This article introduces a new circular distribution, the wrapped size-biased gamma Lindley distribution. The article elucidates the properties of this newly proposed distribution, providing explicit expressions for key statistical measures such as the characteristic function, trigonometric moments, resultant length, mean, circular variance, standard deviation, skewness, and kurtosis. Estimation of model parameters is conducted using the maximum likelihood and weighted least squares methods. Lastly, the article applies the model to real-world data and compares its goodness of fit against the established model in the existing literature.

We introduce a novel probability distribution that may be used to model both skewed and symmetric data. This new distribution, called the skew-symmetric Gudermanian-Laplace (SSGL) distribution, includes a shape parameter that allows it to change the asymmetry. Some fundamental statistical properties of the new distribution have been given explicit analytical expressions. The study also includes parameter estimations and simulation sections. We considered two datasets in the real-world data application. The first dataset is the "heights of 100 Australian athletes" data, which is discussed in many studies examining alternative skewed models. The second dataset contains the average wind speeds recorded by the İstanbul Çatalca meteorological observatory in January 2020. We showed that the SSGL distribution outperforms its well-known alternative, the Skew-Normal distribution, in both datasets. As a result of the study, it was concluded that the SSGL distribution is a suitable alternative for modeling skewed data.