Symmetric Data Sets Research Articles

Calibrated EWMA estimators for time-scaled surveys with diverse applications

Recently, several memory-type mean estimators (including ratio, product, and logarithmic) have been developed. These estimators rely on exponentially weighted moving average (EWMA), which incorporate both historical and present sample data. In this article, we propose EWMA type calibrated estimators under single and double stratified random sampling (StRS). Because calibration method enhances the estimates by modifying the stratification weight, taking advantage of supplementary information. To evaluate the performance of estimators, various real-world time-scaled data sets pertaining to stock market and weather are taken into account. Additionally, we also conduct a simulation study using a bivariate symmetric data set. The numerical results show the superiority of proposed estimators (y¯TM,y¯TaM) over the adapted ones (y¯PM,y¯PaM).

A flexible generalized XLindley distribution with application to engineering

This paper presents a novel three-parameter distribution called the exponentiated generalized XLindley distribution. The distribution’s probability density function can be positively or negatively skewed, reverse-J or symmetric. Both an increasing and decreasing hazard rate function is conceivable. The hazard rate function, moments, residual and reverse residual life function, reliability function, and Rényi entropy are among the mathematical elements that can be ascertained from the new model. To estimate the parameters of the model, the maximum likelihood method is utilized. A simulation study was carried out to assess maximum likelihood estimators’ effectiveness. Two sets of data related to civil engineering were subjected to the new three-parameter model. The model is shown to suit these two symmetric datasets more closely than comparison models shown in this paper.

Analysis, Estimation, and Practical Implementations of the Discrete Power Quasi‐Xgamma Distribution

In this study, we introduce a new three‐parameter discrete power quasi‐Xgamma (DPQXg) distribution. A detailed analysis of the mathematical and statistical properties of the DPQXg distribution demonstrates various important features. It has been observed that the DPQXg distribution can be used for analyzing both asymmetric and symmetric datasets exhibiting platykurtic and leptokurtic shapes. The hazard rate function of the distribution has both increasing and decreasing failure rates. Furthermore, the dispersion index of the DPQXg distribution indicates that the new statistical model can analyze both over‐ and underdispersed datasets. The parameter estimation of the statistical model is conducted using the maximum likelihood estimation approach. A simulation is carried out to assess the performance of the DPQXg estimator. Finally, real‐world datasets from different fields are used to demonstrate the practical utility of the DPQXg distribution.

Optimizing Mean Estimators with Calibrated Minimum Covariance Determinant in Median Ranked Set Sampling

Calibration methods enhance estimates by modifying the initial design weights, for which supplementary information is exploited. This paper first proposes a generalized class of minimum-covariance-determinant (MCD)-based calibration estimators and then presents a novel class of MCD-based calibrated estimators under a stratified median-ranked-set-sampling (MRSS) design. Further, we also present a double MRSS version of generalized and novel classes of estimators. To assess and compare the performance of the generalized and novel classes of estimators, both real and artificial datasets are utilized. In the presented practical scenarios and real-world applications, we utilize information from a dataset comprising 800 individuals in Turkey from 2014. These data include body mass index (BMI) as the primary variable of interest and age values as auxiliary variables. The BMI results shows that the proposed estimators (y¯PMI=581.1897,y¯PaMI=544.8397) have minimum and (y¯PMII=669.1822,y¯PaMII=648.2363) have maximum PREs in the case of single and double MRSS for odd sample sizes. Similarly, (y¯PMI=860.0099,y¯PaMI=844.7803) have minimum and (y¯PMII=974.5859,y¯PaMII=953.7233) have maximum PREs in the case of single and double MRSS for even sample sizes. Additionally, we conduct a simulation study using a symmetric dataset.

A Novel Odd Beta Prime-Logistic Distribution: Desirable Mathematical Properties and Applications to Engineering and Environmental Data

In parametric statistical modeling, it is important to construct new extensions of existing probability distributions (PDs) that can make modeling data more flexible and help stakeholders make better decisions. In the present study, a new family of probability distributions (FPDs) called the odd beta prime generalized (OBP-G) FPDs is proposed to improve the traditional PDs. A new PD called the odd beta prime-logistic (OBP-logistic) distribution has been developed based on the developed OBP-G FPDs. Some desirable mathematical properties of the proposed OBP-logistic distribution, including the moments, moment-generating function, information-generating function, quantile function, stress–strength, order statistics, and entropies, are studied and derived. The proposed OBP-logistic distribution’s parameters are determined by adopting the maximum likelihood estimation (MLE) method. The applicability of the new PD was demonstrated by employing three data sets and these were compared by the known extended logistic distributions, such as the gamma generalized logistic distribution, new modified exponential logistic distribution, gamma-logistic distribution, exponential modified Weibull logistic distribution, exponentiated Weibull logistic distribution, and transmuted Weibull logistic distribution. The findings reveal that the studied distribution provides better results than the competing PDs. The empirical results showed that the new OBP-logistic distribution performs better than the other PDs based on several statistical metrics. We hoped that the newly constructed OBP-logistic distribution would be an alternative to other well-known extended logistic distributions for the statistical modeling of symmetric and skewed data sets.

