New probability density function for biopopulations modelling

Abstract

Background: Biological populations were studied to understand their ecology and to evaluate the relationships between living beings that comprise them. Mathematical functions used in probabilistic models should present multifunctionality, sensitivity, and flexibility to appropriately describe a natural phenomenon. The objective of this study was to develop a new probabilistic distribution with five parameters to maximize its flexibility and ensure a better goodness of fit when compared to other important distributions, such as Beta, Burr, Silva and Pareto.

Methods: New distribution estimators were derived using the mathematical expectation of central and dispersion moments. Estimated values of the parameters were obtained using an optimization process developed by Abel Soares Siqueira, research software engineer at the Netherlands eScience Center in Amsterdam. Data for the application of the developed distribution method were collected at different sites in Brazil, where asymmetry and kurtosis were detected.

Results: The Pellico-Behling Probability Distribution (5P) was applied to fit the datasets for Cariniana legalis, Acacia mearnsii, and Eucalyptus saligna. For the average mortality of 124 species, it was used with (4P). The distribution fitted to sampled datasets was compared with the fitted Beta and Burr (4P) distributions, except for Silva’s polynomial distribution that was fitted to the heights of the species Eucalyptus saligna and the Pareto distribution to mortality of 124 tropical species from a fragment of a semideciduous seasonal forest, to evaluate and verify its potential and robustness.

Conclusions: The new distribution with five parameters is flexible and produced better goodness of fit than those obtained from the other distributions used for comparative purposes.