Weibull Density Function

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A Weibull Density Function is a Probability Density Function that ...



References

2009

  • (Wikipedia, 2009) ⇒ http://en.wikipedia.org/wiki/Weibull_distribution
    • In probability theory and statistics, the Weibull distribution is a continuous probability distribution. It is named after Waloddi Weibull who described it in detail in 1951, although it was first identified by Fréchet (1927) and first applied by Rosin & Rammler (1933) to describe the size distribution of particles. The probability density functionof a Weibull random variable x is [1]:
      • f(x;\lambda,k) = \begin{cases} \frac{k}{\lambda}\left(\frac{x}{\lambda}\right)^{k-1}e^{-(x/\lambda)^{k}} & x\geq0\\ 0 & x<0\end{cases}
    • where k > 0 is the shape parameter and λ > 0 is the scale parameter of the distribution. Its complementary cumulative distribution function is a stretched exponential function. The Weibull distribution is related to a number of other probability distributions; in particular, it interpolates between the exponential distribution (k = 1) and the Rayleigh distribution (k = 2).

2006

2004