Using a beta distribution in MCM multipliers

[mhemstrom]

I’d like to use a beta distribution to generate variation in MCMs for an insect/disease disturbance. The documentation doesn’t say much about how to use either a normal or beta distribution. How would you specify the shape of the beta distribution curve?

[leonardo-frid]

The input parameters for using a beta distribution are:

1. Multiplier: This is the mean value of the distribution
2. Distribution Type: (Beta or Normal)
3. SD: the standard deviation of the distribution
4. Multiplier Min: the minimum value possible in the distribution
5. Multiplier Max: the maximum value possible

Note that the beta is bounded between the min and max value whereas the normal is truncated at these values.

If you wanted to see what your distribution looks like you can do the following

1. Normalize the mean of the distribution: (mean-min)/(max-min)
2. Normalize the standard deviation: (standard deviation)/(max-min)
3. Calculate the normalized variance as (normalized standard deviation)^2
4. Use the formulas on this site and the normalized mean and variance to calculate the alpha and beta paramters:
   1. http://en.wikipedia.org/wiki/Beta_distribution#Parameter_estimation
5. Once you have the alpha and beta parameters calculated you can use the excel "Beta.Dist()" function to plot the shape of your distribution.

If you would like the multiplier to vary between monte carlos only you can leave the timestep field blank.  If you want to sample from the distribution for every timestep you will need to specify a record for every timestep.

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