  To know the statistical distribution of a variable is an important problem in
management of resources. Distributions of the power law type are observed in
many real systems. However power law distributions have an infinite variance
and thus can not be used as a standard distribution. Normally professionals in
the area use normal distribution with variable parameters or some other
approximate distribution like Gumbel, Wakeby, or Pareto, which has limited
validity.
  Tsallis presented a microscopic theory of power law in the framework of
non-extensive thermodynamics considering long-range interactions or long
memory. In the present work, we consider softing of long-range interactions or
memory and presented a generalized distribution which have finite variance and
can be used as a standard distribution for all real complex systems with power
law behaviour. We applied this distribution for a financial system, rain
precipitation and some geophysical and social systems. We found a good
agreement for entire range in all cases for the probability density function
(pdf) as well as the accumulated probability. This distribution shows universal
nature of the size limiting in real systems.
