Exponential Loss Function Research Articles

An artificial neural network-based model for roping prediction in aluminum alloy sheet

Roping is a common macroscopic surface defect in AA6XXX aluminum alloy sheets resulting from the three-dimensional (3-D) spatial distribution of specific textures. The crystal plasticity finite element model (CPFEM) has been applied to study roping behavior and achieves good agreement with experimental observations but suffers from expensive computational consumption due to large-area and multi-layer characteristics of the roping phenomenon. In the present work, an artificial neural network-based (ANN) model is developed to predict thickness strain and corresponding surface roping under tensile deformation. A 3-D artificial orientation map generation algorithm is proposed and combined with CPFEM to produce reliable datasets to train, test, and validate the ANN model. The layer-by-layer random texture replacement strategy is adopted for dataset generation and facilitates the ANN model to capture the effects of individual layer textures on the thickness strain. A novel exponential weight loss function is also introduced to solve the imbalance problem of texture components. The ANN-based model demonstrates good prediction capability and generalizability in multiple validation cases with various artificial and experimental textures. The proposed ANN-based model provides an efficient and accurate alternative to the conventional physics-based method for roping analysis in aluminum alloy and can be also applied to similar microstructure-related deformation prediction in other materials.

General Entropy with Bayes Techniques under Lindley and MCMC for Estimating the New Weibull–Pareto Parameters: Theory and Application

Censored data play a pivotal role in life testing experiments since they significantly reduce cost and testing time. Hence, this paper investigates the problem of statistical inference for a system of progressive first-failure censoring data for a new Weibull–Pareto distribution. Maximum likelihood estimates for the parameters as well as some lifetime indices such as reliability, hazard rate functions, and coefficient of variation are derived. Lindley approximation and the Markov chain Monte Carlo technique are applied to obtain the Bayes estimates relative to two different loss functions: balanced linear exponential and general entropy loss functions. The results of the Bayes estimate are computed under the consideration of informative prior function. A real-life example "the survival times in years of a group of patients given chemotherapy treatment" is presented to illustrate the proposed methods. Finally, a simulation study is carried out to determine the performance of the maximum likelihood and Bayes estimates and compare the performance of different corresponding confidence intervals.

Quantitative Comparison of Tree Ensemble Learning Methods for Perfume Identification Using a Portable Electronic Nose

Perfume identification (PI) based on an electronic nose (EN) can be used for exposing counterfeit perfumes more time-efficiently and cost-effectively than using gas chromatography and mass spectrometry instruments. During the past five years, decision-tree-based ensemble learning methods, also called tree ensemble learning methods, have demonstrated excellent performance when solving multi-class classification problems. However, the performance of tree ensemble learning methods for the EN-based PI problem remains uncertain. In this paper, four well-known tree ensemble learning classification methods, random forest (RF), stagewise additive modeling using a multi-class exponential loss function (SAMME), gradient-boosting decision tree (GBDT), and extreme gradient boosting (XGBoost), were implemented for PI using our self-designed EN. For fair comparison, all the tested classification methods used as input the same feature data extracted using principal component analysis. Moreover, two benchmark methods, neural network and support vector machine, were also tested with the same experimental setup. The quantitative results of experiments undertaken demonstrated that the mean PI accuracy achieved by XGBoost was up to 97.5%, and that XGBoost outperformed other tested methods in terms of accuracy mean and variance based on our self-designed EN.

A New 3-Parameter Bounded Beta Distribution: Properties, Estimation, and Applications

This study presents a new three-parameter beta distribution defined on the unit interval, which can have increasing, decreasing, left-skewed, right-skewed, approximately symmetric, bathtub, and upside-down bathtub shaped densities, and increasing, U, and bathtub shaped hazard rates. This model can define well-known distributions with various parameters and supports, such as Kumaraswamy, beta exponential, exponential, exponentiated exponential, uniform, the generalized beta of the first kind, and beta power distributions. We present a comprehensive account of the mathematical features of the new model. Maximum likelihood methods and a Bayesian method under squared error and linear exponential loss functions are presented; also, approximate confidence intervals are obtained. We present a simulation study to compare all the results. Two real-world data sets are analyzed to demonstrate the utility and adaptability of the proposed model.

