This study reveals that increases in the global population command an augmented demand for products and services that calls for more effective ways of using existing natural resources and materials. The recent development of information and communication technologies, which had a great impact on many areas, also had a damaging effect on the environment and human health. Therefore, societies are moving toward a greener future by reducing the consumption of nonrenewable materials, raw materials, and resources while at the same time decreasing energy pollution and consumption. Since information technology is considered a tool for solving ecological difficulties, the green Internet of things (G-IoT) is playing a vital role in creating a sustainable home. Extensive data analysis is required to obtain a valuable overview of the large and diverse data generated by the G-IoT. The gathered information will facilitate forecasting, decision-making, and other activities related to smart urban services and then contribute to the incessant development of G-IoT technology. Therefore, even if sustainable and smart cities become an actuality, the G-IoT approach and the knowledge gained through big data (BD) analysis will make cities more sustainable, safer, and smarter. The goal of this article is to combine innovation in technological development with the main focus on resource sharing in creating cities that improve the quality of life while reducing pollution and realizing more efficient use of the raw materials. In the practice of big data science, it is always of interest to provide the best description of the data under consideration. Recent studies have pointed out the applicability of the statistical distributions in modeling data in applied sciences. In this article, we introduce a new family of statistical models to provide the best description of the life span of the wireless sensors network’s data. Based on the proposed approach, a special submodel called new exponent power-Weibull distribution is studied in detail. The applicability of the proposed model is shown by analyzing the life span of the wireless sensors network’s data.

The uses of statistical distributions for modeling real phenomena of nature have received considerable attention in the literature. The recent studies have pointed out the potential of statistical distributions in modeling data in applied sciences, particularly in financial sciences. Among them, the two-parameter Lomax distribution is one of the prominent models that can be used quite effectively for modeling data in management sciences, banking, finance, and actuarial sciences, among others. In the present article, we introduce a new three-parameter extension of the Lomax distribution via using a class of claim distributions. The new model may be called the Lomax-Claim distribution. The parameters of the Lomax-Claim model are estimated using the maximum likelihood estimation method. The behaviors of the maximum likelihood estimators are examined by conducting a brief Monte Carlo study. The potentiality and applicability of the Lomax claim model are illustrated by analyzing a dataset taken from financial sciences representing the vehicle insurance loss data. For this dataset, the proposed model is compared with the Lomax, power Lomax, transmuted Lomax, and exponentiated Lomax distributions. To show the best fit of the competing distributions, we consider certain analytical tools such as the Anderson–Darling test statistic, Cramer–Von Mises test statistic, and Kolmogorov–Smirnov test statistic. Based on these analytical measures, we observed that the new model outperforms the competitive models. Furthermore, a bivariate extension of the proposed model called the Farlie–Gumble–Morgenstern bivariate Lomax-Claim distribution is also introduced, and different shapes for the density function are plotted. An application of the bivariate model to GDP and export of goods and services is provided.

When conducting reliability studies, the progressive first-failure censoring (PFFC) method is useful in situations in which the units of the life testing experiment are separated into groups consisting of k units each with the intention of seeing only the first failure in each group. Using progressive first-failure censored samples, the statistical inference for the parameters, reliability, and hazard functions of the extended Rayleigh distribution (ERD) are investigated in this study. The asymptotic normality theory of maximum likelihood estimates (MLEs) is used in order to acquire the maximum likelihood estimates (MLEs) together with the asymptotic confidence intervals (Asym. CIs). Bayesian estimates (BEs) of the parameters and the reliability functions under different loss functions may be produced by using independent gamma informative priors and non-informative priors. The Markov chain Monte Carlo (MCMC) approach is used so that Bayesian computations are performed with ease. In addition, the MCMC method is used in order to create credible intervals (Cred. CIs) for the parameters, which may be used for either informative or non-informative priors. Additionally, computations for the reliability functions are carried out. A Monte Carlo simulation study is carried out in order to provide a comparison of the behaviour of the different estimations that were created for this work. At last, an actual data set is dissected for the purpose of providing an example.

Computer technology plays a prominent role in almost every aspect of daily life including education, health care, online shopping, advertising, and even in homes. Computers help to make daily tasks much easier and convenient. Among social media, YouTube is a well-known social sharing networking service. As more and more people join social media and become everyday users, brands have also increased their online engagement. However, it is still unclear how to effectively measure value and return on advertising using social media. As of 2021, more than 31 million YouTube channels around the globe have been opened. In this paper, we consider YouTube advertising to check its effectiveness and benefits gained. Certain statistical tools are adopted to measure the extent of advertising benefits and their correlation in creating effective advertising campaigns on YouTube. Simple linear regression analysis is performed on the data representing the YouTube advertising budget of a company and the sales data of that company. Furthermore, we develop a new statistical distribution to provide the best description of the YouTube advertising data. The result of this research shows that YouTube is an effective medium for advertising and has a strong relationship with sales.

E-Bayesian inference is of incremental significance in the area related to the reliability of industrial products dealing with censored data sets. In this article, based on the progressive Type-II right censored order statistics (PTIIRCOS), the E-Bayesian estimates (E-BE) for the parameters of Gompertz distribution (GD) and its hazard function are obtained and compared with the maximum likelihood (MLE) and Bayesian (BE) estimates. The squared error loss function (SE), linear-exponential loss function (LINEX), and Al-Bayyati loss function (ALB) are considered for the methods of BE and E-BE. Some properties for the E-BE estimates are discussed based on PTIIRCOS. Real data is established to clear the theoretical procedures. Akaike information criterion (AIC) is used to prove that GD is the best to model the data compared to other competitors and could potentially be very adequate in describing and modeling industrial products data.Finally, simulation study has been operated for comparing the E-BEs with the MLEs and BEs.