article · Axioms
Statistical distributions are widely used across multiple fields to model and predict real-world phenomena. A new statistical model, named the Kavya-Manoharan Kumaraswamy exponential (KMKE) distribution, has been introduced as an extension of the existing Kumaraswamy exponential framework. The mathematical foundation includes computed properties such as quantile functions, moments, incomplete moments, conditional moments, and moment generating functions. To estimate the parameters of the model, both classical maximum likelihood and Bayesian estimation techniques were applied and evaluated through simulation experiments to assess parameter accuracy. The model was also tested on two real datasets associated with food chains. The results demonstrate that the new distribution is highly flexible and outperforms several established distributions in fitting this type of data.
Real-world data often displays complex patterns that standard statistical models fail to capture accurately. By introducing a more adaptable mathematical framework, researchers and analysts can better model non-standard data distributions. This improved flexibility helps provide more accurate representations of real-world phenomena, as demonstrated by the distribution's effectiveness when applied to empirical food chain observations.
The model could enable more precise statistical analysis for data practitioners working with food supply chain information. It represents early-stage, theoretical mathematical research with initial testing on real-world datasets, but the abstract does not indicate any ready software implementation or direct pathway to commercial deployment.
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Statistical models are useful in explaining and forecasting real-world occurrences. Various extended distributions have been widely employed for modeling data in a variety of fields throughout the last few decades. In this article we introduce a new extension of the Kumaraswamy exponential (KE) model called the Kavya–Manoharan KE (KMKE) distribution. Some statistical and computational features of the KMKE distribution including the quantile (QUA) function, moments (MOms), incomplete MOms (INMOms), conditional MOms (COMOms) and MOm generating functions are computed. Classical maximum likelihood and Bayesian estimation approaches are employed to estimate the parameters of the KMKE model. The simulation experiment examines the accuracy of the model parameters by employing Bayesian and maximum likelihood estimation methods. We utilize two real datasets related to food chain data in this work to demonstrate the importance and flexibility of the proposed model. The new KMKE proposed distribution is very flexible, more so than numerous well-known distributions.
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DOI: 10.3390/axioms12040379
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