Calibration Estimation of Cumulative Distribution Function Using Robust Measures

Outliers are observations that are significantly different from the other observations in a dataset. These types of observations are asymmetric in nature due to a lack of symmetry. The estimation of the cumulative distribution function (CDF) is an important statistical measure commonly discussed for symmetric datasets. However, the estimation of the CDF in the case of the asymmetric nature of the dataset is not a much-explored topic. In this article, we use calibration methodology with auxiliary information for modifying the traditional stratification weight, and hence, we obtain efficient estimates of the CDF using robust measures, i.e., mid-range and tri-mean, under the different distance functions. A simulation study is carried out to see the performance of proposed and existing estimators using asymmetric real-life datasets.

Innovations in Urdu Sentiment Analysis Using Machine and Deep Learning Techniques for Two-Class Classification of Symmetric Datasets

Many investigations have performed sentiment analysis to gauge public opinions in various languages, including English, French, Chinese, and others. The most spoken language in South Asia is Urdu. However, less work has been carried out on Urdu, as Roman Urdu is also used in social media (Urdu written in English alphabets); therefore, it is easy to use it in English language processing software. Lots of data in Urdu, as well as in Roman Urdu, are posted on social media sites such as Instagram, Twitter, Facebook, etc. This research focused on the collection of pure Urdu Language data and the preprocessing of the data, applying feature extraction, and innovative methods to perform sentiment analysis. After reviewing previous efforts, machine learning and deep learning algorithms were applied to the data. The obtained results were compared, and hybrid methods were also recommended in this research, enabling new avenues to conduct Urdu language data sentiment analysis.

A Generalization of Burr Type XII Distribution with Properties, Copula and Modeling Symmetric and Skewed Real Data Sets

A new generalization of Burr type XII model is introduced and studied. The genesis of the new model is based on the family of Cordeiro et al. (2016). The new model generalizes at least eight important sub-models. The new density can be unimodal, symmetric and left skewed. Some useful properties related to the new model are derived. The Clayton Copula-based construction is used to generate many bivariate and multivariate type distributions. Graphically, we performed the simulation experiments to assess of the finite sample behavior of the estimations.

Cost-forced and repeated selective information minimization and maximization for multi-layered neural networks1

The present paper aims to propose a new information-theoretic method to minimize and maximize selective information repeatedly. In particular, we try to solve the incomplete information control problem, where information cannot be fully controlled due to the existence of many contradictory factors inside. For this problem, the cost in terms of the sum of absolute connection weights is introduced for neural networks to increase and decrease information against contradictory forces in learning, such as error minimization. Thus, this method is called a “cost-forced” approach to control information. The method is contrary to the conventional regularization approach, where the cost has been used passively or negatively. The present method tries to use the cost positively, meaning that the cost can be augmented if necessary. The method was applied to an artificial and symmetric data set. In the symmetric data set, we tried to show that the symmetric property of the data set could be obtained by appropriately controlling information. In the second data set, that of residents in a nursing home, obtained by the complicated procedures of natural language processing, the experimental results confirmed that the present method could control selective information to extract non-linear relations as well as linear ones in increasing interpretation and generalization performance.

A Deep Learning Model for Network Intrusion Detection with Imbalanced Data

With an increase in the number and types of network attacks, traditional firewalls and data encryption methods can no longer meet the needs of current network security. As a result, intrusion detection systems have been proposed to deal with network threats. The current mainstream intrusion detection algorithms are aided with machine learning but have problems of low detection rates and the need for extensive feature engineering. To address the issue of low detection accuracy, this paper proposes a model for traffic anomaly detection named a deep learning model for network intrusion detection (DLNID), which combines an attention mechanism and the bidirectional long short-term memory (Bi-LSTM) network, first extracting sequence features of data traffic through a convolutional neural network (CNN) network, then reassigning the weights of each channel through the attention mechanism, and finally using Bi-LSTM to learn the network of sequence features. In intrusion detection public data sets, there are serious imbalance data generally. To address data imbalance issues, this paper employs the method of adaptive synthetic sampling (ADASYN) for sample expansion of minority class samples, to eventually form a relatively symmetric dataset, and uses a modified stacked autoencoder for data dimensionality reduction with the objective of enhancing information fusion. DLNID is an end-to-end model, so it does not need to undergo the process of manual feature extraction. After being tested on the public benchmark dataset on network intrusion detection NSL-KDD, experimental results show that the accuracy and F1 score of this model are better than those of other comparison methods, reaching 90.73% and 89.65%, respectively.

