In contemporary statistical research, there has been a notable surge of interest surrounding a suggested extension of the Marshall-Olkin-G distributions. The present extension exhibits a higher degree of flexibility in comparison to its parent distributions. In a similar manner, we present in this context an expansion of the Marshall-Olkin-G distributions proposed by statistical scholars. This study utilizes a specific variant of the extension known as the Marshall-Olkin-Weibull Logarithmic model, which is applied to both complete and censored data sets. It is evident that the aforementioned model has strong competitiveness in accurately characterizing both complete and censored observations in lifetime reliability issues, when compared to other comparative models discussed in this research work.

The humongous increase in carbon emissions in the past few decades presents an environmental challenge to the scientific community. The current study proposes a method of taxation on high-carbon emission fuels. For this purpose, a comparative enviro-economic analysis is carried out on the three most commonly used fuels (gasoline, Liquefied Petroleum Gas (LPG), and Compressed Natural Gas (CNG)). The speed of the test engine varied from 1800 to 4200 Revolution per Minute (RPM) in increments of 400 RPM. Performance parameters (Brake Power (BP), Brake Thermal Efficiency (BTHE), and Brake Specific Fuel Consumption (BSFC)) were measured using a hydro dynamometer. Emission analysis, including Carbon Dioxide (CO2), Carbon Monoxide (CO), Unburned Hydrocarbons (HC), and Nitrogen Oxide (NOx), was conducted using the TESTO 350 analyzer. The application of Weibull distribution with a 95 % confidence interval, on emission data, explained the adequacy of the data. Among test fuels, CNG emerged as an environment-friendly fuel with an emission reduction of 16, 42, and 43 percent for CO2, CO, and HC in comparison to gasoline. Also, BTHE and BSFC of CNG were better than other alternatives. Moreover, the carbon penalty for CNG fuel showed a price reduction of 32 and 20.8 percent in comparison to gasoline and LPG respectively. The study provides a novel approach to assess the environmental impact of fuels by economic analysis based on emitted carbon quantity. In addition, this very idea is novel in promoting the Sustainable Development Goals (SDG) of the United Nations (UN) through carbon taxation.

Since coverage intervals are widely used expressions of measurement uncertainty, this contribution reviews coverage intervals as defined in the Guide to the Expression of Uncertainty in Measurement (GUM), and compares them against the principal types of probabilistic intervals that are commonly used in applied statistics and in measurement science. Although formally identical to conventional confidence intervals for means, the GUM interprets coverage intervals more as if they were Bayesian credible intervals, or tolerance intervals. We focus, in particular, on a common misunderstanding about the intervals derived from the results of the Monte Carlo method of the GUM Supplement 1 (GUM-S1), and offer a novel interpretation for these intervals that we believe will foster realistic expectations about what they can deliver, and how and when they can be useful in practice.

Probability distributions are widely utilized in applied sciences, especially in the field of biomedical science. Biomedical data typically exhibit positive skewness, necessitating the use of flexible, skewed distributions to effectively model such phenomena. In this study, we introduce a novel approach to characterize new lifetime distributions, known as the New Flexible Exponent Power (NFEP) Family of distributions. This involves the addition of a new parameter to existing distributions. A specific sub-model within the proposed class, known as the New Flexible Exponent Power Weibull (NFEP-Wei), is derived to illustrate the concept of flexibility. We employ the well-established Maximum Likelihood Estimation (MLE) method to estimate the unknown parameters in this family of distributions. A simulation study is conducted to assess the behavior of the estimators in various scenarios. To gauge the flexibility and effectiveness of the NFEP-Wei distribution, we compare it with the AP-Wei (alpha power Weibull), MO-Wei (Marshal Olkin Weibull), classical Wei (Weibull), NEP-Wei (new exponent power Weibull), FRLog-Wei (flexible reduced logarithmic Weibull), and Kum-Wei (Kumaraswamy Weibull) distributions by analyzing four distinct biomedical datasets. The results demonstrate that the NFEP-Wei distribution outperforms the compared distributions.

This paper presents a novel approach for analyzing bivariate positive data, taking into account a covariate vector and left-censored observations, by introducing a hierarchical Bayesian analysis. The proposed method assumes marginal Weibull distributions and employs either a usual Weibull likelihood or Weibull-Tobit likelihood approaches. A latent variable or frailty is included in the model to capture the possible correlation between the bivariate responses for the same sampling unit. The posterior summaries of interest are obtained through Markov Chain Monte Carlo methods. To demonstrate the effectiveness of the proposed methodology, we apply it to a bivariate data set from stellar astronomy that includes left-censored observations and covariates. Our results indicate that the new bivariate model approach, which incorporates the latent factor to capture the potential dependence between the two responses of interest, produces accurate inference results. We also compare the two models using the different likelihood approaches (Weibull or Weibull-Tobit likelihoods) in the application. Overall, our findings suggest that the proposed hierarchical Bayesian analysis is a promising approach for analyzing bivariate positive data with left-censored observations and covariate information.

