  Starting from the developed generalized point process model of $1/f$ noise
(B. Kaulakys et al, Phys. Rev. E 71 (2005) 051105; cond-mat/0504025) we derive
the nonlinear stochastic differential equations for the signal exhibiting
1/f^{\beta}$ noise and $1/x^{\lambda}$ distribution density of the signal
intensity with different values of $\beta$ and $\lambda$. The processes with
$1/f^{\beta}$ are demonstrated by the numerical solution of the derived
equations with the appropriate restriction of the diffusion of the signal in
some finite interval. The proposed consideration may be used for modeling and
analysis of stochastic processes in different systems with the power-law
distributions, long-range memory or with the elements of self-organization.