Construction of Integrated Platform for Eco-Sustainable Tourism and Marketing in Southeast Asia Based on Machine Learning

Southeast Asia is one of the most popular tourist destinations in the world, and its tourism model is mainly based on ecological and sustainable tourism characteristics. It is a special practical exploration of this region. However, with the rapid development of the tourism industry, the structural contradictions in the tourism industry have become increasingly prominent, coupled with the weak link of tourism development, making the development of tourism unbalanced. Therefore, this study proposed a platform-related algorithm based on machine learning to build the integration of eco-sustainable tourism and marketing in Southeast Asia and used a collaborative filtering algorithm and a route generation algorithm to recommend information or predict specific needs for specific tourists. The experimental results of this study showed that the difference between different loss functions of the improved transfer algorithm based on machine learning is not significant, which indicated that the method proposed in this study is robust to the choice of a loss function. Compared with the hinge loss function and the logarithmic loss function, the exponential loss function has the highest average classification accuracy of 0.91, of which the average accuracy of the logarithmic loss function is 0.85, and the average classification accuracy of the hinge loss function is 0.79. Therefore, applying the migration algorithm to the architecture of the platform is conducive to the stability of the dataset and to the better display of pages for tourists.

Arctan-Based Family of Distributions: Properties, Survival Regression, Bayesian Analysis and Applications

In this paper, a new class of the continuous distributions is established via compounding the arctangent function with a generalized log-logistic class of distributions. Some structural properties of the suggested model such as distribution function, hazard function, quantile function, asymptotics and a useful expansion for the new class are given in a general setting. Two special cases of this new class are considered by employing Weibull and normal distributions as the parent distribution. Further, we derive a survival regression model based on a sub-model with Weibull parent distribution and then estimate the parameters of the proposed regression model making use of Bayesian and frequentist approaches. We consider seven loss functions, namely the squared error, modified squared error, weighted squared error, K-loss, linear exponential, general entropy, and precautionary loss functions for Bayesian discussion. Bayesian numerical results include a Bayes estimator, associated posterior risk, credible and highest posterior density intervals are provided. In order to explore the consistency property of the maximum likelihood estimators, a simulation study is presented via Monte Carlo procedure. The parameters of two sub-models are estimated with maximum likelihood and the usefulness of these sub-models and a proposed survival regression model is examined by means of three real datasets.

Bayesian Estimation of the Scale Parameter of Weibull Distribution using Ranked Set Samples

This research article is primarily focused on the investigation of Bayes estimators for the scale parameter of the Weibull distribution. Specifically, we focus on a sampling method known as Ranked Set Sample with Unequal Samples (RSSU), as introduced and studied by Bhoj (2001). Our objective is to derive Bayes estimates for the scale parameter utilizing two distinct loss functions: the squared error loss (SEL) function and the linear exponential (LINEX) loss function. We consider the scenario where the scale parameter follows either a gamma prior distribution or a Jeffreys prior distribution. To evaluate the performance of these estimators, we conduct simulations and analyse their bias and mean squared error (MSE). Our findings show that RSSU-based estimators outperform those based on Simple Random Sampling (SRS) and Ranked Set Sampling (RSS), when either Jeffreys prior or gamma prior distribution is used.

Generating Optimal Discrete Analogue of the Generalized Pareto Distribution under Bayesian Inference with Applications

This paper studies three discretization methods to formulate discrete analogues of the well-known continuous generalized Pareto distribution. The generalized Pareto distribution provides a wide variety of probability spaces, which support threshold exceedances, and hence, it is suitable for modeling many failure time issues. Bayesian inference is applied to estimate the discrete models with different symmetric and asymmetric loss functions. The symmetric loss function being used is the squared error loss function, while the two asymmetric loss functions are the linear exponential and general entropy loss functions. A detailed simulation analysis was performed to compare the performance of the Bayesian estimation using the proposed loss functions. In addition, the applicability of the optimal discrete generalized Pareto distribution was compared with other discrete distributions. The comparison was based on different goodness-of-fit criteria. The results of the study reveal that the discretized generalized Pareto distribution is quite an attractive alternative to other discrete competitive distributions.

