Weibull Distribution - Uses

Uses

The Weibull distribution is used

• In survival analysis
• In reliability engineering and failure analysis
• In industrial engineering to represent manufacturing and delivery times
• In extreme value theory
• In weather forecasting
  • To describe wind speed distributions, as the natural distribution often matches the Weibull shape
• In communications systems engineering
  • In radar systems to model the dispersion of the received signals level produced by some types of clutters
  • To model fading channels in wireless communications, as the Weibull fading model seems to exhibit good fit to experimental fading channel measurements

• In General insurance to model the size of Reinsurance claims, and the cumulative development of Asbestosis losses
• In forecasting technological change (also known as the Sharif-Islam model)

• In hydrology the Weibull distribution is applied to extreme events such as annual maximum one-day rainfalls and river discharges. The blue picture illustrates an example of fitting the Weibull distribution to ranked annually maximum one-day rainfalls showing also the 90% confidence belt based on the binomial distribution. The rainfall data are represented by plotting positions as part of the cumulative frequency analysis.

• In describing the size of particles generated by grinding, milling and crushing operations, the 2-Parameter Weibull distribution is used, and in these applications it is sometimes known as the Rosin-Rammler distribution. In this context it predicts fewer fine particles than the Log-normal distribution and it is generally most accurate for narrow particle size distributions. The interpretation of the cumulative distribution function is that F(x; k; λ) is the mass fraction of particles with diameter smaller than x, where λ is the mean particle size and k is a measure of the spread of particle sizes.