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.

The coronavirus pandemic was a global health crisis taking away millions of lives worldwide. People diseased by the virus, differ in the extent of severity of the infection. While it turns out to be fatal for some, for several others the extent of severity is as ordinary as common cold. These people are reported to have recovered from the disease without hospitalization and consuming some relevant medicine and home remedies. But people who have comorbidity like geriatric, high blood pressure, heart and lung problems, diabetes, cancer etc. are at high risk of developing serious illness from the infection. This study is an application of the Cox proportional hazard model with an aim to identify the risk factors that affect the recovery time of the COVID-19 patients. The model is an advanced regression technique that can be utilized to evaluate simultaneously the effect of several factors on the possibility of instantaneous failure in patients. The paper also uses the Mantel-Haenszel test (Log-Rank test) to compare if the probability of survival of different treatment procedures or different groups of patients differ significantly. The information is collected from 129 respondents of Assam, India. The study identifies that the significant risk factors that prolong the recovery time from COVID-19 are pre-disease, location, and food habits.

This article introduces a novel class of skew-logistic distribution, providing flexibility to fit data with up to three modes. Various important properties of this new distribution are thoroughly examined, including its moment generating function, moments, entropy, and characterizations. Considering the location and scale parameters, a model extension and its parameter estimation technique are included. The study also includes a simulation study using the Metropolis--Hastings algorithm to observe the behavior of the estimated parameters. Furthermore, the adaptability and utility of the new model are assessed using three real-life datasets. Finally, a likelihood ratio test is applied to distinguish the introduced model from some other simpler models.