Abstract We examine the distribution characteristics of stock market liquidity by employing the generalized additive models for location, scale and shape (GAMLSS) model and three-minute frequency data from Chinese stock markets. We find that the BCPE distribution within the GAMLSS framework fits the distributions of stock market liquidity well with the diagnosis test. We also find that the stock market index exhibits a significant impact on the distributions of stock market liquidity. The stock market liquidity usually exhibits a positive skewness, but a normal distribution at a low level of stock market index and a high-peak and fat-tail shape at a high level of stock market index.