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Pearson and log Pearson type III distributions have been considered inseveral scientific fields, as in hydrology and seismology. In this paper, wepresent new results for these distributions and we utilize them, for first timein the literature, to investigate the statistical behavior of wireless powertransfer (WPT), assuming that the harvested energy follows a well-establishednonlinear energy harvesting model based on the logistic function. Specifically,we present new closed-form expressions for the statistical properties of ageneral form of Pearson and log Pearson type III distributions and we utilizethem to introduce a new member of the Pearson type III family, the logitPearson type III distribution, through which the logit gamma distribution isalso defined. Moreover, we derive closed-form expressions for the probabilitydensity function, the cumulative distribution function and moments of thedistributions of the sum, the log sum and the logit sum of Pearson type IIIrandom variables. Furthermore, taking into account that Pearson type III familyof distributions is closely related to the considered nonlinear harvestingmodel the statistical properties of the distribution of the harvested power andderived, for both single input single output and multiple input single outputscenarios.

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