Wrapped Exponential Distribution Generalizations for Circular Data Analysis | ||
| Journal of the Egyptian Mathematical Society | ||
| Volume 32, Issue 1, 2024, Pages 57-82 PDF (1.68 M) | ||
| Document Type: Original Article | ||
| DOI: 10.21608/joems.2024.309359.1001 | ||
| Authors | ||
| Esmail Zinhom* 1; Manal Mohamed Nassar1; Ayat Elmasry1; Salwa Said Radwan2 | ||
| 1Department of Mathematics, Faculty of Science, Ain Shams University, Cairo, Egypt | ||
| 2Department of Mathematics, Faculty of Science Girls Section, Al-Azhar University, Cairo, Egypt | ||
| Abstract | ||
| Circular distributions play a crucial role in modeling data characterized by angular properties, offering indispensable tools for analyzing angles, phases, or periodic events. The versatility of these distributions is evident in their application across various domains. There are various strategies available for constructing circular distributions. The exponential distribution is one of the most important models for analyzing lifetime data. In this work, we discuss the wrapped exponential distribution and its properties. Furthermore, we propose three extensions to the wrapped exponential distribution based on the Marshall-Olkin, type I half logistic, and exponentiated generalized generators. We present several mathematical characteristics of these extensions and a unique linear representation of their densities. We investigate the maximum likelihood, least squares, and weighted least squares estimators of the unknown parameters and conduct a simulation study to evaluate their performance. Finally, we compare our novel models against the wrapped exponential and transmuted wrapped exponential distribution using real data in four applications. | ||
| Keywords | ||
| circular distributions; wrapped exponential; trigonometric moments; Marshal-Olkin family; exponentiated generalized family | ||
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