Statistics, Optimization & Information Computing

Estimates for Distributions of Suprema of Spherical Random Fields

Lyudmyla Sakhno — Fri, 04 Nov 2022 00:00:00 +0800

Bounds for distributions of suprema of $\varphi$-sub-Gaussian random fields defined over the $N$-dimensional unit sphere are stated. Applications of the results to the spherical fractional Brownian motion, isotropic Gaussian fields and some other models are presented.

Nonparametric Recursive Kernel Type Eestimators for the Moment Generating Function Under Censored Data

Salim Bouzebda, Issam Elhattab, Yousri Slaoui Slaoui, NourElhouda Taachouche — Fri, 17 Feb 2023 00:00:00 +0800

We are mainly concerned with kernel-type estimators for the moment-generating function in the present paper. More precisely, we establish the central limit theorem with the characterization of the bias and the variance for the nonparametric recursive kernel-type estimators for the moment-generating function under some mild conditions in the censored data setting. Finally, we investigate the methodology’s performance for small samples through a short simulation study.

Reliability Estimation for the Inverse Weibull Distribution Under Adaptive Type-II Progressive Hybrid Censoring: Comparative Study

Majd Alslman, Amal Helu — Mon, 02 Jan 2023 00:00:00 +0800

The aim of this study is to investigate different methods of estimating the stress-strength reliability parameter, $\theta =P(Y<X)$, when the strength (X) and the stress (Y) are independent random variables taken from the inverse Weibull distribution (IWD), with the same shape parameter and different scale parameters. Based on Adaptive Type-II Hybrid progressive censored samples, we employ classical and Bayesian approaches. In the classical approach, we use the maximum likelihood estimator (MLE), the approximate maximum likelihood estimator (AMLE), and the least squares estimator (LSE). In contrast, the Bayesian approach utilizes symmetric and asymmetric loss functions. Due to the absence of explicit forms for Bayes estimators, we propose using Lindley's approximation method for computing the Bayes estimators. We compare these estimators using extensive simulations and two criteria: the bias and the mean square error (MSE). Finally, two real-life data examples are provided for illustrations.

Inference Based on New Pareto-Type Records With Applications to Precipitation and Covid-19 Data

A. Saadati Nik, A. Asgharzadeh, A. Baklizi — Sun, 26 Feb 2023 00:00:00 +0800

We consider estimation and prediction of future records based on observed records from the new Pareto type distribution proposed recently by Bourguignon et al. (2016), “M. Bourguignon, H. Saulo, R. N. Fernandez, A new Pareto-type distribution with applications in reliability and income data, Physica A, 457 (2016), 166-175.”. We derived several point predictors for a future record on the basis of the first n records. Two real data sets on precipitation and Covid 19 are analysed and a Monte Carlo simulation study has been performed to evaluate the statistical performance of point predictors presented in this paper.

Feasible Stein-Type and Preliminary Test Estimations in the System Regression Model

Mina Norouzirad, Mohammad Arashi, Filipe J. Marques, Naushad A. Mamod Khan — Fri, 21 Oct 2022 00:00:00 +0800

In a system of regression models, finding a feasible shrinkage is demanding since the covariance structure is unknown and cannot be ignored. On the other hand, specifying sub-space restrictions for adequate shrinkage is vital. This study proposes feasible shrinkage estimation strategies where the sub-space restriction is obtained from LASSO. Therefore, some feasible LASSO-based Stein-type estimators are introduced, and their asymptotic performance is studied. Extensive Monte Carlo simulation and a real-data experiment support the superior performance of the proposed estimators compared to the feasible generalized least-squared estimator.

The Poisson-Topp-Leone Burr Type-X II Model: Various Uncensored Applications for Statistical Modeling and Some Copulas

Murtadha Abdullah, Wahhab Salim Mohammed, Aqeel Hameed Farhana — Sat, 07 Jan 2023 00:00:00 +0800

The Poisson-Topp-Leone Burr type-X II distribution is studied mainly for illustrating its wide applicability under uncensored engineering and medical real-life datasets. The real-life datasets are checked and analyzed for the statistical modeling purpose. The Poisson-Topp-Leone Burr type-X II model is compared with other nine types of Burr type-X II extensions and provided the best results. For modeling the bivariate uncensored engineering and medical real-life datasets, we presented some bivariate version with some useful theoretical results. Those versions are investigated due to certain and common copulas.

