Search results
Results From The WOW.Com Content Network
In probability theory and statistics, the Weibull distribution / ˈ w aɪ b ʊ l / is a continuous probability distribution. It models a broad range of random variables, largely in the nature of a time to failure or time between events. Examples are maximum one-day rainfalls and the time a user spends on a web page.
In the four survival function graphs shown above, the shape of the survival function is defined by a particular probability distribution: survival function 1 is defined by an exponential distribution, 2 is defined by a Weibull distribution, 3 is defined by a log-logistic distribution, and 4 is defined by another Weibull distribution.
The commonly-used Weibull distribution combines both of these effects, as do the log-normal and hypertabastic distributions. After modelling a given distribution and parameters for h ( t ) {\displaystyle h(t)} , the failure probability density f ( t ) {\displaystyle f(t)} and cumulative failure distribution F ( t ) {\displaystyle F(t)} can be ...
The Weibull modulus is a dimensionless parameter of the Weibull distribution. It represents the width of a probability density function (PDF) in which a higher modulus is a characteristic of a narrower distribution of values.
The Fréchet distribution, also known as inverse Weibull distribution, [2] [3] is a special case of the generalized extreme value distribution. It has the cumulative distribution function ( ) = > . where α > 0 is a shape parameter.
The Rice distribution is a noncentral generalization of the Rayleigh distribution: () = (,). The Weibull distribution with the shape parameter k = 2 yields a Rayleigh distribution. Then the Rayleigh distribution parameter σ {\displaystyle \sigma } is related to the Weibull scale parameter according to λ = σ 2 . {\displaystyle \lambda =\sigma ...
The Weibull distribution or Rosin–Rammler distribution is a useful distribution for representing particle size distributions generated by grinding, milling and crushing operations. The log-hyperbolic distribution was proposed by Bagnold and Barndorff-Nielsen [9] to model the particle-size distribution of naturally occurring sediments. This ...
The finiteness of the weakest-link chain model causes major deviations from the Weibull distribution. As the structure size, measured by , increases, the grafting point of the Weibullian left part moves to the right until, at about =, the entire distribution becomes Weibullian. The mean strength can be computed from this distribution and, as it ...