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Kaniadakis Weibull Distribution
The Kaniadakis Weibull distribution (or ''κ''-Weibull distribution) is a probability distribution arising as a generalization of the Weibull distribution. It is one example of a Kaniadakis ''κ''-distribution. The κ-Weibull distribution has been adopted successfully for describing a wide variety of complex systems in seismology, economy, epidemiology, among many others. Definitions Probability density function The Kaniadakis ''κ''-Weibull distribution is exhibits power-law right tails, and it has the following probability density function: : f_(x) = \frac \exp_\kappa(-\beta x^\alpha) valid for x \geq 0, where , \kappa, 0 is the scale parameter, and \alpha > 0 is the shape parameter or Weibull modulus. The Weibull distribution is recovered as \kappa \rightarrow 0. Cumulative distribution function The cumulative distribution function of ''κ''-Weibull distribution is given byF_\kappa(x) = 1 - \exp_\kappa(-\beta x^\alpha) valid for x \geq 0. The cumulative Wei ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Rate Parameter
In probability theory and statistics, a scale parameter is a special kind of numerical parameter of a parametric family of probability distributions. The larger the scale parameter, the more spread out the distribution. Definition If a family of probability distributions is such that there is a parameter ''s'' (and other parameters ''θ'') for which the cumulative distribution function satisfies :F(x;s,\theta) = F(x/s;1,\theta), \! then ''s'' is called a scale parameter, since its value determines the " scale" or statistical dispersion of the probability distribution. If ''s'' is large, then the distribution will be more spread out; if ''s'' is small then it will be more concentrated. If the probability density exists for all values of the complete parameter set, then the density (as a function of the scale parameter only) satisfies :f_s(x) = f(x/s)/s, \! where ''f'' is the density of a standardized version of the density, i.e. f(x) \equiv f_(x). An estimator of a scale p ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
