This article deliberates a mathematical model for the estimation of speech signals probability density function. Speech recognition is analyzed using an integration of Boltzmann equations with Dirichlet Process Mixture sequences. Usually, environmental noise, white noise, echo noise interferes with the speech signal. So, the speech identification rate decreases abruptly. By estimating the noise sequences in the speech signal, the speech identification rate increases. Rather than using a conventional Gaussian Mixture Model (GMM) procedure to recognize a pure speech, an integration of mathematical equations of Boltzmann and Dirichlet Process Mixture is proposed in this article. An uttered speech signal is identified using mean, variance, and standard deviation generated by Boltzmann-DPM. For an added white, particle, shaver percentage of noises, the speech signal to noise ratio is improved and proved experimentally using the Nil filter, GMM filters, and Extended Kalman filter. © 2021 Elsevier B.V., All rights reserved.