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Triangular Distribution

You may wish to use a Triangular Distribution in some cases, as a rough approximation to a random variable with an unknown distribution.

A Triangular Distribution is specified by its minimum, maximum and mean values. It does not have to be symmetric, and can be skewed either to the left or right by entering a mean value greater than or less than the average of the minimum and maximum values.

Triangular Distribution

Triangular probability density function. Minimum = a, maximum = b, mode = c. For a symmetric distribution, mean = mode.

Mean of a Triangular Distribution

For a non-symmetric Triangular Distribution, the mean value is not equal to the mode. The mode is the value of the variable at the peak of the TRIANGULAR distribution. The mean of a Triangular Distribution has the following behaviour:

  • In general, the mean of a Triangular Distribution is always given by:

TD mean

  • If the distribution is symmetric, then the mean is equal to the mode.
  • For a left Triangular Distribution, the mode = minimum, and the mean = (2*minimum + maximum) / 3.
  • For a right Triangular Distribution, the mode = maximum, and the mean = (2*maximum + minimum) / 3.

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