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The Weibull fit was originally used because of a belief that particle energy levels align to a statistical distribution, but this belief was later proven false [citation needed] and the Weibull fit continues to be used because of its many adjustable parameters, rather than a demonstrated physical basis. [32]
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.
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In probability theory and statistics, the poly-Weibull distribution is a continuous probability distribution. The distribution is defined to be that of a random variable defined to be the smallest of a number of statistically independent random variables having non-identical Weibull distributions .
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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.
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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.