This page lists the features of Simulation Master. Unless noted otherwise, each feature is included in both the standard and premium editions.

### Random Variables

Simulation Master includes a tool to add random variables to your model by selecting the probability distribution and entering parameters. You can also add random variable functions by typing them in cells.

#### Continuous Distributions

Triangular

Trapezoidal

Uniform

Normal

Lognormal

Exponential

Weibull

Beta

PERT

Gamma

Pareto

Logistic

Extreme Value Maximum

Extreme Value Minimum

#### Discrete Distributions

Bernoulli

Categorical

Discrete Uniform

Binomial

Negative Binomial

Geometric

Poisson

#### Empirical Distributions

Empirical distributions can be used to sample directly from data. Simulation Master can sample from data as a discrete distribution where only values present in the data are returned. It can also sample as a continuous distribution where samples are interpolated between data points.

#### Custom Distributions

User defined distribution function allows for the use of custom distributions or distributions not already included in Simulation Master. In addition, mixture distributions can be created.

#### Truncation

Most distributions can be truncated.

### Simulation Output

The simulation output is shown below. It includes summary statistics. There are probability grab bars that can be adjusted to visually shown probabilities. The probability analysis tool calculates probabilities using specific output values.

Simulation data is written to a worksheet. If this worksheet is saved, the simulation results can be retrieved at any time.

### Simulation Report

A simulation report containing output statistics and any probability analysis can be created in a new worksheet or a new workbook. Histogram, frequency polygon, and cumulative frequency charts can also be included. All charts are native Excel objects and can be edited to meet your formatting needs.

### Decision Variables (Premium Edition)

Decision variables are ones that you have control over their values. There are two types of decision variables available:

- Discrete
- Optimization

Discrete decision variables are used in conjunction with multiple simulation runs where the decision variable changes for each simulation run. The discrete values of the variable are enumerated in a range of cells.

Optimization decision variables are used during optimization. The optimal value of the decision variable is found by the software, subject to constraints that you supply.

There is a tool that will aid in creating decision variables. Enter the parameters and the tool will automatically create the decision variable function. You can also enter decision variable functions directly in cells.

### Multiple Simulation Runs (Premium Edition)

Multiple simulation runs can be run automatically in succession. This can be used with decision variables to make different runs while changing decision variables.

### Optimization (Premium Edition)

If you're model has decision variables, that is variables that you can control, you can find the optimum value using Simulation Master premium's optimizer.

An output statistic, such as mean, is maximized, minimized, or set to a target value by changing decision variables while repeatedly simulating the model. This is like a simulation loop embedded within an optimization loop. For more information on optimization with random variables, refer to this page.

You can also set constraints on output statistics, or define your own constraints within cells in the model.

### Distribution Fitting (Premium Edition)

Fit distributions to historical data. Fits are ranked using information criteria and also includes Anderson-Darling, Kolmogorov-Smirnov, and Chi-square goodness of fit statistics. Parameter confidence intervals can be estimated with parametric bootstrapping and goodness of fit p-values can be estimated with simulation.

Random variable functions can be written to cells using the fitted distribution parameters.

#### Fit Report

A fit report can be created that includes all fit measures as well as plots to informally assess distribution fit. Plots include histogram with fitted distribution overlay, fitted cumulative distribution vs. empirical distribution, Q-Q, and P-P.

### Time Series Models

Includes 9 time series models.

- AR(1)
- AR(2)
- MA(1)
- MA(2)
- ARMA(1,1)
- ARMA(2,2)
- Geometric Brownian Motion
- ARCH(1)
- GARCH(1,1)

There is a tool to add time series functions to the model. Enter the model parameters and the tool will create a range of time series functions for each time index. Time series functions can also be entered directly in cells.

### Time Series Fitting (Premium Edition)

Time series data can be fitted to time series models. Fits are ranked using information criteria. The time series function and parameters can be written to a range of cells to set up a time series model.

#### Time Series Fit Report

A report of time series fit information can be created in a new worksheet or new workbook. Time series plots of the fitted series and data can be included. The fitted time series can be plotted over the data or plotted as an extension of the data.

### Time Series Analysis (Premium Edition)

Simulation Master includes the following time series analysis tools:

- Time series plot.
- Autocorrelation correlogram.
- Partial autocorrelation correlogram.

### Copulas

Bivariate copulas can be used to model correlation among random variables. Simulation Master includes four Archimedean copulas:

- Clayton
- Frank
- Gumbel
- Farlie-Gumbel-Morgenstern

There is a tool for adding copulas, including copula visualization which shows the correlation structure and direction. Copula functions can also be entered directly in cells.

### Copula Fitting (Premium Edition)

The correlation structure of two data sets can be fitted to a copula. Fits are ranked using information criteria. Copula functions can be written to cells using the fitted copula and parameter.

### Correlation Reports

Reports can be generated to show correlation between inputs and output. There are two types of reports available:

- Correlation report
- Scatter plots

The correlation report will show the Pearson and Spearman Rank correlation coefficients between each input and the output. Tornado charts of each coefficient can also be included.

Scatter plots of input variable vs. output, and input variable vs. input variable can be generated.

### Function Swap

Workbooks containing Simulation Master functions can be shared with others who do not have Simulation Master installed by using the Function Swap. Random variable cell functions can be exported to a new worksheet and each cell’s contents can either be replaced with the current value shown in the cell or a user entered value.

If another user sends back a modified workbook, the random variable functions can be imported back into the cells.

### Spearman Rho Tool

Spearman Rank correlation between two sets of data can be calculated with this tool.

### Integration Tool

Definite integrals up to four dimensions (quadruple integrals) can be estimated via Monte Carlo simulation. The integration tool simplifies this process and also calculates error.

### Value at Risk | Expected Shortfall Tool

Once a portfolio simulation has been run, this tool easily calculates these risk measures. Alternatively, there are worksheet functions that can calculate VaR and expected shortfall instantly in the worksheet.

### Variable Shading

#### Standard Edition

Cells containing random variable functions can be shaded with one click. There are six colors available. The cell shading can also be cleared with one click.

#### Premium Edition

Cells containing random and decision variable functions can be shaded with one click. There are six colors available. Random and decision variables can be shaded different colors for easy identification. The cell shading can also be cleared with one click.

### One Factor at a Time Sensitivity Analysis

Prior to running a simulation, it is sometimes necessary to limit random variables in a model to only the most important drivers of the model output. This is especially true with large models that are computationally intensive.

Simulation Master comes with a sensitivity analysis tool that performs a static, one factor at a time (OFAT) sensitivity analysis of input variables to determine the variables that have the largest impact on model output.

While a one at a time sensitivity analysis does not account for input variable interactions (such as an increase in price may cause a decrease in demand), it is still a powerful tool to focus on the most important factors in a model. For example, if a variable has a high impact on outcome, this information can be used to investigate the variable further to provide more model fidelity.

Further investigation might include experimentation to learn more about the underlying probability distribution, consulting with experts, or customer queries to name a few ways of providing better input to the model.