In the domain of machine learning, the significance of the loss function is paramount, especially in supervised learning tasks. It serves as a fundamental pillar that profoundly influences the behavior and efficacy of supervised learning algorithms. Traditional loss functions, though widely used, often struggle to handle outlier-prone and high-dimensional data, resulting in suboptimal outcomes and slow convergence during training. In this paper, we address the aforementioned constraints by proposing a novel robust, bounded, sparse, and smooth (RoBoSS) loss function for supervised learning. Further, we incorporate the RoBoSS loss within the framework of support vector machine (SVM) and introduce a new robust algorithm named $\mathcal {L}_{RoBoSS}$ -SVM. For the theoretical analysis, the classification-calibrated property and generalization ability are also presented. These investigations are crucial for gaining deeper insights into the robustness of the RoBoSS loss function in classification problems and its potential to generalize well to unseen data. To validate the potency of the proposed $\mathcal {L}_{RoBoSS}$ -SVM, we assess it on 88 benchmark datasets from KEEL and UCI repositories. Further, to rigorously evaluate its performance in challenging scenarios, we conducted an assessment using datasets intentionally infused with outliers and label noise. Additionally, to exemplify the effectiveness of $\mathcal {L}_{RoBoSS}$ -SVM within the biomedical domain, we evaluated it on two medical datasets: the electroencephalogram (EEG) signal dataset and the breast cancer (BreaKHis) dataset. The numerical results substantiate the superiority of the proposed $\mathcal {L}_{RoBoSS}$ -SVM model, both in terms of its remarkable generalization performance and its efficiency in training time.

In this article, inferences about the multicomponent stress strength reliability are drawn under the assumption that strength and stress follow independent Pareto distribution with different shapes $({\alpha }_1,{\alpha }_2)$ and common scale parameter $\theta$ under the setup of upper record values. The maximum likelihood estimator, Bayes estimator under-squared error and Linear exponential loss function, of multicomponent stress-strength reliability are constructed with corresponding highest posterior density interval for unknown $\theta .$ For known $\theta ,$ uniformly minimum variance unbiased estimator and asymptotic distribution of multicomponent stress-strength reliability with asymptotic confidence interval is discussed. Also, various Bootstrap confidence intervals are constructed. A simulation study is conducted to numerically compare the performances of various estimators of multicomponent stress-strength reliability. Finally, a real life example is presented to show the applications of derived results in real life scenarios. Several researchers have attempted such problems under different distributions e.g., [1] considered the Weibull distribution for estimation of multicomponent stress-strength reliability, [2] considered generalized Rayleigh distribution for the reliability estimation of multicomponent stress-strength setup.

In this study, we have obtained the uniformly minimum variance unbiased estimator (UMVUE) of reliability function and stress–strength reliability for one parameter proportional reversed hazard rate family of distribution based on lower record values. Further, the results are reduced for power function distribution, exponentiated Weibull distribution, generalized exponential distribution, generalized Rayleigh (also known as Burr type X) distribution and Topp–Leone distribution. Also, the UMVU estimator and maximum likelihood estimator are compared through simulation.

The linear exponential distribution is a generalization of the exponential and Rayleigh distributions. This distribution is one of the best models to fit data with increasing failure rate (IFR). But it does not provide a reasonable fit for modeling data with decreasing failure rate (DFR) and bathtub shaped failure rate (BTFR). To overcome this drawback, we propose a new record-based transmuted generalized linear exponential (RTGLE) distribution by using the technique of Balakrishnan and He. The family of RTGLE distributions is more flexible to fit the data sets with IFR, DFR, and BTFR, and also generalizes several well-known models as well as some new record-based transmuted models. This paper aims to study the statistical properties of RTGLE distribution, like, the shape of the probability density function and hazard function, quantile function and its applications, moments and its generating function, order and record statistics, Rényi entropy. The maximum likelihood estimators, least squares and weighted least squares estimators, Anderson-Darling estimators, Cramér-von Mises estimators of the unknown parameters are constructed and their biases and mean squared errors are reported via Monte Carlo simulation study. Finally, the real data sets illustrate the goodness of fit and applicability of the proposed distribution; hence, suitable recommendations are forwarded.

In this article, we consider the estimation problem of Unit Gompertz distribution with parameters α and β under the framework of dual generalized order statistics. This article is purely devoted to present the Bayesian view of estimation of Unit Gompertz distribution. For this purpose, we consider two widely popular approximation methods called Markov chain Monte Carlo and Lindley approximation methods. The results are derived under the symmetric (squared error) and asymmetric (Linear exponential and General entropy) loss functions. Since the order statistics and lower record values are the particular cases of the dual generalized order statistics, a simulation study is provided for order statistics and lower record values to observe the behavior of estimators. The average lengths of highest posterior density intervals of α, β, and R(t) are calculated for 95% confidence coefficient. Finally, real data applications are reported for lower record values and order statistics, separately, to show the practical aspects of the derived results.