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Future wireless networks are expected to provide high spectral efficiency, low hardware cost, and scalable connectivity. An appealing option to meet these requirements is the intelligent reflective surface (IRS), which guarantees a smart propagation environment by adjusting the phase shift and direction of received signals. However, the composite channel of IRS-assisted wireless networks, which is composed of a direct link and cascaded link aided by the IRS, has made it challenging to carry out system design and analysis. This motivates us to find tractable and accurate channel modeling methods to model multiple types of channels. To this end, we adopt mixture Gamma distributions to model the direct link, the cascaded link, and the mixture channel. Moreover, this channel modeling method can be applied to various transmission environments with an arbitrary type of fading as the underlying fading of each link. Additionally, a unified stochastic geometric framework is introduced based on this tractable channel model. First, we derived distributions of the cascaded link and the mixture channel by proving multipliability and quadratic form of mixture Gamma distributed channels. Then, we carried out a stochastic geometric analysis of the system performance of the IRS-assisted wireless network with the proposed channel modeling method. Our simulation shows that the mixture Gamma distributed approximation method guarantees high accuracy and promotes the feasibility of system performance analysis of IRS-assisted networks with complicated propagation environments, especially with a generalized fading model. Furthermore, the proposed analytical framework provides positive insights into the system design regarding reliability and efficiency.