本文延續Baumol（1986）；DeLong（1988）；Barro and Sala-i-Martin（1992）的研究，討論台灣區域發展過程區域發展收斂現象，實證雖支持β收斂假說，但整體解釋力偏低。本文再以關聯結構（copula）方法，就機率的角度，進行收斂假說的探討。首先，估計核函數。根據區域所得的核修勻函數，發現台灣的邊沁式社會福利函數，符合一階隨機優勢理論。其次，利用機率探討區域收斂現象，建構期初所得與成長率的機率關係。由歷史資料的聯合機率結構顯示，區域發展存在否極泰來的可能性。相對低所得水準的區域，有相當大的機率（50%），可以高度成長，但亦存在33%的機率，維持相對貧窮的現狀；反之，相對高所得水準的區域，維持高度成長之機率極低。

This article follows the researches of Baumol (1986), DeLong (1988), Barro and Sala-i-Martin (1992), and discusses the regional convergent facts of Taiwan. The empirical results support the hypothesis of β convergence but the explanatory power is low. Copula methods are applied to explore this finding. This article tries to incorporate the probability function, which is different from the mean and variance estimation method. Firstly, kernel density estimation of regional income has been used to describe the income distribution. The Bentham type social welfare function of Taiwan conforms to the first-order stochastically dominance theory based on the region smoothing kernel function. Secondly, probability analysis has been applied to explore the convergent facts. With the probability analysis, the relationship between growth and initial income is constructed. From the regional development perspective, the joint probability of historical data confirms the possibility of ”out of the depth of misfortune comes bliss” meaning that there are chances for the poor to get out of the poverty. Poor counties have 50% probability to become better, but there are also 33% probabilities that they will stay at relative poverty. However, the growth rate of rich counties has low probability to surpass the current economical advantages.