This study presents a novel method for diagnosing respiratory diseases using image data. It combines Epanechnikov's non-parametric kernel density estimation (EKDE) with a bimodal logistic regression classifier in a statistical-model-based learning scheme. EKDE's flexibility in modeling data distributions without assuming specific shapes and its adaptability to pixel intensity variations make it valuable for extracting key features from medical images. The method was tested on 13808 randomly selected chest X-rays from the COVID-19 Radiography Dataset, achieved an accuracy of 70.14%, a sensitivity of 59.26%, and a specificity of 74.18%, demonstrating moderate performance in detecting respiratory disease while showing room for improvement in sensitivity. While clinical expertise remains essential for further refining the model, this study highlights the potential of EKDE-based approaches to enhance diagnostic accuracy and reliability in medical imaging.