A multimodal skewed extension of normal distribution is proposed by applying the general method as in [Huang WJ, Chen YH. Generalized skew-Cauchy distribution. Stat Probab Lett. 2007;77:1137–1147] for the construction of skew-symmetric distributions by using a trigonometric periodic skew function. Some of its distributional properties are investigated. Properties of maximum likelihood estimation of the parameters are studied numerically by simulation. The suitability of the proposed distribution in empirical data modelling is investigated by carrying out comparative fitting of two real-life data sets.

In this paper a new type of alpha skew distribution is proposed under Balakrishnan (2002) Mechanism and some of its related distributions are investigated. The moments and distributional properties and some extensions related to this distribution are also studied. Suitability of the proposed distribution is tested by conducting data fitting experiments and model adequacy is checked via AIC and BIC in comparison with some related distributions. Likelihood ratio test is carried out to discriminate between normal and proposed distribution.

This paper considers a new family of the trimodal skew logistic distributions. Some properties of this distribution, including moments, moments generating function, entropy, maximum likelihood estimates of parameters and some other properties, are presented. A simulation study is conducted to examine the performance of the parameters. Numerical optimization is carried out via two real-life datasets. Results show that the new distribution is better fitted in terms of these datasets among logistic, skew logistic and alpha skew logistic distributions based on the value of AIC and BIC.

This article introduces a novel family of skew distributions namely Bimodal Tanh Skew Normal (BTSN)distributions, which incorporates a new skew function with the help of hyperbolic tangent function. Thisnew distribution is designed to accommodate data sets with two modes. Besides, the article presents variousessential mathematical properties, such as moments, moment generating function, characteristic function,mean deviation, characterizations and the method for maximum likelihood estimation of this distribution.A simulation study is also conducted using Metropolis–Hastings algorithm to examine the behavior of theobtained parameters. Furthermore, the practical utility of this new distribution is demonstrated througha real life application involving a specific data set. To assess the suitability of the BTSN distribution, thearticle employs Akaike information criterion (AIC) and Bayesian information criterion (BIC). Finally, alikelihood ratio test is conducted to distinguish between the new model and the existing competing models.

In this article, a new extension of the standard Laplace distribution is introduced for house price modeling. Certain important properties of the new distribution are deducted throughout this study. We used the new extension of the Laplace model to conduct a thorough economic risk assessment utilizing several metrics, including the value-at-risk (VaR), the peaks over a random threshold value-at-risk (PORT-VaR), the tail value-at-risk (TVaR), the mean of order-P (MO^P), and the peaks over a random threshold based on the mean of order-P (PORT-MO^P). These metrics capture different facets of the tail behavior, which is essential for comprehending the extreme median values in the Boston house price data. Notably, PORT-VaR improves the risk evaluations by incorporating randomness into the selection of the thresholds, whereas VaR and TVaR focus on measuring the potential losses at specific confidence levels, with TVaR offering insights into significant tail risks. The MO^P method aids in balancing the reliability goals while optimizing the performance in the face of uncertainty.