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value sets an initial failure-free time before the regular Weibull process begins. When θ = 0 {\displaystyle \theta =0} , this reduces to the 2-parameter distribution. The Weibull distribution can be characterized as the distribution of a random variable W {\displaystyle W} such that the random variable
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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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The Discrete Weibull Distribution, first introduced by Toshio Nakagawa and Shunji Osaki, is a discrete analog of the continuous Weibull distribution, predominantly used in reliability engineering. It is particularly applicable for modeling failure data measured in discrete units like cycles or shocks.
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