TrapezoidalDistribution Class

Trapezoidal distributions have been used in many areas and studied under varying scopes, such as in the excellent work of (van Dorp and Kotz, 2003), risk analysis (Pouliquen, 1970) and (Powell and Wilson, 1997), fuzzy set theory (Chen and Hwang, 1992), applied phyisics, and biomedical applications (Flehinger and Kimmel, 1987).

Trapezoidal distributions are appropriate for modeling events that are comprised by three different stages: one growth stage, where probability grows up until a plateau is reached; a stability stage, where probability stays more or less the same; and a decline stage, where probability decreases until zero (van Dorp and Kotz, 2003).

References:

• J. René van Dorp, Samuel Kotz, Trapezoidal distribution. Available on: http://www.seas.gwu.edu/~dorpjr/Publications/JournalPapers/Metrika2003VanDorp.pdf
• Powell MR, Wilson JD (1997). Risk Assessment for National Natural Resource Conservation Programs, Discussion Paper 97-49. Resources for the Future, Washington D.C.
• Chen SJ, Hwang CL (1992). Fuzzy Multiple Attribute Decision-Making: Methods and Applications, Springer-Verlag, Berlin, New York.
• Flehinger BJ, Kimmel M (1987). The natural history of lung cancer in periodically screened population. Biometrics 1987, 43, 127-144.

The following example shows how to create and test the main characteristics of a Trapezoidal distribution given its parameters:

// Create a new trapezoidal distribution with linear growth between
// 0 and 2, stability between 2 and 8, and decrease between 8 and 10.
// 
// 
//            +-----------+
//           /|           |\
//          / |           | \
//         /  |           |  \
//  -------+---+-----------+---+-------
//   ...   0   2   4   6   8   10  ...
// 
var trapz = new TrapezoidalDistribution(a: 0, b: 2, c: 8, d: 10, n1: 1, n3: 1);

double mean = trapz.Mean;     // 2.25
double median = trapz.Median; // 3.0
double mode = trapz.Mode;     // 3.1353457616424696
double var = trapz.Variance;  // 17.986666666666665

double cdf = trapz.DistributionFunction(x: 1.4);           // 0.13999999999999999
double pdf = trapz.ProbabilityDensityFunction(x: 1.4);     // 0.10000000000000001
double lpdf = trapz.LogProbabilityDensityFunction(x: 1.4); // -2.3025850929940455

double ccdf = trapz.ComplementaryDistributionFunction(x: 1.4); // 0.85999999999999999
double icdf = trapz.InverseDistributionFunction(p: cdf);       // 1.3999999999999997

double hf = trapz.HazardFunction(x: 1.4);            // 0.11627906976744187
double chf = trapz.CumulativeHazardFunction(x: 1.4); // 0.15082288973458366

string str = trapz.ToString(CultureInfo.InvariantCulture); // Trapezoidal(x; a=0, b=2, c=8, d=10, n1=1, n3=1, α = 1)

Reference