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Accelerated or partially accelerated life tests are particularly significant in life testing experiments since they save time and cost. Partially accelerated life tests are carried out when the data from accelerated life testing cannot be extrapolated to usual conditions. The constant-stress partially accelerated life test is proposed in this study based on a Type-II censoring scheme and supposing that the lifetimes of units at usual conditions follow the inverted Topp–Leone distribution. The Bayes and E-Bayes estimators of the distribution parameter and the acceleration factor are derived. The balanced squared error loss function, which is a symmetric loss function, and the balanced linear exponential loss function, which is an asymmetric loss function, are considered for obtaining the Bayes and E-Bayes estimators. Based on informative gamma priors and uniform hyper-prior distributions, the estimators are obtained. Finally, the performance of the proposed Bayes and E-Bayes estimates is evaluated through a simulation study and an application using real datasets.

Urban air pollution poses a significant challenge, negatively affecting visibility, agriculture, health, and transportation. This research focused on exploring the variability of aerosols using the autoregressive distributed lag (ARDL) approach. To achieve this, monthly aerosol data were obtained from the Aura satellite's Ozone Monitoring Instrument (OMI) at a distance of 500 nautical miles. In addition, meteorological factors such as Cloud Fraction (CF), Relative Humidity (RH), Tropopause Height (TH), Total Column Water Vapor (TCWV), Water Vapor Mass Mixing Ratio (WVMMR), Surface Skin Temperature (SST), Surface Air Temperature (SAT), and Geopotential Height (GH) were gathered from the atmospheric infrared sounder (AIRS) onboard the AQUA satellite. The MERRA-2 model provided the Total Surface Precipitation (TSP) and Surface Wind Speed (SWS). To assess the short- and long-term relationship between aerosols and meteorological parameters, the ARDL bounds testing technique was applied. The study found evidence of a long-term relationship and co-integration between the variables of interest and aerosols when aerosols were the dependent variable. Particularly, GH, SST, and SWS exhibited both long-term and short-term impacts on aerosol variability. SWS, in particular, was found to have a significant influence on aerosol variability. Conversely, CF, TSP, and WVMMR were found to have no significant impact on aerosol variability. To ensure the stability of the model, the CUSUM test was employed, confirming its stability. Furthermore, the prediction model demonstrated a good fit, bolstering the reliability of our findings. [ABSTRACT FROM AUTHOR]

This article introduces the concept of residual and past Tsallis extropy as a continuous information measure within the context of continuous distribution. Moreover, the characteristics and their relationships with other models are evaluated. Several stochastic comparisons are provided, along with outcomes concerning order statistics. Additionally, the models acquired include instances such as uniform and power function distributions. The measure incorporates its monotonic traits, and the outcomes defining its characteristics are presented. On the other hand, a different portrayal of the Tsallis extropy is introduced, expressed in relation to the hazard rate function. The Tsallis extropy of the lifetime for both mixed and coherent systems is explored. In the case of mixed systems, components' lifetimes are considered independent and identically distributed. Additionally, constraints on the Tsallis extropy of these systems are established, along with a clarification of their practical applicability. Non-parametric estimation using an alternative form of Tsallis function extropy for simulated and real data is performed. [ABSTRACT FROM AUTHOR]

In this article, we extensively study a family of distributions using the trigonometric function. We add an extra parameter to the sine transformation family and name it the alpha-sine-G family of distributions. Some important functional forms and properties of the family are provided in a general form. A specific sub-model alpha-sine Weibull of this family is also introduced using the Weibull distribution as a parent distribution and studied deeply. The statistical properties of this new distribution are investigated and intended parameters are estimated using the maximum likelihood, maximum product of spacings, least square, weighted least square, and minimum distance methods. For further justification of these estimates, a simulation experiment is carried out. Two real data sets are analyzed to show the suggested model's application. The suggested model performed well compares to some existing models considered in the study. [ABSTRACT FROM AUTHOR]

It is well known that ranked set sampling (RSS) is more efficient than simple random sampling (SRS). Furthermore, the presence of missing data vitiates the conventional results. Only a minuscule amount of work has been conducted under RSS with missing data. This paper makes a modest attempt to provide some efficient difference- and ratio-type imputation methods in the presence of missing values under RSS. The envisaged imputation methods are demonstrated to provide better results than the existing imputation methods. The theoretical results are enhanced by a computational analysis using real and hypothetically generated symmetric (Normal) and asymmetric (Gamma and Weibull) populations. The computational results show that the proposed imputation method outperforms the existing imputation methods in terms of its higher percent relative efficiency. Additionally, the impact of skewness and kurtosis on the efficiency of the suggested imputation methods has also been calculated. [ABSTRACT FROM AUTHOR]