A generalized distribution interpolated between the exponential and power law distributions and applied to pill bug (Armadillidium vulgare) walking data

The walking pattern of an organism is typically designated as either a Lévy walk or a Brownian walk based on whether the frequency distribution of its linear step lengths follows a power law distribution or an exponential distribution. However, there are many cases where actual data cannot be classified into either of these categories. In this paper, we propose a general distribution that includes the power law and exponential distributions as special cases. This distribution has two parameters: one parameter represents the exponent, similar to the power law and exponential distributions, and the other is a shape parameter representing the shape of the distribution. By introducing this distribution, an intermediate distribution model can be interpolated between the power law and exponential distributions. In this study, the proposed distribution was fitted to the frequency distribution of the step length calculated from the walking data of pill bugs. The autocorrelation coefficients wer...