Length and Area Biased Exponentiated Weibull Distribution Based on Forest Inventories

Abstract

Length-biased and Area-biased distributions arise in many forestry applications, as well as other environmental, econometric, and biomedical sampling problems.We examine the Length-biased and Area-biased distributions versions of the Exponentiated Weibull distribution (EW).This study introduced a new distribution based on Length-biased Exponentiated Weibull distribution (LBEW) and Area-biased Exponentiated Weibull distribution (ABEW).Some characteristics of the new distributions were obtained.Plots for the cumulative distribution function, pdf and tables with values of skewness and kurtosis were also provided.Height-Diameter (H-D) data on Bombax and Pines (Pinus caribaea) were used to demonstrate the application of the distributions.Estimation of parameters of EW, LBEW and ABEW distributions were done using the maximum likelihood approach and compared across the distributions using criteria like AIC and Loglikelihood.We therefore proposed that similar to Exponentiated Weibull distribution (EW), a better fitting of Bombax and Pines H-D data are possible by LBEW and ABEW distributions.We hope in numerous fields of theoretical and applied sciences, the findings of this study will be useful for the practitioners.