A New Extension of Topp-Leone Distribution (NETD) Using Generalized Logarithmic Function

Anthony Anate Obafemi; Abubakar Usman; Ibrahim Abubakar Sadiq; Ubong Okon

doi:10.56919/usci.2434.011

Authors

Anthony Anate Obafemi Department of General Studies, Nigerian Institute of Leather and Science Technology, Zaria, Nigeria https://orcid.org/0009-0000-1600-5322
Abubakar Usman Department of Statistics, Faculty of Physical Sciences, Ahmadu Bello University, Zaria, Nigeria https://orcid.org/0000-0002-9104-1937
Ibrahim Abubakar Sadiq Department of Statistics, Faculty of Physical Sciences, Ahmadu Bello University, Zaria, Nigeria https://orcid.org/0000-0002-2122-9344
Ubong Okon Department of General Studies, Nigerian Institute of Leather and Science Technology, Zaria, Nigeria https://orcid.org/0009-0008-5528-8482

DOI:

https://doi.org/10.56919/usci.2434.011

Keywords:

New Extension, Topp-Leone Distribution, Logarithmic Function, Continuous Distribution

Abstract

Study’s Excerpt

New Extension of Topp-Leone Distribution (NETD), derived using a generalized logarithm function, expanding the Topp-Leone family of distributions, is introduced.
Mathematical properties of the NETD, including its quantile function, moments, Renyi entropy, and order statistics were investigated.
The model demonstrates superior goodness-of-fit over existing models across four real-world datasets.

Full Abstract

In this study, we introduce a novel statistical model termed the New Extension of Topp-Leone Distribution (NETD), constructed using a generalized logarithm function. The derivation of the cumulative density function (CDF) and the probability density function (PDF) for this new distribution is thoroughly detailed. A validity test was conducted to confirm the legitimacy of the proposed NETD, and the results affirm that it is indeed a valid probability distribution. We investigate several key mathematical and statistical properties of the NETD, including the quantile function, moments, Renyi entropy, probability-weighted moments, and order statistics. These properties provide a comprehensive understanding of the distribution's behaviour and characteristics. To estimate the parameters of the NETD, we applied the Maximum Likelihood Estimation (MLE) method, which is known for its efficiency and asymptotic properties. The flexibility, versatility, and performance of the NETD were evaluated using four diverse real-world datasets. Through the application of model selection criteria such as the Akaike Information Criterion (AIC), Bayesian Information Criterion (BIC), Corrected Akaike Information Criterion (CAIC), and Hannan-Quinn Information Criterion (HQIC), we demonstrated that the NETD exhibits superior goodness-of-fit compared to existing variants of the Topp-Leone distribution. Our findings suggest that the NETD is a robust and adaptable distribution, capable of effectively modelling a wide range of empirical data. This new extension not only broadens the applicability of the Topp-Leone family of distributions but also enhances the toolkit available for statistical analysis and modelling in various fields.

References

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A New Extension of Topp-Leone Distribution (NETD) Using Generalized Logarithmic Function

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