--- title: Monte Carlo Simulation | Statgraphics description: Monte Carlo simulation is used to estimate the distribution of variables when it is impossible or impractical to determine that distribution theoretically. It is used in many areas, including engineering, finance, and DFSS (Design for Six Sigma). Use Statgraphics 18 run Monte Carlo Simulations on this page. --- [![Statgraphics 19 logo](https://www.statgraphics.com/hs-fs/hubfs/stat19plain-01-1.png?width=2272&height=484&name=stat19plain-01-1.png "Statgraphics 19 logo")](https://www.statgraphics.com) - [Products](https://www.statgraphics.com/product) - [Learn](https://www.statgraphics.com/statistics-library) - [Training](https://www.statgraphics.com/training-and-consulting) - [Product](https://www.statgraphics.com/product) - [Centurion XVIII](https://www.statgraphics.com/centurion-xvii) - [Sigma Express](https://www.statgraphics.com/statgraphics-sigma-express) - [Online](https://www.statgraphics.com/statgraphics-stratus) - [Web Services](https://www.statgraphics.com/statgraphics-web-services) - [Learn](https://www.statgraphics.com/statistics-library) - [Statistics Library](https://www.statgraphics.com/statistics-library) - [Six Sigma & Lean](https://www.statgraphics.com/six-sigma-lean) - [Instructional Videos](https://www.statgraphics.com/instructional-videos) - [Applications/ Case Studies](https://www.statgraphics.com/application) - [Training & Consulting](https://www.statgraphics.com/training-and-consulting) - [Statpoint Seminars](https://www.statgraphics.com/statpoint-seminar) - [Statpoint Instructors](https://www.statgraphics.com/statpoint-instructor) - [Training Partners](https://www.statgraphics.com/training-partners) - [Webinars](https://www.statgraphics.com/webinars) - [Support](https://www.statgraphics.com/customer-support-overview) - [Blog](https://www.statgraphics.com/blog) - [Store](http://store.statgraphics.com) ### Statgraphics ## [Centurion](https://www.statgraphics.com/centurion-overview) #### [LEARN MORE](https://www.statgraphics.com/centurion-overview) ### Statgraphics ## [Sigma *express*](https://www.statgraphics.com/statgraphics-sigma-express) #### [LEARN MORE](https://www.statgraphics.com/statgraphics-sigma-express) ### Statgraphics ## [*Stratus*](https://www.statgraphics.com/statgraphics-stratus) #### [LEARN MORE](https://www.statgraphics.com/statgraphics-stratus) ### Statgraphics ## [Web Services](https://www.statgraphics.com/statgraphics-web-services) #### [LEARN MORE](https://www.statgraphics.com/statgraphics-web-services) ## [Statistics Library](https://www.statgraphics.com/statistics-library) #### [LEARN MORE](https://www.statgraphics.com/statistics-library) ## [Six Sigma & Lean](https://www.statgraphics.com/six-sigma-lean) #### [LEARN MORE](https://www.statgraphics.com/six-sigma-lean) ## [Instructional Videos](https://www.statgraphics.com/instructional-videos) #### [LEARN MORE](https://www.statgraphics.com/instructional-videos) ## [Applications/ Case Studies](https://www.statgraphics.com/statistical-applications) #### [LEARN MORE](https://www.statgraphics.com/statistical-applications) ## [Statgraphics Seminars](https://www.statgraphics.com/statpoint-seminar) #### [LEARN MORE](https://www.statgraphics.com/statpoint-seminar) ## [Statgraphics Instructors](https://www.statgraphics.com/statpoint-instructor) #### [LEARN MORE](https://www.statgraphics.com/statpoint-instructor) ## [Training Partners](https://www.statgraphics.com/public-seminar) #### [LEARN MORE](https://www.statgraphics.com/public-seminar) ## [Webinars](https://www.statgraphics.com/webinars) #### [LEARN MORE](https://www.statgraphics.com/webinars) #### Statistical Capabilities - [Analysis of Variance](https://www.statgraphics.com/analysis-of-variance) - [Basic Statistical Methods](https://www.statgraphics.com/basic-statistical-methods) - [Categorical Data Analysis](https://www.statgraphics.com/categorical-data-analysis) - [Data