Weibull Density Function

References

(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).

(Dubnicka, 2006g) ⇒ Suzanne R. Dubnicka. (2006). “Special Continuous Distributions - Handout 7." Kansas State University, Introduction to Probability and Statistics I, STAT 510 - Fall 2006.
- TERMINOLOGY : A random variable X is said to have a Weibull distribution with parameters a > 0 and > 0 if its pdf is given by fX(x) =
  - a axa−1e−( x)a, x > 0
  - 0, otherwise.