Cosine Topp–Leone family of distributions: Properties and Regression

ABSTRACT

The relevance of trigonometric distributions in modeling datasets is gaining a lot of interest in recent times because of their many desirable properties. This paper contributes to the area by introducing a new family of distributions called the cosine Topp–Leone family of distributions by combining the cosine-G family and the Topp–Leone generated family of distributions. The statistical properties of the new family such as the quantile function, moments, moment generating functions, incomplete moments, mean residual life, stress-strength reliability, and entropies are derived. The method of maximum likelihood estimation was used to estimate the parameters of the new family. The new family gave rise to the development of five additional distributions. The distributions exhibited left-skew, right-skew, increasing and decreasing shapes as well as monotonic and non-monotonic failure rates. A demonstration of the usefulness of the models revealed that the cosine Topp–Leone Weibull and the cosine Topp–Leone Cauchy distributions performed better than competing distributions using two real datasets. Finally, the log-cosine Topp–Leone Weibull regression model was developed and its applicability was demonstrated by using real datasets.

KEYWORDS:

• cosine-G family
• Topp–Leone-G family
• moments
• maximum likelihood estimation
• real datasets
• regression

Supplemental data

Supplemental data for this article can be accessed online at https://doi.org/10.1080/27684830.2023.2208935.

Acknowledgements

The authors would like to express their sincere gratitude to the editorial team for their contribution towards the publication of this research paper. We also thank the reviewers for their comments which improved the paper. The first author wishes to thank the University of Health and Allied Sciences, Ghana, for providing support for the research. The first author also wishes to acknowledge that, the results are part of his PHD research at the C.K. Tedam University of Technology and Applied Sciences, Ghana.

Disclosure statement

No potential conflict of interest was reported by the authors.

Additional information

Notes on contributors

Salifu Nanga

Salifu Nanga is doctoral candidate with the Department of Statistics and Actuarial Science, School of Mathematical Sciences, C. K. Tedam University of Technology and Applied Sciences, Navrongo, Ghana. He is also an Assistant Lecturer with the University of Health and Allied Sciences, Ho, Ghana. His research interest includes Distribution Theory, Survival Analysis and Population Studies.

Suleman Nasiru

Suleman Nasiru is an Associate Professor of Statistics with the Department of Statistics and Actuarial Science, School of Mathematical Sciences, C. K. Tedam University of Technology and Applied Sciences, Navrongo, Ghana. His research interest includes Distribution Theory, Quality Control and Time Series analysis.

Jakperik Dioggban

Jakperik Dioggban is a Senior Lectuer in Statistics with the Department of Biometry, School of Mathematical Sciences, C. K. Tedam University of Technology and Applied Sciences, Navrongo, Ghana. His research interest includes Sample Survey Theory, Experimental Design and Survival Analysis.