 Part 1. Introduction to MM4XL
 Part 2. MM4XL Tools
 1. Strategic Tools
 BCG Matrix
 Brand Mapping
 Brand Switch
 Decision Tree
 Forecast Manager
 McKinsey Matrix
 Profile Manager
 Quality Manager
 Risk Analyst
 Risk Analyst Expert in a Few Minutes
 Introduction to Decision Analysis
 Introducing Risk Analyst with an example
 1. How to run Risk Analyst
 2. Simulation Never heard of it
 3. Examples
 4. Functions
 1. Property Functions
 2. Utility Functions
 3. Distribution Functions
 mmBETA (Scale, Shape)
 mmBETAGEN (Scale, Shape, [Optional: Lower], [Optional: Upper])
 mmBINOMIAL (Trials, Successes)
 mmCHI2 (Degrees)
 mmDISCRETE (InputRange, Probabilities)
 mmERF (Mean)
 mmERLANG (Scale, Shape)
 mmEXPON (Mean)
 mmEXTVAL (ModalValue, StDeviation)
 mmGAMMA (Scale, Shape)
 mmGAUSSINV (Mean, Scale)
 mmGEO (Trials)
 mmHYPERGEO (Sample, Defects, BatchSize)
 mmINTUNI (Lower, Upper)
 mmLOGISTIC (Mean, StDeviation)
 mmLOGNORMAL (Mean, StDeviation)
 mmNEGBIN (Failures, Successes)
 mmNORMAL (Mean, StDeviation)
 mmPARETO (Location, ModalValue)
 mmPARETO2 (Location, ModalValue)
 mmPERT (Lower, ModalValue, Upper)
 mmPOISSON (Mean)
 mmRANDBETWEEN (Lower, Upper)
 mmRAYLEIGH (ModalValue)
 mmSTUDENT (Degrees)
 mmTRI (Lower, ModalValue, Upper)
 mmUNIFORM (Lower, Upper)
 mmWEIBULL (Life, Shape)
 Probability functions
 Technicalities
 Sources
 2. Analytical Tools
 Business Formulas
 mmBASS, Bass Diffusion Model
 mmBEI, Brand Equity Index
 mmBEP, BreakEven Point
 mmBEPR, BreakEven Point with Fixed Rate of Return
 mmBUYRATE, Purchase Rate Model
 mmCAGR, Compound Annual Growth
 mmCHIp, Chi Squared Test
 mmCODING, Coding of variables
 1. Customer Satisfaction
 2. Database Functions
 mmDHMS, Number to Time
 mmEI, Evolution Index
 mmEXPECT, Expected values
 3. Forecast Errors
 mmGROWTH
 mmGROWTHBACK
 mmGRP, Gross Rating Points
 mmHERF, Herfindahl Index
 mmINTERPOLE, Linear Interpolation
 mmLEARN, Learning Curve
 mmMSAR, Market Share to Advertising Ratio
 4. Opportunity Index
 5. Performance Ranking
 6. Project Management
 mmPREMIUM, Price Premium
 mmPRESS, Product Performance Index
 7. Price Indexes
 8. Queuing Theory
 mmRANGE
 mmREBUY, Repeat Purchase Rate
 mmREBUYS, Estimated Number of RePurchases
 mmRELATIVE
 mmSAMPLE, Sample Size
 mmSAMPLEMIN, Minimum Sample for Significant Values
 mmSEASON, Seasonality Indexes
 mmSHARE
 mmSIGNIF, Significance Test
 mmVARc, Coefficient of Variation
 Cluster Analysis
 CrossTab
 Descriptive Analyst
 Gravitation Analysis
 Proportion Analyst
 Sample Manager
 Segmentation Tree
 Variation Analyst
 3. Charts and Maps
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 Part 1. Introduction to MM4XL
 Part 2. MM4XL Tools
 1. Strategic Tools
 BCG Matrix
 Brand Mapping
 Brand Switch
 Decision Tree
 Forecast Manager
 McKinsey Matrix
 Profile Manager
 Quality Manager
 Risk Analyst
 1. How to run Risk Analyst
 2. Simulation Never heard of it
 3. Examples
 4. Functions
 1. Property Functions
 2. Utility Functions
 3. Distribution Functions
 mmBETA (Scale, Shape)
 mmBETAGEN (Scale, Shape, [Optional: Lower], [Optional: Upper])
 mmBINOMIAL (Trials, Successes)
 mmCHI2 (Degrees)
 mmDISCRETE (InputRange, Probabilities)
 mmERF (Mean)
 mmERLANG (Scale, Shape)
 mmEXPON (Mean)
 mmEXTVAL (ModalValue, StDeviation)
 mmGAMMA (Scale, Shape)
 mmGAUSSINV (Mean, Scale)
 mmGEO (Trials)
 mmHYPERGEO (Sample, Defects, BatchSize)
 mmINTUNI (Lower, Upper)
 mmLOGISTIC (Mean, StDeviation)
 mmLOGNORMAL (Mean, StDeviation)
 mmNEGBIN (Failures, Successes)
 mmNORMAL (Mean, StDeviation)
 mmPARETO (Location, ModalValue)
 mmPARETO2 (Location, ModalValue)
 mmPERT (Lower, ModalValue, Upper)
 mmPOISSON (Mean)
 mmRANDBETWEEN (Lower, Upper)
 mmRAYLEIGH (ModalValue)
 mmSTUDENT (Degrees)
 mmTRI (Lower, ModalValue, Upper)
 mmUNIFORM (Lower, Upper)
 mmWEIBULL (Life, Shape)
 Probability functions
 Risk Analyst Expert in a Few Minutes
 Introduction to Decision Analysis
 Introducing Risk Analyst with an example
 Technicalities
 Sources
 2. Analytical Tools
 Business Formulas
 1. Customer Satisfaction
 2. Database Functions
 3. Forecast Errors
 4. Opportunity Index
 5. Performance Ranking
 6. Project Management
 7. Price Indexes
 8. Queuing Theory
 mmBASS, Bass Diffusion Model
 mmBEI, Brand Equity Index
 mmBEP, BreakEven Point
 mmBEPR, BreakEven Point with Fixed Rate of Return
 mmBUYRATE, Purchase Rate Model
 mmCAGR, Compound Annual Growth
