<p>Digital image watermarking technology has become a critical approach for safeguarding information security. The key performance metrics for evaluating watermarking algorithms include watermark capacity, robustness, and imperceptibility; however, these factors are often in tension with one another. Achieving an optimal balance among these factors remains a central challenge in watermarking algorithm research. This study presents an image watermarking algorithm founded on statistical principles, utilizing the vector bivariate generalized linear exponential (BGLE) distribution as its core model. To begin, we employ the undecimated dual-tree complex wavelet transform (UDTCWT) in conjunction with the improved polar harmonic Fourier moments (IPHFMs) transform to extract the UDTCWT-IPHFMs magnitude domain, which exhibits high resistance to attacks. The vector BGLE distribution is then used to model the magnitude domain of UDTCWT-IPHFMs, capturing the dependencies across different scales, directions, and subbands effectively. We apply the maximal evidential likelihood estimates (MELEs) method to estimate the model parameters. Leveraging the vector BGLE model, we construct a novel watermark decoder. To further enhance the security of the embedded information, we introduce an innovative dual watermarking technique based on the statistical modeling algorithm. The security is reinforced through mutual authentication between the authentication watermark and the target watermark. Experimental evaluations indicate that the proposed method successfully balances robustness, imperceptibility, and watermark capacity. Compared with existing state-of-the-art techniques, the performance of the constructed decoder in watermark extraction is significantly improved.</p>