In the current scenario, the outbreak of a pandemic disease COVID-19 is of great interest. A broad statistical analysis of this event is still to come, but it is immediately needed to evaluate the disease dynamics in order to arrange the appropriate quarantine activities, to estimate the required number of places in hospitals, the level of individual protection, the rate of isolation of infected persons, and among others. In this article, we provide a convenient method of data comparison that can be helpful for both the governmental and private organizations. Up to date, facts and figures of the total the confirmed cases, daily confirmed cases, total deaths, and daily deaths that have been reported in the Asian countries are provided. Furthermore, a statistical model is suggested to provide a best description of the COVID-19 total death data in the Asian countries.

Proportional hazard (PH) models can be formulated with or without assuming a probability distribution for survival times. The former assumption leads to parametric models, whereas the latter leads to the semi-parametric Cox model which is by far the most popular in survival analysis. However, a parametric model may lead to more efficient estimates than the Cox model under certain conditions. Only a few parametric models are closed under the PH assumption, the most common of which is the Weibull that accommodates only monotone hazard functions. We propose a generalization of the log-logistic distribution that belongs to the PH family. It has properties similar to those of log-logistic, and approaches the Weibull in the limit. These features enable it to handle both monotone and nonmonotone hazard functions. Application to four data sets and a simulation study revealed that the model could potentially be very useful in adequately describing different types of time-to-event data.

In the present study, a new class of heavy tailed distributions using the T-X family approach is introduced. The proposed family is called type-I heavy tailed family. A special model of the proposed class, named Type-I Heavy Tailed Weibull (TI-HTW) model is studied in detail. We adopt the approach of maximum likelihood estimation for estimating its parameters, and assess the maximum likelihood performance based on biases and mean squared errors via a Monte Carlo simulation framework. Actuarial quantities such as value at risk and tail value at risk are derived. A simulation study for these actuarial measures is conducted, proving that the proposed TI-HTW is a heavy-tailed model. Finally, we provide a comparative study to illustrate the proposed method by analyzing three real data sets from different disciplines such as reliability engineering, bio-medical and financial sciences. The analytical results of the new TI-HTW model are compared with the Weibull and some other non-nested distributions. The Baysesian analysis is discussed to measure the model complexity based on the deviance information criterion.

Statistical distributions play a prominent role in applied sciences, particularly in biomedical sciences. The medical data sets are generally skewed to the right, and skewed distributions can be used quite effectively to model such data sets. In the present study, therefore, we propose a new family of distributions to model right skewed medical data sets. The proposed family may be named as a flexible reduced logarithmic-X family. The proposed family can be obtained via reparameterizing the exponentiated Kumaraswamy G-logarithmic family and the alpha logarithmic family of distributions. A special submodel of the proposed family called, a flexible reduced logarithmic-Weibull distribution, is discussed in detail. Some mathematical properties of the proposed family and certain related characterization results are presented. The maximum likelihood estimators of the model parameters are obtained. A brief Monte Carlo simulation study is done to evaluate the performance of these estimators. Finally, for the illustrative purposes, three applications from biomedical sciences are analyzed and the goodness of fit of the proposed distribution is compared to some well-known competitors.

Marketing means the strategies and tactics an organization undertakes for attracting consumers to promote the buying or selling of a product or service. Active marketing is about receiving messages from potential buyers to create ways to influence their purchasing decisions. Advertising is one of the most prominent marketing strategies to promote products to consumers. It is well known that advertisement has a significant impact on the sale of certain goods or services. In this paper, we consider two mediums of advertisement, such as Facebook (which is an online medium) and Newspaper (which is a printed medium). We consider a dataset representing the advertising budget (in hundreds of US dollars) of an electronic company and the sales of that company. We apply the quantitative research approach, and the data which are used in this research are secondary data. For analysis purposes, we consider a statistical tool called simple linear regression modeling. To check the significance of the advertising on sale, definite statistical tests are applied. Based on the findings of this research, it is observed that advertising has a significant impact on sales. It is also showed that spending money on advertising through Facebook has better sales than newspapers. The finding of this research shows that the use of computer-based technologies and online mediums has a brighter future for advertising. Furthermore, a new statistical model is introduced using the Z family approach. The proposed model is very interesting and possesses heavy-tailed properties. Finally, the applicability of the proposed model is illustrated by considering the financial dataset.