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Add Triangle Distribution specification #33

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2 changes: 2 additions & 0 deletions mef/schema/random_deviate.rnc
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Expand Up @@ -12,3 +12,5 @@ beta-deviate = element beta-deviate { expression, expression }
histogram = element histogram { expression, bin+ }

bin = element bin { expression, expression }

triangle = element triangle { expression, expression, expression }
1 change: 1 addition & 0 deletions mef/schema/stochastic_layer.rnc
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Expand Up @@ -18,5 +18,6 @@ random-deviate =
| gamma-deviate
| beta-deviate
| histogram
| triangle

test-event = test-initiating-event | test-functional-event
15 changes: 15 additions & 0 deletions mef/stochastic_layer.rst
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Expand Up @@ -556,6 +556,8 @@ As for arithmetic operators and built-ins, this list can be extended on demand.
+-----------------------+------------+-------------------------------------------------------------------------------------------------------------+
| **histograms** | any | discrete distributions defined by means of a list of pairs |
+-----------------------+------------+-------------------------------------------------------------------------------------------------------------+
| **triangle** | 3 | triangle (or triangular) distribution defined by its two limits and mode |
+-----------------------+------------+-------------------------------------------------------------------------------------------------------------+

Uniform Deviates
These primitives describe uniform distributions in a given range
Expand Down Expand Up @@ -713,6 +715,19 @@ Histograms
with the initial value
:math:`x_0 = 0, x_1 = 2m_1, \text{ and } x_i = x_{i-1} + 2(m_i - x_{i-1})`.

Triangle Distributions
A triangle (or triangular) distribution is a special case of a piecewise-linear distribution
defined only by three bounds :math:`(a, b, c)`,
a lower limit, mode, and upper limit respectively.
The lower and upper limit weights are 0,
and the most probable value :math:`b` has :math:`\frac{2}{c - a}` weight.

The expected value of a triangle distribution is the arithmetic mean of its bounds.

.. math::

E(x) = \frac{a + b + c}{3}


XML Representation
------------------
Expand Down