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There exists considerable interest in the probabilistic modeling of economic variables to compute financial estimates with the least possible uncertainty. Most studies are based on symmetric probability distributions, specifically on the normal distribution; however, empirical evidence indicates that the probability distributions of variables such as economic returns present a certain degree of skewness. Therefore, the main issue in this paper is to propose a probability distribution which provides a good fit to economic returns. In particular, this article focuses on the analysis of the economic returns of the Mexican S&PBMV IPC Index, and it is found that the skew-t distribution might be a plausible model for this variable. A new probability property of the skew-t family of distributions is introduced here, and it is used to propose a procedure for testing the skew-t distribution hypothesis. The results of a Monte Carlo simulation study conducted in order to study the power properties of this test are also presented.

The usual ways to increase the capital in a corporation are convertible debt offerings, rights issues and new shares issues, which make the announcement effects in the financial market. This paper focuses on the announcement effects of new shares issues during the financial crisis, and event study is used to analyze the announcement effects. The data are collected from 100 firms in Shanghai stock exchange market and Nyse stock exchange market in 2008 to show the announcement effects of new shares issues existed during this crisis period. In addition, the reasons of the announcement effects during the crisis period are discussed in these two different financial markets.

Keywords: Announcement Effects, New Shares Issues, Financial Crisis, Event Study.

In this paper, an extension of the Chen distribution is defined. The new distribution is based on the odd-log-logistic-G family of distributions, which adds an extra shape parameter to the baseline distribution. Here, the proposed distribution is called odd-log-logistic-Chen. Some properties have been defined. A regression model with parameterization on the median is also proposed. The maximum likelihood method is used to estimate the unknown parameters. The accuracy of the maximum likelihood estimators is shown through Monte Carlo simulations. The usefulness of the new model is shown with three applications to real uncensored data, the odd-log-logistic-Chen distribution being better than other three models known in the literature. From the defined regression model, an application to censored data of laryngeal cancer is also considered.

Keywords: Chen distribution; bimodal distribution; regression model; maximum likelihood; quantile function; Monte Carlo simulation; failure rate function

In this paper, from the inverse Weibull distribution, a new bi-parametric distribution is proposed. This new distribution has support in (0, 1), being an alternative to other distributions for double limited data analysis. Based on this distribution, a regression model is proposed. This model has a regression structure at the median and is called the unit inverse Weibull regression model. The maximum likelihood method is used to obtain the estimates of the unknown parameters. Analytical expressions for the score vector and for the Fisher observed information matrix are performed. The good performance of the maximum likelihood estimators, for the proposed model, is demonstrated through Monte Carlo simulations. The usefulness of the model is shown through an application to real data. In this application, the proposed model is superior to beta, Kumaraswamy and unit Weibull regression models.

Keywords: Unit inverse Weibull; Quantile function; Maximum likelihood; Regression model; Monte Carlo simulation
Mathematical Subject Classification 2010: 60E05, 62F12, 65C05, 65C10, 62Jxx

Analysing the mass of time series data accumulating from the COVID-19 coronavirus pandemic has become increasingly important as the pandemic has progressed through its numerous phases.  This paper investigates the changing dynamic relationship between infections, hospital admissions and deaths using daily data from regions and age groups from England using balanced growth models.  It is found that there has been a substantial decrease over time in the number of deaths and hospital admissions associated with an increase in infections as clinical practice has improved, and the vaccination program rolled out.  These responses may be tracked and monitored through time to ascertain whether such improvements have been maintained.

The objective of this paper is to provide insights on some widely used Panel Data Econometric Models to determine the best one. With this aim, data of Organized Manufacturing Sector from the Annual Survey of Industries has been used. Pooled OLS, First-Difference, Time-Demeaning and Random Effects models have been estimated using a sample of 26 states, over an 18-year period (2000-2017), where Input Variables are in a non-linear relationship with Total Output. The findings of the study recommend that in a panel setting the most robust model is the Time-Demeaning Fixed Effects model.

Keywords: Annual Survey of Industries; Fixed Effects; Panel Data; Pooled OLS; R; Random Effects

A modified upside-down bathtub-shaped hazard function distribution that we have recommended in this study is created by modifyinga three-parameter life-time distribution. The skewness, and kurtosis measures, quantile function, survival function, hazard rate function, the probability density function, and  cumulative distribution function are only a few of the mathematical and statistical properties of the distribution that we have been covered.Utilizing MLE, LSE, and CVME approaches, the model parameters of the suggested model are estimated. The suggested model's goodness of fit is also assessed by fitting it against a number of other life-time models using two real data sets.

Keywords: Modified distribution, Maximum likelihood estimation, Quantile function, Reliability function,