Power new generalized class of Kavya-Manoharan distributions with an application to exponential distribution

Recently, Verma et al. (2025) introduced a novel generalized class of Kavya-Manoharan distributions, which have demonstrated significant utility in reliability analysis and the modeling of lifetime data. This paper proposes an extension of this class by applying the power generalization technique, thereby enhancing more flexibility and applicability. We take the exponential distribution as the baseline distribution to introduce a new model capable of accommodating both monotonic and non-monotonic hazard rate functions. Our model includes eleven submodels. We present several statistical properties of the introduced model, including moments, generating and characteristic functions, mean deviations, quantile function, mean residual life function, Rényi entropy, order statistics, and reliability. To estimate the unknown model parameters, we use the maximum likelihood approach. A simulation study is conducted to assess the validity of the maximum likelihood estimator. The superiority of the new distribution is demonstrated through the use of a real data application.