In this study, product of two independent and non-identically distributed (i.n.i.d.) random variables (RVs) for κ-µ fading distribution and α-µ fading distribution is considered. The statistics of the product of RVs has been broadly applied in a large number of communications fields, such as cascaded fading channels, multiple input multiple output (MIMO) systems, radar communications and cognitive radios (CR). Exact close-form expressions of probability density function (PDF) and cumulative distribution function (CDF) with exact series formulas for the product of two i.n.i.d. fading distributions κ-µ and α-µ are deduced more accurately to represent the provided product expressions and generalized composite multipath shadowing models. Furthermore, ergodic channel capacity (ECC) is obtained to measure maximum fading channel capacity. At last, interestingly unlike κ-µ, η-µ, α-µ in [9], [17], [18], these analytical results are validated with Monte Carlo simulations and it shows that for provided κ-µ/α-µ model, non-linear parameter has more important influence than multipath component in PDF and CDF, and when the ratio between the total power of the dominant components and the total power of the scattered waves is same, higher α can significantly improve channel capacity over composite fading channels.