Summary: To explore the relationship between income inequality and economic development, and particularly to prove the existence of the S. Kuznets curve [“Economic growth and income inequality”, Am. Econ. Rev. 45, No. 1, 1–28 (1955), https://www.jstor.org/stable/1811581] in Thailand’s economy along these two decades, we propose the simultaneous smooth transition kink equations (SKE) model in which each regression parameter can be present in two different regimes, lower and upper. The regression coefficients split into two parts based on the unknown kink and smooth parameters in the logistic function. Thus, the model provides a flexible structure to capture and explain the relationship between income inequality and economic development following the inverted-U curve called the Kuznets curve. Also, we extend the analysis of the SKE model by modelling its nonlinear dependence structure through various Copula functions. Thus, the model becomes more flexible in coupling together the different marginal distributions. Before investigating the Kuznets curve, we conduct a simulation study to confirm the performance and accuracy of our proposed model. The satisfactory results are obtained from this simulation study as the estimated coefficient results are close to the true values under a wide array of simulated data models and distributions together with three smooth transition functions. Finally, according to the present empirical results, the Kuznets hypothesis does not hold at the country level, but it does for the North and Northeast regions. Also, our findings show alternative ways to reduce income inequality by increasing private sector contribution, GDP per capita, government expenditure and government subsidy. Additionally, this study applies the same method for investigating the Kuznets curve in the regions to answer the question ‘Are there regional Kuznets curves in Thailand?’ Our model shows some exciting results in income distribution in the different areas that may support the theory of Kuznets.