Performance-efficient distributed transfer and transformation of big spatial histopathology datasets in the cloud

Whole Slide Image (WSI) datasets are giga-pixel resolution, unstructured histopathology datasets that consist of extremely big files (each can be as large as multiple GBs in compressed format). These datasets have utility in a wide range of diagnostic and investigative pathology applications. However, the datasets present unique challenges: The size of the files, propriety data formats, and lack of efficient parallel data access libraries limit the scalability of these applications. Commercial clouds provide dynamic, cost-effective, scalable infrastructure to process these datasets, however, we lack the tools and algorithms that will transfer/transform them onto the cloud seamlessly, providing faster speeds and scalable formats. In this study, we present novel algorithms that transfer these datasets onto the cloud while at the same time transforming them into symmetric scalable formats. Our algorithms use intelligent file size distribution, and pipelining transfer and transformation tasks without introducing extra overhead to the underlying system. The algorithms, tested in the Amazon Web Services (AWS) cloud, outperform the widely used transfer tools and algorithms, and also outperform our previous work. The data access to the transformed datasets provides better performance compared to the related work. The transformed symmetric datasets are fed into three different analytics applications: a distributed implementation of a content-based image retrieval (CBIR) application for prostate carcinoma datasets, a deep convolutional neural network application for classification of breast cancer datasets, and to show that the algorithms can work with any spatial dataset, a Canny Edge Detection application on satellite image datasets. Although different in nature, all of the applications can easily work with our new symmetric data format and performance results show near-linear speed-ups as the number of processors increases.

A discrete analogue of odd Weibull-G family of distributions: properties, classical and Bayesian estimation with applications to count data

In the statistical literature, several discrete distributions have been developed so far. However, in this progressive technological era, the data generated from different fields is getting complicated day by day, making it difficult to analyze this real data through the various discrete distributions available in the existing literature. In this context, we have proposed a new flexible family of discrete models named discrete odd Weibull-G (DOW-G) family. Its several impressive distributional characteristics are derived. A key feature of the proposed family is its failure rate function that can take a variety of shapes for distinct values of the unknown parameters, like decreasing, increasing, constant, J-, and bathtub-shaped. Furthermore, the presented family not only adequately captures the skewed and symmetric data sets, but it can also provide a better fit to equi-, over-, under-dispersed data. After producing the general class, two particular distributions of the DOW-G family are extensively studied. The parameters estimation of the proposed family, are explored by the method of maximum likelihood and Bayesian approach. A compact Monte Carlo simulation study is performed to assess the behavior of the estimation methods. Finally, we have explained the usefulness of the proposed family by using two different real data sets.

A Flexible Extension to an Extreme Distribution

The aim of this paper is not only to propose a new extreme distribution, but also to show that the new extreme model can be used as an alternative to well-known distributions in the literature to model various kinds of datasets in different fields. Several of its statistical properties are explored. It is found that the new extreme model can be utilized for modeling both asymmetric and symmetric datasets, which suffer from over- and under-dispersed phenomena. Moreover, the hazard rate function can be constant, increasing, increasing–constant, or unimodal shaped. The maximum likelihood method is used to estimate the model parameters based on complete and censored samples. Finally, a significant amount of simulations was conducted along with real data applications to illustrate the use of the new extreme distribution.

A New Parametric Life Family of Distributions: Properties, Copula and Modeling Failure and Service Times

A new family of probability distributions is defined and applied for modeling symmetric real-life datasets. Some new bivariate type G families using Farlie–Gumbel–Morgenstern copula, modified Farlie–Gumbel–Morgenstern copula, Clayton copula and Renyi’s entropy copula are derived. Moreover, some of its statistical properties are presented and studied. Next, the maximum likelihood estimation method is used. A graphical assessment based on biases and mean squared errors is introduced. Based on this assessment, the maximum likelihood method performs well and can be used for estimating the model parameters. Finally, two symmetric real-life applications to illustrate the importance and flexibility of the new family are proposed. The symmetricity of the real data is proved nonparametrically using the kernel density estimation method.