This paper presents an effort to investigate the estimations of the Weibull distribution using an improved adaptive Type-II progressive censoring scheme. This scheme effectively guarantees that the experimental time will not exceed a pre-fixed time. The point and interval estimations using two classical estimation methods, namely maximum likelihood and maximum product of spacing, are considered to estimate the unknown parameters as well as the reliability and hazard rate functions. The approximate confidence intervals of these quantities are obtained based on the asymptotic normality of the maximum likelihood and maximum product of spacing methods. The Bayesian estimations are also considered using MCMC techniques based on the two classical approaches. An extensive simulation study is implemented to compare the performance of the different methods. Further, we propose the use of various optimality criteria to find the optimal sampling scheme. Finally, one real data set is applied to show how the proposed estimators and the optimality criteria work in real-life scenarios. The numerical outcomes demonstrated that the Bayesian estimates using the likelihood and product of spacing functions performed better than the classical estimates.

A complete framework of predicting the attributes of sea clutter under different operational conditions, specified by wind speed, wind direction, grazing angle, and polarization, is proposed for the first time. This framework is composed of empirical spectra to characterize sea-surface profiles under different wind speeds, the Monte Carlo method to generate realizations of sea-surface profiles, the physical-optics method to compute the normalized radar cross-sections (NRCSs) from individual sea-surface realizations, and regression of NRCS data (sea clutter) with an empirical probability density function (PDF) characterized by a few statistical parameters. JONSWAP and Hwang ocean-wave spectra are adopted to generate realizations of sea-surface profiles at low and high wind speeds, respectively. The probability density functions of NRCSs are regressed with K and Weibull distributions, each characterized by two parameters. The probability density functions in the outlier regions of weak and strong signals are regressed with a power-law distribution, each characterized by an index. The statistical parameters and power-law indices of the K and Weibull distributions are derived for the first time under different operational conditions. The study reveals succinct information of sea clutter that can be used to improve the radar performance in a wide variety of complicated ocean environments. The proposed framework can be used as a reference or guidelines for designing future measurement tasks to enhance the existing empirical models on ocean-wave spectra, normalized radar cross-sections, and so on.

The aging intensity (AI), defined as the ratio of the instantaneous hazard rate and a baseline hazard rate, is a useful tool for the describing reliability properties of a random variable corresponding to a lifetime. In this work, the concept of AI is introduced in step-stress accelerated life testing (SSALT) experiments, providing new insights to the model and enabling the further clarification of the differences between the two commonly employed cumulative exposure (CE) and tampered failure rate (TFR) models. New AI-based estimators for the parameters of a SSALT model are proposed and compared to the MLEs in terms of examples and a simulation study.

Understanding and harnessing renewable energy potential is imperative for developing nations in the context of climate change. However, the wind potential of Yamoussoukro, Côte d\'Ivoire, remains inadequately explored. This study employs a Longitudinal Observational Study design, acquiring data at 1-min intervals to capture the dynamic wind characteristics. The research focuses on refining ground data and estimating wind potential using a DAVIS Pro weather station with a cup anemometer for speed and a wind vane for direction. Wind speed and direction are measured in meters per second and degrees. Two distinct approaches are employed for data analysis: arithmetic and cubic averages provide representative values, and the Two-Parameter Weibull Probability Distribution Functions, determined through the method of moments, offer insights into the wind distribution pattern. The study\'s findings indicate an 8-h time slot during which the wind potential permits obtaining an annual energy production of 53,38 kW/h/m2, a valuable window of opportunity. The rainy season, particularly May, has the highest average monthly wind speed, while the dry season in December has the lowest. Furthermore, the wind rose analysis reveals that the prevailing winds blow from south to north, further highlighting the region\'s wind potential. The results affirm that Yamoussoukro harbors a moderate wind potential, aptly harnessed through Vertical Axis Wind Turbines (VAWT). This discovery holds significant implications for sustainable development, highlighting the city\'s potential to transition towards a greener, more energy-efficient economy. Yamoussoukro is poised to contribute substantially to renewable energy and climate change mitigation efforts by unlocking the untapped wind energy potential.

of wind characteristics and assessment of wind energy resource is carried out at a location in Tonga with the help of twelve months of measurements carried out at 34 m and 20 m heights above ground level. The daily, monthly and annual averages are computed. The wind shear analysis and its diurnal variation were studied and compared with the temperature variation. The turbulence levels at the two heights were estimated for the entire measurement period as well as for some typical days. For estimating the Weibull parameters, eleven methods were employed along with goodness of fit and error estimates to find the best method. The overall averaged wind speed for the entire period of study is estimated to be 4.41 m/s at 34 m above ground level. The predominant wind direction was south-east for Tonga. \'Moments\' is seen to be the best method to determine accurate Weibull parameters. The average net annual energy production from one Vergnet 275 kW wind turbine is 198.57 MWh. A payback period of 8.95 years by installing five turbines near the measurement location was estimated, which is very encouraging in terms of investment. Installing wind turbines will lower the heavy reliance on the imported fossil fuels in the country and also help in achieving Sustainable Development Goal 7.