Statistical inference with modeling radiation data for a new extension of inverse unit exponential probability distribution

Despite numerous statistical distributions, many fail to adequately capture complex data patterns, emphasizing the need for more flexible models. This paper proposes a novel extension of the inverse unit exponential probability distribution, known as the power inverse unit exponential probability distribution, which was produced using power transformation. The quantile function, non-central moments, incomplete moments, moment-generating function, probability-weighted moments, Rényi entropy, and order statistics are all calculated. Parameter estimation employs different approaches. Monte Carlo simulations assessed the performance of the estimating methods. The results suggest that as the sample size increases, accuracy improves. Application to the radiation dataset demonstrates the model’s versatility and superiority over numerous existing distributions, including the inverse unit exponential probability distribution, hence improving statistical modeling capabilities.