Parameter estimation by fixed point of function of information processing intensity

We present a new method of estimating the dispersion of a distribution which is based on the surprising property of a function that measures information processing intensity. It turns out that this function has a maximum at its fixed point. Fixed-point equation is used to estimate the parameter of the distribution that is of interest to us. The main result consists in showing that only part of available experimental data is relevant for the parameters estimation process. We illustrate the estimation method by using the example of an exponential distribution.