 mmCHIp, Chi Squared Test
 mmCODING, Coding of variables
 mmDHMS, Number to Time
 mmEI, Evolution Index
 mmEXPECT, Expected values
 mmGROWTH
 mmGROWTHBACK
 mmGRP, Gross Rating Points
 mmHERF, Herfindahl Index
 mmINTERPOLE, Linear Interpolation
 mmLEARN, Learning Curve
 mmMSAR, Market Share to Advertising Ratio
 mmPREMIUM, Price Premium
 mmPRESS, Product Performance Index
 mmRANGE
 mmREBUY, Repeat Purchase Rate
 mmREBUYS, Estimated Number of RePurchases
 mmRELATIVE
 mmSAMPLE, Sample Size
 mmSAMPLEMIN, Minimum Sample for Significant Values
 mmSEASON, Seasonality Indexes
 mmSHARE
 mmSIGNIF, Significance Test
 mmVARc, Coefficient of Variation
 Cluster Analysis
 CrossTab
 Descriptive Analyst
 Gravitation Analysis
 Proportion Analyst
 Sample Manager
 Segmentation Tree
 Variation Analyst
 3. Charts and Maps
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Part 2. MM4XL Tools > 1. Strategic Tools > Risk Analyst > 1. How to run Risk Analyst > 2. Model Report > Model report
Risk Analyst Model report The Complete report of a simulation model analyzed with the Risk Analyst tool is made up of 6 sheets:  Simulation page
 Statistics page
 Sensitivity page
 Input charts
 Output charts
 Time series charts
Two different activities are required when modeling scenarios: calibration and simulation. During the calibration phase you should usually limit the number of trials, while trying to refine the variables in order to produce believable scenarios. During this phase take advantage of the Preview utility available in Risk Analyst. In Preview the results of a simulation can be seen for evaluation before printing them on sheet. All report pages begin with a heading and general information, such as the date, file name, number of simulations, print time, etc. A print report does not allow printing more than 256 columns of data. Therefore, models using more than 256 variables will automatically be cut when the results are printed to sheet. This limitation does not apply to the Tables page of the Preview form. Simulation report When the checkboxes Simulations of outputs and Simulations of inputs are active in the Report page of the Simulation Settings window, Risk Analyst prints all simulated values for all reported variables. Rows 13 to 16 of the simulation report show identifiers for the variables included in the model (more precisely, for all variables not locked with the mmLOCK function). Row 13 contains the Variable type. Models in Risk Analyst use two kinds of variables: Output and Input. Formula and Cell address are displayed as indicated, and the Name row shows the name, if any, that the modeler entered in the function mmNAME for the variable. Examples of simulation reports can be found in the example files accompanying the Risk Analyst tool of MM4XL software. From row 18 on the individual simulated values for all unlocked variables are shown. Column A contains progressive numbers, and from column B on the simulated values are contained. These values may be useful to inspect the shape of the distribution modeled by any one function. You wont often need to go into such analytical detail when inspecting a model, unless you have a good reason to do it. Other reports may help you get a better understanding of the simulated values. If you really need to, consider using the function mmHISTO to group simulated variables in intervals as shown in histogram charts. Statistics When the checkbox Detailed statistics is active in the Report page of the Simulation Settings window, Risk Analyst prints, for all reported variables, a number of descriptive statistics and percentile values. In rows 916 there are 8 descriptive statistics for each variable. The same values can be produced with Descriptive Analyst, one of the MM4XL software tools, which can also print a box plot that shows in a very intuitive manner the characteristics of the shape of a variable. In rows 1836 there are percentile values that show limits at fixed intervals of 5%. For instance, a percentile value equal to 0.125 for 10% means that all random values for the variable with a value of 0.125 or less are 10% of all sampled values. If there are 1000 trials, about 100 would be equal to or smaller than 0.125. Percentile values are also used to draw the Time Series report. They can be computed with the Excel formula: =PERCENTILE(InputRange, %Level) Sensitivity When the checkboxes