 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 > 4. Functions > 2. Utility Functions > mmOPTNUM(InputRng, [Optional: StablePeriods], [Optional: SelectionLimit])
Risk Analyst mmOPTNUM(InputRng, [Optional: StablePeriods], [Optional: SelectionLimit]) This function finds the number of simulations for an Output variable where the standard deviation (sd) of the mean of the simulation trials tends to stabilize. This is useful information to reduce the number of trials and save time during the simulation or, alternately, to increase the number of trials if the analysis is not stable enough. There is no real statistical backup to the assumption that the sd of the mean is an estimator of the time to stop producing simulation values because the next value will not contribute to the analysis with enough incremental information. However, Koller suggests that: A simple method for determining whether a sufficient number of comparisons have been made is to inspect the mean of the answer variable distribution. An answer variable in Risk Analyst software is clearly an Output variable. This function takes three arguments InputRng is the range with the simulation values for the variable under inspection. StablePeriods is an optional argument that sets the number of periods that the sd of the mean has to be equal or smaller than the SelectionLimit. When missing, the default number of stable periods is set to 20. SelectionLimit is an optional argument that sets the level at which the absolute difference between the sd at time t+1 has to be equal to or smaller than the same limit for the sd at time t. When missing, the default level is 0.0005. The function returns zero if it cannot find an optimal number of simulations. This suggests that more simulation trials have to be produced. The following two functions produce the same result: =mmOPTNUM(B14:B5013, 20, 0.0005) =mmOPTNUM(B14:B5013) The following chart refers to the sd of the mean of 5000 trials. The function mmOPTNUMSIM suggests that 976 trials are required to achieve stability at the 0.0005 level. Note that the maximum value of the vertical axis was rescaled to allow the curve to be seen, which otherwise was pushed down to the zero level by extreme values occurring in the initialization phase of the algorithm. 