Size-biased distributions in the generalized beta distribution family, with applications to forestry

Size-biased distributions arise in many forestry applications, as well as other environmental, econometric, and biomedical sampling problems. We examine the size-biased versions of the generalized beta of the first kind, generalized beta of the second kind and generalized gamma distributions. These distributions include, as special cases, the Dagum (Burr Type III), Singh-Maddala (Burr Type XII) and Fisk distributions as well as better-studied distributions such as the Weibull, lognormal, beta (of the first and second kind), gamma and exponential. Our results indicate that specification and estimation of the size-biased forms of these distributions can be viewed within a unified framework. This should facilitate broader application of size-biased distributions in forestry sampling, modeling and analysis.