Two-parameter Kavya–Manoharan cosine inverse Rayleigh distribution: Statistical properties and application on radiation data

Abstract

A novel two-parameter probability distribution, termed the Kavya–Manoharan Cosine Inverse Rayleigh (TPKMCIR), is proposed in this paper, based on combining the inverse Rayleigh distribution with the cosine family and Kavya–Manoharan transform. This combination improves flexibility by representing a wider variety of asymmetric and heavy-tailed data. The basic statistical parameters of the proposed distribution such as the density function, cumulative function, survival and hazard function were derived. In addition to the quantile values, we studied moments, skewness, and kurtosis, to reveal the probabilistic behavior of the model under the various parameters. Using Monte Carlo simulation, varying sample sizes and different estimation approaches, eight different approaches were tested to determine the efficiency of parameter estimation methods. The simulation results showed that estimation accuracy improves as the sample grows in size, and it can be realized that MLE, LSE and WLSE exhibit competitive performance under several settings in terms of bias and mean squared error. From the model empirical comparison with multiple alternative distributions in the radiation-related susceptibility data in the applied data, the proposed model performs well in the empirical setting. Notably, it achieves the best values according to information-based criteria and remains competitive under common goodness-of-fit metrics. These results indicate that the TPKMCIR distribution proves to be a useful and flexible model for skewed lifetime-type data arising in radiation, reliability and related applied fields.