In this paper, we develop a framework to assess the perceptual quality of Virtual Reality (VR) images by studying the joint dependencies between luminance and disparity pairs using Bivariate Generalized Gaussian Distribution (BGGD) model. We compute model parameters ($\alpha,\ \beta$) of BGGD at multi-scale and multi-orient steerable pyramid decomposition of the cube map projection (CMP) faces of both left and right views of a VR image. We learn Multivariate Gaussian (MVG) model parameters from BGGD features of CMP faces of pristine images as a reference quality representative. We compute Mahalanobis distance between pristine MVG model parameters and distorted image BGGD features to estimate the joint luminance and disparity quality score of a CMP face of a test VR image. We generate an inner map from saliency and phase congruency maps of CMP faces of both left and right views of a VR image. We compute entropy scores of the inner map to pool the joint luminance and disparity quality score of a VR image. Further, we apply IL-NIQE model on CMP faces to derive the overall spatial quality score of a test VR image. Finally, we pool the spatial IL-NIQE score and CMP face level quality score to estimate the overall quality score of a test VR image. The proposed model, dubbed Blind Virtual Reality Image Quality Evaluator (BVRIQE) delivered a consistent performance across all distortion types of the LIVE 3D VR IQA dataset.