The Poisson Inverted Shifted Gompertz distribution is a new type of distribution that comes from the Poisson-generating family of distributions and is based on the "inverted shifted Gompertz distribution." This distribution has significant statistical characteristics, with clear formulations obtained mathematically. We use three distinct approaches to estimate the parameters of the distribution: maximum likelihood estimation (MLE), least-squares estimation (LSE), and Cramer-Von-Mises estimation (CVME). We undertake a simulation experiment to thoroughly assess the efficacy of maximum likelihood estimation (MLE). Empirical data from engineering and medical fields demonstrate the relevance of our suggested model. We meticulously evaluate the goodness-of-fit of the Poisson Inverted Shifted Gompertz distribution using several statistical tests and graphical techniques. Our suggested distribution demonstrates enhanced fitting capabilities and more flexibility compared to many widely used lifespan distributions. Furthermore, we investigate the Bayesian viewpoint of the proposed model by using Hamiltonian Monte Carlo (HMC) simulation methods. This detailed study gives you a full picture of how the Poisson Inverted Shifted Gompertz distribution can be used in many different areas.

In this article, our main aim is to suggest enhanced families of estimators for estimating the population distribution function (DF) using twofold auxiliary evidence within the framework of simple random sampling. Numerical analysis is performed on four different actual data sets. The precision of the estimators is further investigated exhausting a simulation study. As equated with existing estimators, the suggested families of estimators have minimum mean square error (MSE) and higher percentage relative efficiency (PRE). The succeeding recommended family of estimators outperforms the first family of estimators across all data sets. These are positive indicators of its performance. The theoretical result shows that the recommended family of estimators performs better than the existing estimators. The extent of improvement in efficiency is noteworthy, indicating the superiority of the suggested estimators in terms of minimum MSE.

We aim in this paper to propose a novel class of distributions that was created by merging the Topp-Leone distribution and the Generated families of Kumaraswamy and Marshall-Olkin. Its cumulative distribution function characterizes it and includes rational and polynomial functions. In particular, the following desirable properties of the new family are presented: Shannon entropy, order statistics, the quantile power series, and several associated measures and functions. Then, using a specific family member identified before, we create a parametric statistical model with the basic distribution being the inverse exponential distribution. Finally, a thorough investigation has been made to implement this new distribution with three data sets: the glass fibers data set, the glass Alumina data set and the hailing times data set. In comparison to six prominent competitors, the new model performs favorably on all statistical tests and criteria that were examined.

In the present work, magnesium oxide (MgO) and lead oxide (PbO) nanoparticles were prepared by the co-precipitation method. Their structural parameters and morphology were investigated using XRD, HRTEM, and FTIR. The formation of the phases was seen to have small average crystallite sizes and an orthorhombic crystal structure for both MgO and PbO nanoparticles. The results of HR-TEM showed irregularly shaped nanoparticles: quasi-spherical or rod-like shapes and spherical-like shapes for MgO and PbO nanoparticles, respectively. The produced nanoparticles’ size using X-ray diffraction analysis was found to be 17 nm and 41 nm for MgO and PbO nanoparticles, respectively. On the other hand, it was observed from the calculations that the optical band gap obeys an indirect allowed transition. The calculated values of the band gap were 4.52 and 4.28 eV for MgO and PbO NPs, respectively. The MB was extracted from the wastewater using the prepared composites via absorption. Using a variety of kinetic models, the adsorptions were examined. Out of all the particles, it was discovered that the composites were best. Furthermore, of the models currently under consideration, the pseudo-second-order model best fit the degradation mechanism. The resultant composites could be beneficial for degrading specific organic dyes for water purification, as well as applications needing a wider optical band gap.

The usefulness of a new heavy-tailed distribution is studied in this article. The type-I heavy-tailed exponential (TI-HTE) distribution studied here has been suggested in the literature but has not been studied anywhere other than now. Some of its properties, together with graphical representations, were considered. The study utilized the maximum likelihood method in the estimation of the parameters. The primary goal is to create group acceptance sampling plans (GASP) using the TI-HTE model to determine whether units from a production process should be accepted or rejected. Through simulation studies and real-world examples, the importance of the TI-HTE model in identifying extreme behaviors beyond typical distributions like exponential or heavy-tailed distributions is emphasized.