BAYESIAN ESTIMATION OF BETA-TYPE DISTRIBUTIONPARAMETERS BASED ON GROUPED DATA

要約

This study considers the estimation method of generalized beta (GB) distribution parameters based on　grouped data from a Bayesian　point of view. Because the GB distribution, which was proposed by McDonald　and Xu (1995), includes several kinds of familiar　distributions as special or limiting cases, it performs at least　as well as those special or limiting distributions. Therefore, it is reasonable to estimate the parameters of the　GB distribution. However, when the number of groups is small or when the number of parameters increases,　it may become difficult to estimate the distribution parameters for grouped data using the existing estimation　methods. This study uses a Tailored randomized block Metropolis–Hastings (TaRBMH) algorithm proposed　by Chib and Ramamurthy (2010) to estimate the GB distribution parameters, and this method is applied to　one simulated and two real datasets. Moreover, the Gini coefficients from the estimated parameters for the　GB distribution are examined.