Mining & Machine Learning](https://www.statgraphics.com/data-mining) - [Design of Experiments](https://www.statgraphics.com/design-of-experiments) - [Exploratory Data Analysis](https://www.statgraphics.com/exploratory-data-analysis) - [Life Data Analysis & Reliability](https://www.statgraphics.com/life-data-analysis-and-reliability) - [Measurement Systems Analysis](https://www.statgraphics.com/measurement-systems-analysis) - [Monte Carlo Simulation](https://www.statgraphics.com/monte-carlo) - [Multivariate Methods](https://www.statgraphics.com/multivariate-methods) - [Nonparametric Methods](https://www.statgraphics.com/nonparametric-methods) - [Probability Distributions](https://www.statgraphics.com/probability-distributions) - [Process Capability Analysis](https://www.statgraphics.com/process-capability-analysis) - [Regression Analysis](https://www.statgraphics.com/regression-analysis) - [Sample Size Determination](https://www.statgraphics.com/sample-size-determination) - [Six Sigma & Lean](https://www.statgraphics.com/six-sigma-lean) - [Statistical Process Control Charts](https://www.statgraphics.com/statistical-process-control-charts) - [Time Series Analysis & Forecasting](https://www.statgraphics.com/time-series-analysis-and-forecasting) - [Visualization](https://www.statgraphics.com/visualization) # Monte Carlo Simulation Monte Carlo simulation is used to estimate the distribution of variables when it is impossible or impractical to determine that distribution theoretically. It is used in many areas, including engineering, finance, and DFSS (Design for Six Sigma). A typical Monte Carlo simulation includes: (1) One or more input variables X, some of which usually follow a probability distribution. (2) One or more output variables Y, whose distribution is desired. (3) A mathematical model coupling the X’s and the Y’s. Statgraphics also includes a wide array of random number generators for use in simulation models. [![Download a trial copy today!](https://no-cache.hubspot.com/cta/default/402067/f19af21b-1b53-4e49-b59e-4ad4dcc50c0e.png)](https://cta-redirect.hubspot.com/cta/redirect/402067/f19af21b-1b53-4e49-b59e-4ad4dcc50c0e) | Procedure | Statgraphics Centurion 18/19 | Statgraphics Sigma *express* | Statgraphics *stratus* | Statgraphics Web Services | StatBeans | | --- | --- | --- | --- | --- | --- | | [General Simulation Models](https://www.statgraphics.com/monte-carlo#GENERAL) | ![](https://www.statgraphics.com/hubfs/migrated-pages-image/checkmark.png) | ![](https://www.statgraphics.com/hubfs/migrated-pages-image/checkmark.png) |   |   |   | | [ARIMA Time Series Models](https://www.statgraphics.com/monte-carlo#ARIMA) | ![](https://www.statgraphics.com/hubfs/migrated-pages-image/checkmark.png) |   |   |   |   | | [Random Number Generation](https://www.statgraphics.com/monte-carlo#RANDOM) | ![](https://www.statgraphics.com/hubfs/migrated-pages-image/checkmark.png) | ![](https://www.statgraphics.com/hubfs/migrated-pages-image/checkmark.png) | ![](https://www.statgraphics.com/hubfs/migrated-pages-image/checkmark.png) | ![](https://www.statgraphics.com/hubfs/migrated-pages-image/checkmark.png) | ![](https://www.statgraphics.com/hubfs/migrated-pages-image/checkmark.png) | | [Multivariate Normal Random Numbers](https://www.statgraphics.com/monte-carlo#MULT) | ![](https://www.statgraphics.com/hubfs/migrated-pages-image/checkmark.png) |   |   |   |   | #### General Simulation Models This procedure is used to find the distribution of one or more output variables defined by mathematical models coupling them with one of more input variables. A probability distribution for each input variable may be specified. The primary output includes estimated percentiles for the output variables. ![monte carlo-2.png](https://www.statgraphics.com/hs-fs/hubfs/monte%20carlo-2.png?width=650&height=374&name=monte%20carlo-2.png) More:[Monte