The unit exponentiated half logistic power series (UEHLPS), a family of compound distributions with bounded support, is introduced in this study. This family is produced by compounding the unit exponentiated half logistic and power series distributions. In the UEHLPS class, some interesting compound distributions can be found. We find formulas for the moments, density and distribution functions, limiting behavior, and other UEHLPS properties. Five well-known estimating approaches are used to estimate the parameters of one sub-model, and a simulation study is created. The simulated results show that the maximum product of spacing estimates had lower accuracy measure values than the other estimates. Ultimately, three real data sets from various scientific areas are used to analyze the performance of the new class.

Convexity is crucial in obtaining many forms of inequalities. As a result, there is a significant link between convexity and integral inequality. Due to the significance of these concepts, the purpose of this study is to introduce a new class of generalized convex interval-valued functions called LR-preinvex interval-valued functions (LR-preinvex I-V-Fs) and to establish Hermite–Hadamard type inequalities for LR-preinvex I-V-Fs using partial order relation (${\le }_p$). Furthermore, we demonstrate that our results include a large class of new and known inequalities for LR-preinvex interval-valued functions and their variant forms as special instances. Further, we give useful examples that demonstrate usefulness of the theory produced in this study. These findings and diverse approaches may pave the way for future research in fuzzy optimization, modeling, and interval-valued functions.

The half-logistic modified Kies exponential (HLMKEx) distribution is a novel three-parameter model that is introduced in the current work to expand the modified Kies exponential distribution and improve its flexibility in modeling real-world data. Due to its versatility, the density function of the HLMKEx distribution offers symmetrical, asymmetrical, unimodal, and reversed-J-shaped, as well as increasing, reversed-J shaped, and upside-down hazard rate forms. An infinite linear representation can be used to represent the HLMKEx density. The HLMKEx model’s fundamental mathematical features are obtained, such as the quantile function, moments, incomplete moments, and moments of residuals. Additionally, some measures of uncertainty as well as stochastic ordering are derived. To estimate its parameters, eight estimation methods are used. With the use of detailed simulation data, we compare the performance of each estimating technique and obtain partial and total ranks for the accuracy measures of absolute bias, mean squared error, and mean absolute relative error. The simulation results demonstrate that, in contrast to other competing distributions, the proposed distribution can actually fit the data more accurately. Two actual data sets are investigated in the field of engineering to demonstrate the adaptability and application of the suggested distribution. The findings demonstrate that, in contrast to other competing distributions, the provided distribution can actually fit the data more accurately.

Any nation’s growth depends on the trend of the price of fuel. The fuel price drifts have both direct and indirect impacts on a nation’s economy. Nation’s growth will be hampered due to the higher level of inflation prevailing in the oil industry. This paper proposed a method of analyzing Gasoline and Diesel Price Drifts based on Self-organizing Maps and Bayesian regularized neural networks. The US gasoline and diesel price timeline dataset is used to validate the proposed approach. In the dataset, all grades, regular, medium, and premium with conventional, reformulated, all formulation of gasoline combinations, and diesel pricing per gallon weekly from 1995 to January 2021, are considered. For the data visualization purpose, we have used self-organizing maps and analyzed them with a neural network algorithm. The nonlinear autoregressive neural network is adopted because of the time series dataset. Three training algorithms are adopted to train the neural networks: Levenberg-Marquard, scaled conjugate gradient, and Bayesian regularization. The results are hopeful and reveal the robustness of the proposed model. In the proposed approach, we have found Levenberg-Marquard error falls from − 0.1074 to 0.1424, scaled conjugate gradient error falls from − 0.1476 to 0.1618, and similarly, Bayesian regularization error falls in − 0.09854 to 0.09871, which showed that out of the three approaches considered, the Bayesian regularization gives better results.

It is well known that ranked set sampling (RSS) is superior to conventional simple random sampling (SRS) in that it frequently results in more effective inference techniques. One of the most popular and broadly applicable models for lifetime data is the Weibull distribution. This article proposes different modified goodness-of-fit tests based on the empirical distribution function (EDF) for the Weibull distribution. The recommended RSS tests are compared to their SRS counterparts. For each scheme, the critical values of the relevant test statistics are computed. A comparison of the power of the suggested goodness-of-fit tests based on a number of alternatives is investigated. RSS tests are more effective than their SRS equivalents, according to simulated data.

In this paper, we provide a novel method to determine the survivor equivalence factors for coherent systems, whatever the unit?s lifetime distribution and the struc?ture of the system. In order to determine the survivor equivalence factors for com?plex systems with independent units, we employ the idea of a survival signature and the Reliability Theory R package. Survival functions and mean times to failure are computed using the Reliability Theory package for systems were improved us?ing: reduction technique and duplication techniques, including: hot duplication, cold duplication with reliable switch, and cold duplication with unreliable switch. Survival survivor equivalence factors and mean survivor equivalence factors are taken into consideration as measures for comparing system improvements. For the new survivor equivalence factors method to be understood, numerical example for complex system is provided.