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The Weibull modulus is a dimensionless parameter of the Weibull distribution. ... which can be intrinsic or extrinsic in origin, arising from factors such as cavity ...
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 mean strength can be computed from this distribution and, as it turns out, its plot is identical with the plot of Eq. 5 seen in Fig. 2g. The point of deviation from the Weibull asymptote is determined by the location of the grafting point on the strength distribution of one RVE (Fig. 2g).
The Kaniadakis κ-Weibull distribution is exhibits power-law right tails, and it has the following probability density function: [3] = + ()valid for , where | | < is the entropic index associated with the Kaniadakis entropy, > is the scale parameter, and > is the shape parameter or Weibull modulus.
The Poisson distribution is often used to model the number of rare event occurrences during a fixed period of time. It is characterized by a single parameter, λ, which is both the mean and variance of the distribution. The discrete Weibull distribution, on the other hand, is more flexible and can handle both over- and under-dispersion in count ...
They showed that the exponentiated Weibull distribution has increasing, decreasing, bathtub, and unimodal hazard rates. The exponentiated exponential distribution proposed by Gupta and Kundu (1999, 2001) is a special case of the exponentiated Weibull family.
The q-Weibull is a generalization of the Weibull, as it extends this distribution to the cases of finite support (q < 1) and to include heavy-tailed distributions (+ +). The q -Weibull is a generalization of the Lomax distribution (Pareto Type II), as it extends this distribution to the cases of finite support and adds the κ {\displaystyle ...
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.