The Tsallis entropy is an extension of the Shannon entropy and is used extensively in physics. The cumulative residual Tsallis entropy, which is a generalization of the Tsallis entropy, plays an important role in the measurement uncertainty of random variables and has simple relationships with other important information and reliability measures. In this paper, some novel properties of the cumulative residual Tsallis entropy are disclosed. Moreover, this entropy measure is applied to testing the uniformity, where the limit distribution and an approximation of the distribution of the test statistic are derived. In addition, the property of stability is discussed. Furthermore, the percentage points and power against seven alternative distributions of this test statistic are presented. Finally, to compare the power of the suggested test with that of other tests of uniformity, a simulation study is conducted.

In the present paper, we use the fractional and weighted cumulative residual entropy measures to test the uniformity. The limit distribution and an approximation of the distribution of the test statistic based on the fractional cumulative residual entropy are derived. Moreover, for this test statistic, percentage points and power against seven alternatives are reported. Finally, a simulation study is carried out to compare the power of the proposed tests and other tests of uniformity.

A pandemic caused by the novel coronavirus (COVID‐19) is causing an unprecedented situation for the world’s health services. Health, local communities, and government are adversely affected by the COVID‐19 pandemic. Moreover, on January 21, 2020, the WHO Emergency Committee declared a global health emergency because of increasing numbers of COVID‐19 case notifications from countries overseas. While the pandemic caused grave damage to socioeconomic phenomena and multiple global phenomena such as commodity prices, remittances, trade, tourism, significant job loss, and drastically lower wages, the pandemic has also negatively affected multiple global phenomena. The advent of technology has spurred significant changes in many aspects of our lives and improved the exchange of information, the presentation of data, and the management of medical resources through telemedicine. In this article, we present a mathematical data visualization approach for analyzing pandemic data behaviors, such as exponential growth and deviations using the data related to COVID‐19 events. Furthermore, this article will include studies on the implications of the COVID‐19 pandemic on finance sector.

Extropy, as a complementary dual of entropy, has been discussed in many works of literature, where it is declared for other measures as an extension of extropy. In this article, we obtain the extropy of generalized order statistics via its dual and give some examples from well‐known distributions. Furthermore, we study the residual and past extropy for such models. On the other hand, based on Farlie–Gumbel–Morgenstern distribution, we consider the residual extropy of concomitants of m‐generalized order statistics and present this measure with some additional features. In addition, we provide the upper bound and stochastic orders of it. Finally, nonparametric estimation of the residual extropy of concomitants of m‐generalized order statistics is included using simulated and real data connected with COVID‐19 virus.

In this paper, the Tsallis and Renyi extropy is presented as a continuous measure of information under the continuous distribution. Furthermore, the features and their connection to other information measures are introduced. Some stochastic comparisons and results on the order statistics and upper records are given. Moreover, some theorems about the maximum Tsallis and Renyi extropy are discussed. On the other hand, numerical results of the non-parametric estimation of Tsallis extropy are calculated for simulated and real data with application to time series model and its forecasting.

Motivated by the connotation of survival Rényi entropy and its related dynamic version, we introduce them in terms of their lower bounds and mean residual life function. Moreover, we illustrate the relation between survival Rényi entropy and some of measures of information. Furthermore, the hazard rate order implies ordering of dynamic survival Rényi entropy. Our models are considered a more comprehensive version of generalized order statistics and give some properties and characterization results. Finally, a non-parametric estimation of survival Rényi entropy is included based on real COVID-19 data and simulated data.