New Results for Pearson Type III Family of Distributions and Application in Wireless Power Transfer

Pearson and log Pearson type III distributions have been considered in several scientific fields, as in hydrology and seismology. In this paper, we present new results for these distributions and we utilize them, for first time in the literature, to investigate the statistical behavior of wireless power transfer (WPT), assuming that the harvested energy follows a well-established nonlinear energy harvesting model based on the logistic function. Specifically, we present new closed-form expressions for the statistical properties of a general form of Pearson and log Pearson type III distributions and we utilize them to introduce a new member of the Pearson type III family, the logit Pearson type III distribution, through which the logit gamma distribution is also defined. Moreover, we derive closed-form expressions for the probability density function, the cumulative distribution function and moments of the distributions of the sum, the log sum and the logit sum of Pearson type III random variables. Furthermore, taking into account that Pearson type III family of distributions is closely related to the considered nonlinear harvesting model the statistical properties of the distribution of the harvested power and derived, for both single input single output and multiple input single output scenarios.