  Probability distributions which emerge from the formalism of nonextensive
statistical mechanics have been applied to a variety of problems. In this paper
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 in is proposed, as well.