Sensitivities and Tornado charts are active in the Report page of the Simulation Settings window, Risk Analyst prints a table of values and a bar chart for each output variable. The analysis shows the correlation values (range from 1 to 1) of one output variable with each input variable in the model. The same result can be obtained with the CORREL function available in MS Excel. Correlation values help to identify the impact of each input variable on the output variable(s). The following chart shows the correlation values of four input variables (bars) and an output variable called Gross Profit. It is clear that the variable in cell C19 is exerting a strong positive influence in orientating the results of the output variable, while all other inputs have only a marginal impact. If we need to change the model in order to produce a different outcome, variable C19 is the best candidate to start with. Input charts When the checkbox Input charts is active in the Report page of the Simulation Settings window, Risk Analyst prints, for each input variable in the model, a table of values and a histogram chart. The chart below is from an input variable that refers to 1000 runs drawn with mmBINOMIAL(100,0.25). The chart shows the shape of the distribution, which should be coherent with the simulationists assumption, the frequency and relative frequency for each class. The smallest bar on the left, for instance, refers to 8 simulated values with the value 14.727 and lower; in class 2, 39 values reported a value above 14.727 but equal to (although impossible with a discrete pdf, which can return only integer values) or smaller than 17.455, and so on. The same chart can be produced using the simulated values of any variable either with the function mmHISTO or using the MM4XL tool called Descriptive Analyst. The latter tool can also draw box plots, which are very useful charts to describe the shape of a distribution. Output charts When the checkbox Output charts is active in the Report page of the Simulation Settings window, Risk Analyst prints, for each output variable in the model, a table of values and a histogram chart, exactly as described in the section Input charts of this Help chapter. Time Series charts Time series are arrays of values that follow a same time pattern and refer to the same process, such as monthly sales, yearly net profit, etc. In Risk Analyst time series are modeled using the mmNAME function. If there is at least one time series in a model, in the Report page of the Simulation Settings window the checkbox Time series charts and the listbox on its right are both active. Select an option from the listbox and Risk Analyst prints a table of values and a line chart, for all or only one time series in the model. When modeling scenarios aimed at simulating economic processes, Time series analysis helps you see the curve shape over time of the observed variable. In the following example the series named Loan was modeled using 6 variables as in the following picture. In the picture below, the formula used to model cell C48 is: =mmOUTPUT()+mmNAME("Loan", 0)+MAX(C4C21, 0) The time series chart produced with Risk Analyst follows. The upper green line shows percentile values at the 95% level for each variable in the time series, and the lower green line does the same for percentile val at the 5% level. The upper purple line (middle) refers to values at the 1 standard deviation level above the mean value of the variable. Intuitively, the lower purple line (middle) shows values 1 standard deviation below the mean, which is the bold red line in the middle. The chart shows the entire range of values within which the model took form. If we were modeling market share, for instance, we would have seen the boundaries within which the various share levels had been generated across time. The table of the Time Series report shows duplicated values from the Statistics report page. Short report From the Report page there is an option called Short that prints a compact summary report like the one in the following picture. A compact summary like this is useful in cases where the analyst is only interested in one or a few output variables, such as a sales forecast, the value of a market share, the size of a market, etc. In the Examples section of this help chapter you will find more information about the Short report. 