Home Site Statistics  |   Contact  |   About Us       Tuesday, September 21, 2021   

j0110924 - Back to Home



Skip Navigation Links.

   Skip Navigation LinksHOME ›  AREAS OF EXPERTISE ›   Distribution Function ›  ~ Expontl Distribution


"Distribution Functions"
Exponential Distribution Method
Exponential Distribution Results



Number of Points:
Number of Bins:



[ Initial Number of Bins: {20) ]
[ Initial Number of Points: {2000} ]

IMPLEMENTATION
Exponential Distribution Method

The Exponential distribution is used to model events that occur randomly over time. In particular, this distribution is very powerful for studying lifetimes.


Probability Density Function

The probability density function of the exponential distribution is presented in the following formula:

f(x;ç) = ç e-çx

where ç > 0 is a parameter of the distribution, often called the rate parameter. This distribution is defined in the range 0 ≤ x < ∞


Exponential Random Number Generator

The random numbers from the exponential variate exp(ç), (code not shown nor discussed), with the relationship:

exp(ç) ≈ - 1 / ç ln u(0,1)


Testing the Exponential Distribution Method

To test the Exponential Distribution method, a new static method has been added. The TestExponentialDistribution() method has been written and executed. No additional code is shown. The user can change variables as desired.

For the test, two parameters were set:

number of bins = 20; (nBins)
number of points = 2000; (nPoints)

where the parameter (nBins) is the number of bins in the histogram and (nPoints) is the number of random points. A random array is created using the exponential distribution. A comparison is made between the histogram of random data and the theoretical probability density function of the exponential distribution. One can see the results from the exponential random generator are very close to the theoretical exponential distribution function.

Running this example generates the results shown above.


           static void TestExponentialDistribution();
              {
                  for (int i = 0; i < nBins; i++)
                 {
                     ListBox1.Items.Add(" x = " + xdata[i] + "," + " - - - - -> Random Data = " + ydata[i] + "," + " - - - - -> Density Distribution = " + Math.Round(ydistribution[i] * normalizeFactor, 0).ToString());
                 }
              }



Other Implementations...


Object-Oriented Implementation
Graphics and Animation
Sample Applications
Ore Extraction Optimization
Vectors and Matrices
Complex Numbers and Functions
Ordinary Differential Equations - Euler Method
Ordinary Differential Equations 2nd-Order Runge-Kutta
Ordinary Differential Equations 4th-Order Runge-Kutta
Higher Order Differential Equations
Nonlinear Systems
Numerical Integration
Numerical Differentiation
Function Evaluation


Consulting Services - Back to Home
Home

Home Math, Analysis,
  expertise..."

EIGENVALUE SOLUTIONS...
Eigen Inverse Iteration
Rayleigh-Quotient Method
Cubic Spline Method

 

Applied Mathematical Algorithms

Home A complex number z = x + iy, where...

Complex Functions
Home Non-linear system methods...

Non Linear Systems
Home Construction of differentiation...

Differentiation
Home Consider the function where...

Integration
 
About Us

KMP Engineering is an independent multidisciplinary engineering consulting company specializing in mathematical algorithms.

  ABOUT
  SITE STATISTICS
Contact Us

KMP ENGINEERING
2461 E Orangethorpe Ave Fullerton, CA 92631 USA info@keystoneminingpost.com
Site Map

   Home
   Areas of Expertise
   Reference Items
   Managed Services
   Login

Mining & Software Engineering

Home
Since 2006 All Rights Reserved  © KMP Engineering LINKS | PRIVACY POLICY | LEGAL NOTICE