A new class of cosine trigonometric lifetime distribution with applications

This work investigates a new class of statistical models and presents a specific example from this class. We created a new family of distributions using trigonometric functions, known as the cosine pie-power odd-G family. The paper details the fundamental properties of this proposed family of distributions. By using the Weibull distribution as the underlying model, we present a specific distribution within this family that exhibits various hazard function shapes, including bathtub, reverse-j, increasing, and j-shaped curves. The statistical characteristics of this new distribution are thoroughly analyzed. Parameters of the suggested distribution are determined using the maximum likelihood estimation (MLE) method. To verify the precision of this estimation process, Monte Carlo simulations are conducted, which show a decrease in biases and mean square errors as sample sizes increase, even when samples are small. To demonstrate the practical utility of the proposed distribution, two real-world datasets are analyzed. The performance of the proposed distribution model is assessed through various criteria of model selection and fitness results. Results from these assessments indicate that the recommended model execute better than seven other existing models.