Statistical Modelling with Applications in Forestry
Description
Developed for the following tasks. I) Computing the probability density function, cumulative distribution function, random generation, and estimating the parameters of the eleven mixture models including mixture of Birnbaum-Saunders, BurrXII, Chen, F, Frechet, gamma, Gompertz, log-logistic, log-normal, Lomax, and Weibull. II) Point estimation of the parameters of two- and three-parameter Weibull distributions. In the case of two-parameter, twelve methods consist of generalized least square type 1, generalized least square type 2, L-moment, maximum likelihood, logarithmic moment, moment, percentile, rank correlation, least square, weighted maximum likelihood, U-statistic, weighted least square are used and investigated methods for the three-parameter case are: maximum likelihood, modified moment type 1, modified moment type 2, modified moment type 3, modified maximum likelihood type 1, modified maximum likelihood type 2, modified maximum likelihood type 3, modified maximum likelihood type 4, moment, maximum product spacing, T-L moment, and weighted maximum likelihood. III) The Bayesian estimators of the three-parameter Weibull distribution. IV) Estimating parameters of the three-parameter Weibull distribution fitted to grouped data using three methods including approximated maximum likelihood, expectation maximization, and maximum likelihood. V) Estimating the parameters of the gamma, log-normal, and Weibull mixture models fitted to the grouped data through the EM algorithm. VI) Estimating parameters of the non-linear growth curve fitted to the height-diameter observations.