The impact of the COVID-19 pandemic on the mortality in Austria is investigated. A recent pre-pandemic generation life table is developed. Using this pre-pandemic life table, the expected number of deaths for the years 2020 to 2023 is derived. Comparing the expected number of deaths to the observed number of deaths during the pandemic years yields the excess mortality for Austria in the years 2020 to 2023. The Austrian life table can be adjusted to the Austrian federal states, yielding for each Austrian federal state the excess mortality for the pandemic years. The excess mortality varies substantially across federal states and during the pandemic years. The results are discussed against some state-specific health-related and economic quantities, yielding correlations of excess mortality with age, medical care, economic quantities, and COVID-19 related quantities.

In this manuscript, we proposed a new extension of the Rayleigh distribution named as MTI Rayleigh distribution (MTIRD) that provides better fits than the Rayleigh distribution and some of its known generalizations. Various properties of the proposed distribution, including moments, moment generating function, hazard rate, conditional moments, Bonferroni and Lorenz curve, mean residual life, mean waiting time, Renyi entropy and order statistics are derived. Maximum likelihood estimation procedure is employed to estimate the unknown parameters. An extensive simulation study is carried out to illustrate the behaviour of MLEs on the basis of Mean Square Errors. The flexibility of the new distribution is assessed by applying it to two real data sets of COVID-19 mortality. The comparative behaviour of MTIRD with Rayleigh distribution, Power Rayleigh distribution, Transmuted Rayleigh distribution, Exponentiated Rayleigh distribution, Weibull Rayleigh distribution provided the evidence that it outperforms the other competing distributions based on Akaike Information Criterion, Bayesian Information Criterion, Akaike Information criterion Corrected, and other goodness of fit measures.

Grain producers in Brazil often depend on third-party services for the transportation, processing and storage of their production, as, for the most part, they do not have silos on their properties. In this context, efficient logistics is essential to optimize processes and increase reliability between customers and service providers. This study focuses on the logistical analysis of truck traffic at two grain processing plants, examining different receiving protocols to evaluate internal vehicle flow during peak production conditions. The data is analyzed using a multiple regression model with two systematic components based on the proposed New Weibull inverse Gaussian distribution. The research is conducted in grain processing and storage units in the southwest region of São Paulo-SP, belonging to an agro-industrial cooperative. The study monitors all stages of soybean receipt during the peak harvest month, in March 2020. The results indicate the dependence of service times on the sector's logistical variables. This research addresses the pressing need for efficient logistics in the grain industry, especially in soybean processing. By focusing on truck traffic and receiving protocols, the study aims to provide a better understanding to optimize internal logistics processes, thus contributing to improving operational efficiency and customer service in grain processing units.

One-inflation in zero-truncated count data has recently found considerable attention. In this regard, zero-truncated Geometric distribution and distribution to a point mass at one are used to create a one-inflated model, namely, one-inflated zero-truncated Geometric distribution. Its reliability characteristics, generating functions, and distributional properties are investigated in detail, which includes survival function, hazard rate function, reverse hazard rate function, probability generating function, characteristic function, variance, skewness, and kurtosis. Monte Carlo simulation have been undertaken to evaluate the effectiveness of the maximum likelihood estimators. To test the compatibility of our proposed model, the baseline model and the proposed model are distinguished by using the two different test procedures. The adaptability of the suggested model is demonstrated using two real-life datasets from separate domains by taking various performance measures into consideration.

We propose an original classification of several discrete and continuous probability distributions. We establish links between these distributions, in particular the little known relationship between the negative hypergeometric distribution and the beta distribution. These relations allow us to propose a structure of relations which is summarized in graphic form.Our classification emphasises the analogy between certain discrete and continuous distributions. This analogy makes it possible to establish relations between the theory of point processes and the theory of survey sampling. It also makes it possible to envisage the use of link functions that are little used in generalised regression.

In this paper, we apply the Ranked Set Sampling (RSS) technique to economic data in the form of homescan market research data set for the meat food group. The RSS method is then extended to select sampling units based on the Probability-Proportional-to-Size (PPS) approach. The new proposed ranked set sampling, using the PPS-derived method, RPPS, is assessed via Monte Carlo investigations and an extensive homescan data set to evaluate its performances. The results are promising and in line with theoretical and simulation studies, showing that the RPPS technique is more reliable and has a smaller variance than the PPS route.

Extensions of the Autoregressive Moving Average, ARMA(p, q), class for modeling non-Gaussian time series have been proposed in the literature in recent years, being applied in phenomena such as counts and rates. One of them is the Generalized Autoregressive Moving Average, GARMA(p, q), that is supported by the Generalized Linear Models theory and has been studied under the Bayesian perspective. This paper aimed to study models for time series of counts using the Poisson, Negative binomial and Poisson inverse Gaussian distributions, and adopting the Bayesian framework. To do so, we carried out a simulation study and, in addition, we showed a practical application and evaluation of these models by using a set of real data, corresponding to the number of vehicle thefts in Brazil.

The half-logistic (HL) distribution is a widely considered statistical model for studying lifetime phenomena arising in science, engineering, finance, and biomedical sciences. One of its weaknesses is that it has a decreasing probability density function and an increasing hazard rate function only. Due to that, researchers have been modifying the HL distribution to have more functional ability. This article provides an extensive overview of the HL distribution and its generalization (or extensions). The recent advancements regarding the HL distribution have led to numerous results in modern theory and statistical computing techniques across science and engineering. This work extended the body of literature in a summarized way to clarify some of the states of knowledge, potentials, and important roles played by the HL distribution and related models in probability theory and statistical studies in various areas and applications. In particular, at least sixty-seven flexible extensions of the HL distribution have been proposed in the past few years. We give a brief introduction to these distributions, emphasizing model parameters, properties derived, and the estimation method. Conclusively, there is no doubt that this summary could create a consensus between various related results in both theory and applications of the HL-related models to develop an interest in future studies.

The notion of ageing plays an important role in reliability and survival analysis as it is an inherent property of all systems and products. Jiang, Ji, and Xiao (2003) proposed a new quantitative measure, known as ageing intensity (AI) function, an alternative measureto study the ageing pattern of probability models. In this paper, we propose a nonparametric estimator for ageing intensity function. Asymptotic properties of the estimator are established under suitable regularity conditions. A set of simulation studies are carriedout based on various probability models to examine the performance of estimator and to establish its efficiency over the classical estimator. The usefulness of the estimator is also examined through a real data set.

This work focusses on estimation the standard deviation (SD) and coefficient of variation (CV) in the normal distribution. These two measures are useful in applications and widely used to report the spread or variability of continuous data. We develop the confidence intervals for these parameters using the two pivotal quantity methods with the unbiased estimator of SD. The first confidence interval uses the pivot function based on a chi-square distribution and the second one is based on a generalized pivotal quantity. The performance of our approaches is conducted via simulations. We show that the confidence intervals for SD and CV based on the new pivots have coverage probabilities greater than existing confidence intervals. Furthermore, they have acceptable short expected lengths. We also provide two real-data sets on the SET50 index of Thailand to demonstrate the proposed methods.