How do you choose the appropriate probability distributions and parameters for Monte Carlo simulation?

1 Understand your data

Before you select a distribution, you need to understand the characteristics of your data, such as the mean, standard deviation, skewness, kurtosis, and outliers. You can use descriptive statistics, histograms, box plots, or other tools to explore your data and identify patterns and trends. You should also consider the source and reliability of your data, and how it relates to your project objectives and assumptions.

2 Choose a suitable distribution

There are many types of probability distributions, each with different shapes, properties, and applications. Some of the most common ones used in project estimation are normal, triangular, uniform, lognormal, beta, and PERT. You should choose a distribution that matches the behavior and variability of your data, and that is easy to understand and communicate. For example, if your data is symmetric and bell-shaped, you can use a normal distribution; if your data is skewed and has a long tail, you can use a lognormal or a beta distribution; if your data is bounded and has an uncertain mode, you can use a triangular or a PERT distribution.

3 Estimate the parameters

Once you have chosen a distribution, you need to estimate the parameters that define its shape and location. For example, a normal distribution has two parameters: the mean and the standard deviation; a triangular distribution has three parameters: the minimum, the maximum, and the mode. You can use different methods to estimate the parameters, such as historical data, expert judgment, regression analysis, or maximum likelihood estimation. You should also check the fit of your distribution to your data, and adjust the parameters if needed.

4 Test the sensitivity

After you have defined the distributions and parameters for your inputs, you should test the sensitivity of your model to changes in these values. You can use sensitivity analysis, tornado charts, or other techniques to identify which inputs have the most impact on your output, and how they affect the uncertainty and variability of your results. You should also perform scenario analysis, where you change the values of one or more inputs to see how they affect the outcomes. This can help you evaluate the best-case, worst-case, and most likely scenarios, and plan for contingencies.

5 Validate the results

Finally, you should validate the results of your Monte Carlo simulation by comparing them to your expectations, benchmarks, or other sources of information. You should check the accuracy, validity, and reliability of your results, and look for any errors, biases, or anomalies. You should also interpret the results in the context of your project goals, constraints, and risks, and communicate them clearly and effectively to your stakeholders.