Bayes Analysis for the Scale Parameter of Gompertz Distribution

In this paper, we investigate the behavior of the bayes estimators, for the scale parameter of the Gompertz distribution under two different loss functions such as, the squared error loss function, the exponential loss function (proposed), based different double prior distributions represented as erlang with inverse levy prior, erlang with non-informative prior, inverse levy with non-informative prior and erlang with chi-square prior.
 The simulation method was fulfilled to obtain the results, including the estimated values and the mean square error (MSE) for the scale parameter of the Gompertz distribution, for different cases for the scale parameter of the Gompertz distribution, with different samples sizes. The estimates have been compared in terms of their mean-squared error (MSE).
 The results of this paper show that bayes estimators of the scale parameter of the Gompertz distribution, under the exponential loss function (proposed) are superior to the bayes estimators under the squared error loss function , based on erlang-chi-square double prior with for all samples sizes and for all the true values of , in terms of their mean-squared error (MSE)

A Bayesian estimation of the Gini index and the Bonferroni index for the Dagum distribution with the application of different priors

Abstract Bayesian estimators and highest posterior density credible intervals are obtained for two popular inequality measures, viz. the Gini index and the Bonferroni index in the case of the Dagum distribution. The study considers informative and non-informative priors, i.e. the Mukherjee-Islam prior and the extension of Jeffrey’s prior, respectively, under the presumption of the Linear Exponential (LINEX) loss function. A Monte Carlo simulation study is carried out in order to obtain the relative efficiency of both the Gini and Bonferroni indices while taking into consideration different priors and loss functions. The estimated loss proves lower when using the Mukherjee-Islam prior in comparison to the extension of Jeffrey’s prior and the LINEX loss function outperforms the squared error loss function (SELF) in terms of the estimated loss. Highest posterior density credible intervals are also obtained for both these measures. The study used real-life data sets for illustration purposes.

A Photovoltaic System Fault Identification Method Based on Improved Deep Residual Shrinkage Networks

With the increasing installed capacity of photovoltaic (PV) power generation, it has become a significant challenge to detect abnormalities and faults of PV modules in a timely manner. Considering that all the fault information of the PV module is contained in the current-voltage (I-V) curve, this pioneering study takes the I-V curve as the input and proposes a PV-fault identification method based on improved deep residual shrinkage networks (DRSN). This method can not only identify single faults (e.g., short-circuit, partial-shading, and abnormal aging), but also effectively identify the simultaneous existence of hybrid faults. Moreover, it can achieve end-to-end fault diagnosis. The diagnostic accuracy of the proposed method on the measured data reaches 97.73%, is better than the convolutional neural network (CNN), the support vector machine (SVM), the deep residual network (ResNet), and the stage-wise additive modeling using multi-class exponential loss function based on the classification and regression tree (SAMME-CART). In addition, the possibility of the aforementioned method running on the Raspberry Pi has been verified in this study, which is of great significance for realizing the edge diagnosis of PV fault.

A classification for complex imbalanced data in disease screening and early diagnosis.

Imbalanced classification has drawn considerable attention in the statistics and machine learning literature. Typically, traditional classification methods often perform poorly when a severely skewed class distribution is observed, not to mention under a high‐dimensional longitudinal data structure. Given the ubiquity of big data in modern health research, it is expected that imbalanced classification in disease diagnosis may encounter an additional level of difficulty that is imposed by such a complex data structure. In this article, we propose a nonparametric classification approach for imbalanced data in longitudinal and high‐dimensional settings. Technically, the functional principal component analysis is first applied for feature extraction under the longitudinal structure. The univariate exponential loss function coupled with group LASSO penalty is then adopted into the classification procedure in high‐dimensional settings. Along with a good improvement in imbalanced classification, our approach provides a meaningful feature selection for interpretation while enjoying a remarkably lower computational complexity. The proposed method is illustrated on the real data application of Alzheimer's disease early detection and its empirical performance in finite sample size is extensively evaluated by simulations.

