A Weighted Cosine Exponential Distribution with Application

The Weighted Cosine Exponential Distribution (WCED) is proposed as a novel lifetime model, incorporating a trigonometric weighting mechanism into the exponential distribution to enhance flexibility and capture complex hazard behaviors, particularly the inverted bathtub shape common in reliability and survival analysis. Fundamental statistical properties are derived. A simulation study evaluates five estimation methods (MLE, MME, OLS, WLS, CVM), showing improved accuracy with larger samples. Applied to three cancer survival datasets, WCED demonstrates superior fit over existing weighted distributions, evidenced by lower information criteria (AIC, AICC, HQIC) and higher statistical significance. The model offers a parsimonious and adaptable tool for analyzing lifetime data with nonmonotonic failure patterns, proving valuable for reliability engineering and biomedical applications.