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The Weibull distribution (usually sufficient in reliability engineering) is a special case of the three parameter exponentiated Weibull distribution where the additional exponent equals 1. The exponentiated Weibull distribution accommodates unimodal, bathtub shaped [33] and monotone failure rates.
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.
This arises because the ordinary Weibull distribution is used for cases that deal with data minima rather than data maxima. The distribution here has an addition parameter compared to the usual form of the Weibull distribution and, in addition, is reversed so that the distribution has an upper bound rather than a lower bound.
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.
In mathematics, the stretched exponential is also known as the complementary cumulative Weibull distribution. The stretched exponential is also the characteristic function, basically the Fourier transform, of the Lévy symmetric alpha-stable distribution.
The geometric distribution models the probability of the first success in a sequence of Bernoulli trials and is characterized by a single parameter, p, which is the probability of success on an individual trial. In contrast, the discrete Weibull distribution can model a broader range of data patterns due to its two parameters.
In statistics, the exponentiated Weibull family of probability distributions was introduced by Mudholkar and Srivastava (1993) as an extension of the Weibull family obtained by adding a second shape parameter. The cumulative distribution function for the exponentiated Weibull distribution is
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 ...