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

TL;DR

This paper introduces a power generalized class of Kavya-Manoharan distributions based on the exponential distribution, offering enhanced flexibility for reliability analysis and lifetime data modeling, supported by theoretical properties and real data application.

Contribution

It extends the Kavya-Manoharan distribution class via power generalization, creating a more flexible model with eleven submodels for lifetime data analysis.

Findings

The new distribution can model both monotonic and non-monotonic hazard rates.

Simulation confirms the maximum likelihood estimators are valid.

Real data application demonstrates the model's superiority.

Abstract

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, R\'enyi 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.