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The two-parameter Weibull probability density function
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Interface

C++
HTML

PDF

 
doublePDFdoublex
doublea
doubleb )
The Weibull distribution is a two-parameter distribution named after Waloddi Weibull. It is often also called the Rosin-Rammler distribution when used to describe the size distribution of particles.

The probability density function, given by
\graph  x=50:150, a=5:20:4, b=100

In its standard form, b=1, therefore
\graph  x=0:2, a=5:20:4, b=1

References:

  • M.Abramowitz and I.A.Stegun, Handbook of Mathematical Functions, 1964 chapt.26.1; http://www.weibull.com
  • Weibull, W. (1951) A statistical distribution function of wide applicability. J. Appl. Mech.-Trans. ASME 18(3), 293-297

Example 1

#include <iostream>
#include <codecogs/statistics/distributions/continuous/weibull/pdf.h>
using namespace Stats::Dists::Continuous::Weibull;
 
int main()
{
  std::cout << "PDF(105,20,100) = " << PDF( 105, 20, 100 ) << std::endl;
  return 0;
}
Output
PDF(105,20,100) = 0.035589

Parameters

xthe value at which to evaluate the distribution
ashape parameter
bscale parameter

Returns

probability density value

Authors

Anatoly Prognimack (Mar 19, 2005)
Developed and tested with: Borland C++ 3.1 for DOS and Microsoft Visual C++ 5.0, 6.0
Updated by Will Bateman (March 2005)
Source Code

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