Power(Obs-mean,3)] for report)
    Avg(Power(Obs-mean,2))average([Power(Obs-mean,2)] for report)
    Power(Avg(Power(Obs-mean,2)),3/2)power([Avg(Power(Obs-mean,2))],3/2)
    Skewness[Avg(Power(Obs-mean,3))]/[Power(Avg(Power(Obs-mean,2)),3/2)]
    Avg(Power(Obs-mean,4))average([Power(Obs-mean,4)] for report)
    Power(SD,4)power([SD],4)
    Kurtosis[Avg(Power(Obs-mean,4))]/[Power(SD,4)]-3
  5. In Page Explorer, go back to Page1. Drag a 2x1 table from the Toolbox under the Column Chart. Then place the Column Chart into the first cell. In the second cell drag a 2x2 table from the Toolbox so that it’s nested inside the first table.
  6. Drag Text Items from the Toolbox to each cell of the first row of the nested table. Give these Text Items the names Skewness and Kurtosis respectively as shown in Figure 2.
  7. Create singletons using the Skewness and Kurtosis Data Items from Query1 in the second row of the nested table (Figure 2).
    Figure 2 – Shows Skewness and Kurtosis singletons
    Figure 2 – Shows Skewness and Kurtosis singletons

    Click to see larger image

    Figure 2 – Shows Skewness and Kurtosis singletons

    Figure 2 – Shows Skewness and Kurtosis singletons
  8. Set the Trendlines property by selecting the Column Chart and from the Properties pane under the Chart Annotations section, click on Trendlines.
  9. In the Trendlines window, click the New button and select Polynomial as shown below in Figure 3. Click OK.
    Figure 3 – Properties pane of chart showing trendline of type polynomial
    Figure 3 – Properties pane of chart showing trendline of type polynomial
  10. When report is executed, skewness and kurtosis values will get calculated based on the data set.
    Figure 4 – Shows report upon execution
    Figure 4 – Shows report upon execution

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