Add Triangle Distribution specification

The specification references piecewise-linear distribution
as the general case distribution.
This makes explanation of the distribution simpler
without any need to give its probability density function.

Author: rakhimov

mef/stochastic_layer.rst

@@ -673,6 +673,8 @@ 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
@@ -808,6 +810,19 @@ 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
 ------------------
@@ -824,6 +839,7 @@ The Backus-Naur grammar for the XML representation of random deviates is given
         | <gamma-deviate> [ expression ]:2 </gamma-deviate>
         | <beta-deviate> [ expression ]:2 </beta-deviate>
         | histogram
+        | <triangle> [ expression ]:3 </triangle>
 
     histogram ::= <histogram > expression /bin/+ </histogram>