  This paper proposes a new Bayesian approach to estimate the Gini coefficient
from the Lorenz curve based on grouped data. The proposed approach assumes a
hypothetical income distribution and estimates the parameter by directly
working on the likelihood function implied by the Lorenz curve of the income
distribution from the grouped data. It inherits the advantages of two existing
approaches through which the Gini coefficient can be estimated more accurately
and a straightforward interpretation about the underlying income distribution
is provided. Since the likelihood function is implicitly defined, the
approximate Bayesian computational approach based on the sequential Monte Carlo
method is adopted. The usefulness of the proposed approach is illustrated
through the simulation study and the Japanese income data.
