γ = 1 equals 1.010836, which means that the relative error of this value is approx. 1.08%. We estimated the parameter in
question with greater accuracy both for the right and left fixed point by using only a part of the data.
The codes of programs that calculate the experimental values of the ρ function are presented in the appendices.
562 R. Jankowski et al. / Physica A 416 (2014) 558–563
Fig. 2. The part of the graph of theoretical (continuous line) and experimental (points) left intensity function ρ(b), b ∈ [0, 1].
5. Conclusion
In this paper we analysed a new method of estimating a distribution parameter by using the function of information
processing intensity as well as its property, i.e. a maximum at the fixed point. Theorem 1 also has other interesting
applications [5–9].
What is characteristic of the method we have presented is that when calculating the function of information processing
intensity (both on the left and on the right), only those values which meet the condition specified by the cut-off parameter
are used. Therefore, only a part of the available data influences the final result.
The presented method of parameter estimation based on the intensity of the random variable intercept resembles,
because of the extreme properties of the fixed point, a popular approach to this problem, such as the maximum likelihood
estimate or the Bayesian most probable estimate. However, in contrast to those method its interpretation does not require
direct calls to the typical (most probable) measurement situation. Here we are dealing with the most favourable cutting of
the distribution and not the most probable statistical hypothesis.