Measures of inequality are used by economists to answer a wide range of questions. For example, sociologists are interested in the distribution of income. In this paper, the term "inequality" is used in a purely described sense. It is not intended to describe any message on the fairness of the differences in health geographically, as implied by the term "inequity". One of the famous measures is the Gini-style index. The Gini index is often described in terms of Lorenz curve. This measure is mainly used in the social science to evaluate the relationship between two variables. The index also provides appealing criteria without any unnecessary parametric assumptions about the specific form of the inequality index or the social welfare function. In spite of the disadvantage of the Gini index, the Gini index of multivariate variables is not well defined. Therefore, quantile regression (QR) is used in the paper.

QR proposed by Koenker (1978) is used to analyze the distribution and change of health practitioners in Taiwan between 1994 and 2000. The aspects of measuring the extreme and intermediate of a distribution have important meanings in many fields. Many studies have used the least squares estimator to predict interesting variable although the least squares estimator cannot describe the whole distribution sufficiently only depending on a mean equation. Besides, there is an impact on parameters solved by using the least square estimators which have higher sensitivities to extreme values. QR is avoided by the influence of extreme values. The QR of multivariate data is well defined. The distribution of health practitioners can be described completely by the distribution of practitioners at different quantiles. QR provides an alternative way to investigate the distribution of health manpower. It is interested to investigate that if inequalities reduce after applying the National Health Insurance (NHI).