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To reduce total test time and increase the efficiency of statistical analysis of a life-testing experiment adaptive progressive Type-II censoring scheme has been proposed. This paper addresses the statistical inference of the unknown parameters, reliability, and hazard rate functions of logistic exponential distribution under adaptive progressive Type-II censored samples. Maximum likelihood estimates (MLEs) and maximum product spacing estimates (MPSEs) for the model parameters, reliability, and hazard rate functions can not be obtained explicitly, hence these are derived numerically using the Newton–Raphson method. Bayes estimates for the unknown parameters and reliability and hazard rate functions are computed under squared error loss function (SELF) and linear exponential loss function (LLF). It has been observed that the Bayes estimates are not in explicit forms, hence an approximation method such as Markov Chain Monte Carlo (MCMC) method is employed. Further, asymptotic confidence intervals (ACIs) and highest posterior density (HPD) credible intervals for the unknown parameters, reliability, and hazard rate functions are constructed. Besides, point and interval Bayesian predictions have been derived for future samples. A Monte Carlo simulation study has been carried out to compare the performance of the proposed estimates. Furthermore, three different optimality criteria have been considered to obtain the optimal censoring plan. Two real-life data sets, one from electronic industry and other one from COVID-19 data set containing the daily death rate from France are re-analyzed to demonstrate the proposed methodology. [ABSTRACT FROM AUTHOR]

In the atmosphere, aerosols can originate from numerous sources, leading to the mixing of different particle types. This paper introduces an approach to the partitioning of aerosol mixtures in terms of backscattering coefficients. The method utilizes data collected from the Mie-Raman-fluorescence lidar, with the primary input information being the aerosol backscattering coefficient, particle depolarization ratio (δ), and fluorescence capacity (GF). The fluorescence capacity is defined as the ratio of the fluorescence backscattering coefficient to the particle backscattering coefficient at the laser wavelength. By solving a system of equations that model these three properties (bF, δ and GF), it is possible to characterize a three-component aerosol mixture. Specifically, the paper assesses the contributions of smoke, urban, and dust aerosols to the overall backscattering coefficient at 532 nm. It is important to note that aerosol properties (δ and GF) may exhibit variations even within a specified aerosol type. To estimate the associated uncertainty, we employ the Monte Carlo technique, which assumes that GF and δ are random values uniformly distributed within predefined intervals. In each Monte Carlo run, a solution is obtained. Rather than relying on a singular solution, an average is computed across the whole set of solutions, and their dispersion serves as a metric for method uncertainty. This methodology was tested using observations conducted at the ATOLL observatory, Laboratoire d'Optique Atmosphérique, University of Lille, France. [ABSTRACT FROM AUTHOR]