Cumulative Residual Extropy for Pareto Distribution in the Presence of Outliers: Bayesian and Non-Bayesian Methods

The extropy is considered to be a complementary dual of the well-known Shannon’s entropy and has wide applications in many fields. This article discusses estimating the extropy and cumulative residual extropy of the Pareto distribution using the maximum likelihood and Bayesian methods. We obtain the maximum likelihood of extropies measures in presence of outliers. These estimators are specialized to homogenous case. The Bayesian estimators of both extropy measures are derived based on symmetric and asymmetric loss functions. The Markov chain Monte Carlo methods are used to accomplish some complex calculations. The precision of the Bayesian and the maximum likelihood estimates for extropy estimates are examined through simulations. Regarding results of simulation study, we conclude that the performances of both estimation methods improve with sample sizes. Also, Bayesian estimates of the extropy and cumulative residual extropy under linear exponential loss function are superior to the other Bayesian estimates under the other loss functions in most of cases. The performance for the extropy and cumulative residual extropy estimates increase with number of outliers in almost cases. Generally, there is a great agreement between the theoretical and empirical results. Further performance comparison is conducted by the experiments with real data.

Asymmetric Power Hazard Distribution for COVID-19 Mortality Rate under Adaptive Type-II Progressive Censoring: Theory and Inferences.

This article investigates the estimation of the parameters for power hazard function distribution and some lifetime indices such as reliability function, hazard rate function, and coefficient of variation based on adaptive Type-II progressive censoring. From the perspective of frequentism, we derive the point estimations through the method of maximum likelihood estimation. Besides, delta method is implemented to construct the variances of the reliability characteristics. Markov chain Monte Carlo techniques are proposed to construct the Bayes estimates. To this end, the results of the Bayes estimates are obtained under squared error and linear exponential loss functions. Also, the corresponding credible intervals are constructed. A simulation study is utilized to assay the performance of the proposed methods. Finally, a real data set of COVID-19 mortality rate is analyzed to validate the introduced inference methods.

Posterior Estimates for the Parameter of the Poisson Distribution by Using Two Different Loss Functions

In this paper, Bayes estimators of Poisson distribution have been derived by using two loss functions: the squared error loss function and the proposed exponential loss function in this study, based on different priors classified as the two different informative prior distributions represented by erlang and inverse levy prior distributions and non-informative prior for the shape parameter of Poisson distribution. The maximum likelihood estimator (MLE) of the Poisson distribution has also been derived. A simulation study has been fulfilled to compare the accuracy of the Bayes estimates with the corresponding maximum likelihood estimate (MLE) of the Poisson distribution based on the root mean squared error (RMSE) for different cases of the parameter of the Poisson distribution and different sample sizes.

Bayesian Risk Analysis for Length Biased Log Logistic Distribution Under Different Loss

The aim of this paper is parametric and reliability estimation for the two parameter length biased log-logistic distribution under squared error, generalized exponential, linear exponential and precautionary loss functions. Bayes estimates obtained under non informative priors through Lindleys approximation and through Markov Chain Monte Carlo are then compared with the classical parametric estimates. Bayesian risk analysis based on a simulated and a real data set are used to demonstrate application of the theoretic results.

