Probability distributions that emerge from the formalism of nonextensive statistical mechanics have been applied to a variety of problems. In this article we unite modeling of such distributions with the model of widespread 1/f noise. We propose a class of nonlinear stochastic differential equations giving both the q-exponential or q-Gaussian distributions of signal intensity, revealing long-range correlations and 1/f(beta) behavior of the power spectral density. The superstatistical framework to get 1/f(beta) noise with q-exponential and q-Gaussian distributions of the signal intensity is proposed, as well.
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