A Generalization of Binomial Exponential-2 Distribution: Copula, Properties and Applications

In this paper, we propose a new three-parameter lifetime distribution for modeling symmetric real-life data sets. A simple-type Copula-based construction is presented to derive many bivariate- and multivariate-type distributions. The failure rate function of the new model can be “monotonically asymmetric increasing”, “increasing-constant”, “monotonically asymmetric decreasing” and “upside-down-constant” shaped. We investigate some of mathematical symmetric/asymmetric properties such as the ordinary moments, moment generating function, conditional moment, residual life and reversed residual functions. Bonferroni and Lorenz curves and mean deviations are discussed. The maximum likelihood method is used to estimate the model parameters. Finally, we illustrate the importance of the new model by the study of real data applications to show the flexibility and potentiality of the new model. The kernel density estimation and box plots are used for exploring the symmetry of the used data.

A Generalization of Reciprocal Exponential Model: Clayton Copula, Statistical Properties and Modeling Skewed and Symmetric Real Data Sets

We introduce a new extension of the reciprocal Exponential distribution for modeling the extreme values. We used the Morgenstern family and the clayton copula for deriving many bivariate and multivariate extensions of the new model. Some of its properties are derived. We assessed the performance of the maximum likelihood estimators (MLEs) via a graphical simulation study. The assessment was based on the sample size. The new reciprocal model is employed for modeling the skewed and the symmetric real data sets. The new reciprocal model is better than some other important competitive models in statistical modeling.

Cost-conscious mutual information maximization for improving collective interpretation of multi-layered neural networks

The present paper aims to improve the collective interpretation realized by compressing multi-layered neural networks and to make the interpretation as natural and stable as possible. We collectively interpret the final representations by maximizing mutual information between inputs and neurons, expecting that mutual information maximization can disentangle complex features into simpler ones. However, we have had difficulty in increasing mutual information and in obtaining interpretable features for several data sets. By examining closely the processes of information maximization, we found that, in addition to the information maximization, we need to consider the cost associated with this information maximization. Thus, we try to maximize not simply mutual information but the ratio of mutual information to the cost, and this method can be called “cost-conscious mutual information maximization.” The cost-conscious method aims to extend Linsker’s maximum information preservation principle to a variety of data sets by more directly taking into account the cost associated with the process of information maximization. The method was applied to two data sets: the artificial and symmetric data set and the credit default data set. First, by using the symmetric data set injected with random noises, the cost-conscious information maximization method could extract the symmetric property almost perfectly against the random noises. In the experimental results on the credit default data set, the present method could make it possible to interpret the final results the most naturally, showing why and how the credit default could occur very naturally. The experimental results show that the neural networks can be used to interpret data sets more naturally than the conventional methods such as the logistic regression analysis.

A New Flexible Three-Parameter Model: Properties, Clayton Copula, and Modeling Real Data

In this article, we introduced a new extension of the binomial-exponential 2 distribution. We discussed some of its structural mathematical properties. A simple type Copula-based construction is also presented to construct the bivariate- and multivariate-type distributions. We estimated the model parameters via the maximum likelihood method. Finally, we illustrated the importance of the new model by the study of two real data applications to show the flexibility and potentiality of the new model in modeling skewed and symmetric data sets.

Generalized inverted Kumaraswamy generated family of distributions: theory and applications

This paper proposes a new generator function based on the inverted Kumaraswamy distribution and introduces ‘generalized inverted Kumaraswamy-G’ family of distributions. We provide a comprehensive account of some of its mathematical properties that include the ordinary and incomplete moments, quantile and generating functions and order statistics. The infinite mixture representations for probability density and cumulative distribution and entropy functions of the new family are also established. The density function of the ith-order statistics is expressed as an infinite linear combination of baseline densities and model parameters are estimated by maximum likelihood method. Four special models of this family are also derived along with their respective hazard rate functions. The maximum likelihood estimation (MLE) method is used to obtain the model parameters. Monte Carlo simulation experiments are executed to assess the performance of the ML estimators under the corresponding generated models while some data applications are also illustrated. The results of the study show that the proposed distribution is more flexible as compared to the baseline model. This distribution especially can be used to model symmetric, left-skewed, right-skewed and reversed-J data sets.

Axially Symmetric Data Clustering Through Dirichlet Process Mixture Models of Watson Distributions.

This paper proposes a Bayesian nonparametric framework for clustering axially symmetric data. Our approach is based on a Dirichlet processes mixture model with Watson distributions, which can also be considered as the infinite Watson mixture model. In this paper, first, we extend the finite Watson mixture model into its infinite counterpart based on the framework of truncated Dirichlet process mixture model with a stick-breaking representation. Second, we propose a coordinate ascent mean-field variational inference algorithm that can effectively learn the parameters of our model with closed-form solutions; Third, to cope with a massive data set, we develop a stochastic variational inference algorithm to learn the proposed model through the method of stochastic gradient ascent; Finally, the proposed nonparametric Bayesian model is evaluated through simulated axially symmetric data sets and a real-world application, namely, gene expression data clustering.