A new class of probability distributions via cosine and sine functions with applications

ABSTRACT

In this paper, we introduce a new class of (probability) distributions, based on a cosine-sine transformation, obtained by compounding a baseline distribution with cosine and sine functions. Some of its properties are explored. A special focus is given to a particular cosine-sine transformation using the exponential distribution as baseline. Estimations of parameters of a particular cosine-sine exponential distribution are performed via the maximum likelihood estimation method. A simulation study investigates the performances of these estimates. Applications are given for four real data sets, showing a better fit in comparison to some existing distributions based on some goodness-of-fit tests.

KEYWORDS:

• Cosine-sine transformation
• Estimation
• Goodness-of-fit statistics
• Hazard rate function
• Statistical distributions

MATHEMATICS SUBJECT CLASSIFICATION:

• 2000 MSC
• 60E05
• 62E15
• 62F10

Acknowledgements

We thank the reviewers for providing comments that helped us to improve the presentation of our work.