Cosine Topp–Leone family of distributions: Properties and Regression

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.