One of the most effective methods in speech recognition is the HMM which has been used to model speech statistically. The discrete distribution and the continuos distribution HMMs have been widely used in various applications. However, in recent years, HMMs with various output probability functions have been proposed to further improve recognition performance, e.g. the Gaussian mixture continuous and the semi-continuous distributed HMMs. We recently have also proposed the RBF (radial basis function)-based HMM and the VQ-distortion based HMM which use a RBF function and VQ-distortion measure at each state instead of an output probability density function used by traditional HMMs. In this paper, we describe the RBF-based HMM and the VQ-distortion based HMM and compare their performance with the discrete distributed, the Gaussian mixture distributed and the semi-continuous distributed HMMs based on their speech recognition performance rates through experiments on speaker-independent spoken digit recognition. Our results confirmed that the RBF-based and VQ-distortion based HMMs are more robust and superior to traditional HMMs.