# Probabilistic Modeling

## Models Illustrating Probabilistic Modeling

All the models assigned to the selected category are listed below.

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• #### Dashboard-Defined Distributions

The purpose of this model is to allow an arbitrary cumulative or discrete distribution to be specified by entering values and probabilities in a Dashboard.

• #### Risk Board Game

These two models simulate different aspects of the classic board game Risk.

• #### Ito-Process Random Walk Model

A History Generator Element is used to model an Ito-process random walk. The distribution of the future value is lognormal with mean and variance that both increase linearly with time.

• #### Markov Process Example Model

Simple two state, continuous time Markov chain model which compares two theoretical probability distributions

• #### Vector Distributions

This example shows how a vector of sampled values can be generated from a single distribution definition for Sampled, Cumulative and Discrete stochastics

• #### Indexing Data Records

This model demonstrates two different ways to index a data record for use in a GoldSim model, either sequentially or randomly.

• #### Defining Vector Distributions

This example shows how to define and sample vector discrete and cumulative distributions using (1) a vector uniform 0-1 stochastic to sample probability levels and (2) a script element to get the corresponding values.

• #### Export Statistical Histories to Excel

For a Monte Carlo simulation, export statistical histories to Excel

• #### Polya Urn Problem

This simple model simulates the classic Polya urn problem in which stones, either black or white, are randomly selected (with replacement and addition) from a pot.

• #### Time Shifting a Time Series

The purpose of this model is to demonstrate time shifting historic data in a Time Series element. This type of model makes it easy to show summary statistics like exceedance probability of annual peak flow rate or mean annual flow rate.

• #### Marketing Program Pick

Three different types of promotional campaigns are compared across a 180 day campaign period.

• #### Project Simulator

This model illustrate how conditional containers can be used to simulate projects.

• #### What-If Simulation Case Study

Simple ECommerce, decision-making case study using GoldSim "what-if" simulation

• #### Markov Process Rainfall Model

This model simulates a Markov process that randomly switches between a wet state and a dry state to simulate rainfall given some key historic statistics.

• #### Probabilistic Detention Pond Model

This model presents a pond discharge versus pond capacity optimization problem.

• #### Generation of a Stochastic Precipitation Record

This model illustrates one way in which GoldSim can be used to generate a stochastic precipitation record.

• #### Dam Breach Risk

Monte Carlo Simulation of the Dam Breach algorithm to calculate risk of failure

• #### Risk Assessment of Lunar Base

This is a model that simulates the performance of a lunar base over its planned 20 year lifespan. It illustrates how GoldSim's Reliability Module can be use to carry out a probabilistic risk assessment of a complex system.

• #### Risk Assessment of Planetary Mission

This is a model that simulates an unmanned scientific mission to another planet. It illustrates how GoldSim's Reliability Module can be used to carry out a probabilistic risk assessment of a complex system.

• #### Ships with Containers

This model simulates ships entering the harbor where each ship carries a random number of containers.

• #### Simulating Failure Risk of a Pump Station

Use the Reliability Module of GoldSim to calculate the failure modes of various components of a pumping station and water delivery system.