Unit-Exponentiated Lomax Distribution: Estimation and Regression Performance

What is it about?

The study proposes a new distribution, the unit-exponentiated Lomax (UEL) distribution, for modeling data on the unit interval. The UEL distribution's mathematical characteristics, such as moments, PWMs, IM, entropy measures, and S-S reliability, are explored. The maximum likelihood, Bayesian, and maximum product of spacing methods are employed for estimating the parameter of the suggested distribution. Results from simulations show that the criteria measurements of Bayesian estimates are preferred. The UEL regression model is demonstrated as a reasonable alternative to unit-Weibull regression, beta regression, and the original linear regression models using mock jurors and food spending data. The proposed model outperforms the beta, Kumaraswamy-Kumaraswamy, Topp-Leone generalized exponential, Marshall-Olkin Kumaraswamy, Topp-Leone Weibull Lomax, and type II power Topp-Leone inverse exponential across different comparison criteria when using Covid-19 data. Future research will discuss the application of UEL distribution based on these points.

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Why is it important?

This research is important because it proposes a new distribution, the unit-exponentiated Lomax (UEL) distribution, which is specifically designed to model data on the unit interval (0, 1). This has practical applications in various fields such as reliability, ecology, and economics, among others. By introducing the UEL distribution, the study extends the existing knowledge on Lomax distribution and its various applications. Key Takeaways: 1. The unit-exponentiated Lomax (UEL) distribution is a new distribution introduced for modeling data on the unit interval, extending the Lomax distribution's applicability. 2. The UEL distribution's characteristics, such as moments, PWMs, IM, entropy measures, and S-S reliability, are investigated. 3. Parameter estimation techniques like ML, MPS, and Bayesian methods are employed to estimate the UEL distribution's parameters. 4. The UEL distribution outperforms other unit distributions in various comparison criteria when applied to real-world data sets, showcasing its potential as an alternative model.