Carlo Simulation (General Simulation Models).pdf](https://www.statgraphics.com/hubfs/PDFs/Monte_Carlo_Simulation_General_Simulation_Models.pdf) or [Watch Video](https://youtu.be/NSzUWxepejo)   #### ARIMA Time Series Models This procedure generates random samples from ARIMA time series models. ![monte carol arima.png](https://www.statgraphics.com/hs-fs/hubfs/monte%20carol%20arima.png?width=649&height=451&name=monte%20carol%20arima.png) More: [Monte\_Carlo\_Simulation\_ARIMA\_Time\_Series\_Models.pdf](https://www.statgraphics.com/hubfs/PDFs/Monte_Carlo_Simulation_ARIMA_Time_Series_Models.pdf)  [![Sign Up for Special Offers](https://no-cache.hubspot.com/cta/default/402067/f26a5e52-963b-43b8-b1d8-23139cf3e7e2.png)](https://cta-redirect.hubspot.com/cta/redirect/402067/f26a5e52-963b-43b8-b1d8-23139cf3e7e2) #### Random Number Generation It is frequently necessary to generate random numbers from different probability distributions. This procedure simplifies the process of creating multiple samples of random numbers. 49 probability distributions are available. ![monte carlo random.png](https://www.statgraphics.com/hs-fs/hubfs/monte%20carlo%20random.png?width=649&height=371&name=monte%20carlo%20random.png) More: [Monte\_Carlo\_Simulation\_Random\_Number\_Generation.pdf](https://www.statgraphics.com/hubfs/PDFs/Monte_Carlo_Simulation_Random_Number_Generation.pdf)   #### Multivariate Normal Random Numbers This procedure generates random numbers from a multivariate normal distribution involving up to 12 variables. The user inputs the variable means, standard deviations, and the correlation matrix. Random samples are generated which may be saved to the Statgraphics databook. ![matrix-1.png](https://www.statgraphics.com/hs-fs/hubfs/matrix-1.png?width=649&height=649&name=matrix-1.png) More:[Multivariate\_Normal\_Random\_Numbers.pdf](https://www.statgraphics.com/hubfs/PDFs/Multivariate_Normal_Random_Numbers.pdf) or [Watch Video](https://www.youtube.com/watch?v=I46JuWBHXjc&t=10s) [![Start Using Statgraphics Today!](https://no-cache.hubspot.com/cta/default/402067/c789137b-a473-4625-b762-f58a173c4a21.png)](https://cta-redirect.hubspot.com/cta/redirect/402067/c789137b-a473-4625-b762-f58a173c4a21) [![contact-icon](https://www.statgraphics.com/hs-fs/hubfs/stat19web/sales.png?width=50&name=sales.png "contact-icon.fw")](https://www.statgraphics.com/contact-us-dealers-global-partners) ### [CONTACT SALES](https://www.statgraphics.com/contact-us-dealers-global-partners) Contact our Sales team today [![youtube-icon.fw](https://www.statgraphics.com/hubfs/stat19web/watchr.png)](https://www.statgraphics.com/instructional-videos) ### [WATCH A VIDEO](https://www.statgraphics.com/instructional-videos) Learn more about the many enhancements added to Version 19 [![download](https://www.statgraphics.com/hubfs/stat19web/downloadr.png)](https://www.statgraphics.com/download18) ### [DOWNLOAD TRIAL](https://www.statgraphics.com/download19) Try Statgraphics 19 today for free! [![eye icon](https://www.statgraphics.com/hubfs/stat19web/viewr.png)](https://www.statgraphics.com/download-brochure-0) ### [VIEW BROCHURE](https://www.statgraphics.com/download-brochure-0) Discover Statgraphics 19 with our product brochure. ![contact us](https://www.statgraphics.com/hubfs/stat19web/contactr.png) © 2025 Statgraphics Technologies, Inc. The Plains, Virginia [CONTACT US](https://www.statgraphics.com/contact-us-partner) ![Statgraphics download center](https://www.statgraphics.com/hs-fs/hubfs/stat19web/downloadcr.png?width=50&name=downloadcr.png) Have you purchased Statgraphics Centurion or Sigma Express and need to download your copy? [CLICK HERE](https://www.statgraphics.com/download-center) - [Support](https://www.statgraphics.com/customer-support-overview) - [Company](https://www.statgraphics.com/contact-us-dealers-global-partners) - [Blog](https://blog.statgraphics.com) -   -           -