Inverse Exponentiated Lomax Power Series Distribution: Model, Estimation, and Application

In this paper, we introduce the inverse exponentiated Lomax power series (IELoPS) class of distributions, obtained by compounding the inverse exponentiated Lomax and power series distributions. The IELoPS class contains some significant new flexible lifetime distributions that possess powerful physical explications applied in areas like industrial and biological studies. The IELoPS class comprises the inverse Lomax power series as a new subclass as well as several new flexible compounded lifetime distributions. For the proposed class, some characteristics and properties are derived such as hazard rate function, limiting behavior, quantile function, Lorenz and Bonferroni curves, mean residual life, mean inactivity time, and some measures of information. The methods of maximum likelihood and Bayesian estimations are used to estimate the model parameters of one optional model. The Bayesian estimators of parameters are discussed under squared error and linear exponential loss functions. The asymptotic confidence intervals, as well as Bayesian credible intervals, of parameters, are constructed. Simulations for a one‐selective model, say inverse exponentiated Lomax Poisson (IELoP) distribution, are designed to assess and compare different estimates. Results of the study emphasized the merit of produced estimates. In addition, they appeared the superiority of Bayesian estimate under regarded priors compared to the corresponding maximum likelihood estimate. Finally, we examine medical and reliability data to demonstrate the applicability, flexibility, and usefulness of IELoP distribution. For the suggested two real data sets, the IELoP distribution fits better than Kumaraswamy–Weibull, Poisson–Lomax, Poisson inverse Lomax, Weibull–Lomax, Gumbel–Lomax, odd Burr–Weibull–Poisson, and power Lomax–Poisson distributions.

Classical and objective Bayesian estimation and confidence intervals of an asymmetric loss based capability index Cpmk′$\mathcal {C}^{\prime }_{pmk}$

AbstractIn this paper, we introduce a new process capability index, based on an asymmetric loss function (linear exponential) for normal process. To estimate , we first obtain eight different classical methods of estimation and then consider objective Bayesian methods of estimation under the squared error loss function and the linear exponential loss function. Extensive simulations are carried out to investigate the performance of these estimation methods in terms of the mean squared errors. In addition, we compare the performance of four bootstrap confidence intervals and the highest posterior density interval of in terms of average width and coverage probability. Finally, three real‐data applications from electronic industries are provided for illustrative purposes.

A New Two-Parameter Burr-Hatke Distribution: Properties and Bayesian and Non-Bayesian Inference with Applications

This article introduces a two-parameter flexible extension of the Burr-Hatke distribution using the inverse-power transformation. The failure rate of the new distribution can be an increasing shape, a decreasing shape, or an upside-down bathtub shape. Some of its mathematical properties are calculated. Ten estimation methods, including classical and Bayesian techniques, are discussed to estimate the model parameters. The Bayes estimators for the unknown parameters, based on the squared error, general entropy, and linear exponential loss functions, are provided. The ranking and behavior of these methods are assessed by simulation results with their partial and overall ranks. Finally, the flexibility of the proposed distribution is illustrated empirically using two real-life datasets. The analyzed data shows that the introduced distribution provides a superior fit than some important competing distributions such as the Weibull, Fréchet, gamma, exponential, inverse log-logistic, inverse weighted Lindley, inverse Pareto, inverse Nakagami-M, and Burr-Hatke distributions.

Selection of Efficient Parameter Estimation Method for Two-Parameter Weibull Distribution

Several studies have considered various scheduling methods and reliability functions to determine the optimum maintenance time. These methods and functions correspond to the lowest cost by using the maximum likelihood estimator to evaluate the model parameters. However, this paper aims to estimate the parameters of the two-parameter Weibull distribution (α, β). The maximum likelihood estimation method, modified linear exponential loss function, and Wyatt-based regression method are used for the estimation of the parameters. Minimum mean square error (MSE) criterion is used to evaluate the relative efficiency of the estimators. The comparison of the different parameter estimation methods is conducted, and the efficiency of these methods is observed, both mathematically and experimentally. The simulation study is conducted for comparison of samples sizes (10, 50, 100, 150) based on the mean square error (MSE). It is concluded that the maximum likelihood method was found to be the most efficient method for all sample sizes used in the research because it achieved the least MSE compared with other methods.