A Multiobjective Optimization Approach to Pulmonary Rehabilitation Effectiveness in COPD

Jorge Cabral, Vera Afreixo, Cristiana J Silva, Ana Tavares, Alda Marques — Sun, 10 Jul 2022 00:00:00 +0800

Chronic obstructive pulmonary disease (COPD) is a common disease that accounts for a significant individual and societal burden. Pulmonary rehabilitation (PR) is a key management strategy but it is highly inaccessible, making prioritisation highly needed. This study aimed to determine and optimize predictive models of PR outcomes and build a tool to help healthcare professionals in their clinical decision-making about PR prioritisation. Data from patients who performed a 12-week community-based PR programme were analysed. Exercise capacity with the six-minutes walk test distance (6MWD), isometric quadriceps muscle strength with the handheld dynamometry (QMS) and dyspnoea with the modified Medical Research Council dyspnoea scale (mMRC) were assessed before and after PR. Multiple linear regression models were determined based on the Akaike information criteria and a cross-validation method. The resultant multiobjective problem was solved using the Nondominated Sorting Genetic Algorithm-II. R Shiny package was used to create a web-based user interface. Data from 95 patients with COPD (median age of 69 years, 19 female and generally overweight), resulted in linear predictive models for the post-pre difference of the 6MWD, QMS and mMRC with cross-validation R² of 0.49, 0.53 and 0.51, respectively. 6MWD and mMRC were common statistically significant predictors. Pareto front patients were obese ex-smoker women that do not do long-term oxygen therapy and that performed PR. The distance to the Pareto front along with the estimates given by our models are easily obtained using the designed R Shiny interface and may help healthcare professionals decide on the prioritisation to PR programmes.

Winning a Tournament According to Bradley-Terry Probability Model

Shuyang Gao, Hosam Mahmoud — Sat, 07 Jan 2023 00:00:00 +0800

We analyze the chances of winning a tournament under the assumption that the probabilities of winning individual matches follow Bradley-Terry model [2]. We present an exact solution and show a few examples of its use. The examples are from California volleyball tournaments, the round of sixteen in the World Cup and the Champions League, the group stage of the Association of Tennis Professionals tournament, and the volleyball SuperLega in Italy.

The computational complexity of the solution grows exponentially fast
with the number of teams and we seek approximations via multivariate Gaussian laws.

A Novel Two-Parameter Compound G Family of Probability Distributions With Some Copulas, Statistical Properties and Applications

Mohamed Refaie, Hisham Abdeltawab Mahran — Sat, 31 Dec 2022 00:00:00 +0800

In this work, we introduce a new G family with two-parameter called the compound reversed Rayleigh-G family. Several relevant mathematical and statistical properties are derived and analyzed. The new density can be heavy tail and right skewed with one peak, symmetric density, simple right skewed density with one peak, asymmetric right skewed with one peak and a heavy tail and right skewed with no peak. The new hazard function can be "upsidedown-constant", "constant", "increasing-constant", "revised J shape", "upside-down", "J shape" and "increasing". Many bivariate types have been also derived via di¤erent common copulas. The estimation of the model parameters is performed by maximum likelihood method. The usefulness and ‡exibility of the new family is illustrated by means of two real data sets.

On Kernel-Based Estimator of Odds Ratio Using Different Stratified Sampling Schemes

Abbas Eftekharian, Hani Samawi, Haresh Rochani — Thu, 22 Dec 2022 00:00:00 +0800

The kernel-based estimator of Cochran Mantel-Haenszel odds ratio based on stratified simple and ranked set sampling is proposed. The expectation and variance of the estimator are analytically obtained. Using a simulation study, the estimator based on stratified ranked set sampling is more efficient than its counterpart based on stratified simple random sampling. Finally, the estimator's performance is investigated by using base deficit data.

Analysis of Household Income, Expenditure and Consumption Survey Research Data for North Sinai Governorate in Egypt Using Length Biased Truncated Lomax Distribution

Amal S. Hassan, Ahmed Wael Shawki, Hiba Z. Muhammed — Sat, 07 Jan 2023 00:00:00 +0800

The length biased truncated Lomax distribution is introduced in this study as a weighted form of the truncated Lomax distribution. The length biased truncated Lomax distribution’s essential distributional features are investigated. In the case of complete and type-II censored data, the maximum likelihood method is provided for estimating population parameter. The model parameter asymptotic confidence interval is calculated. To demonstrate the pattern of the estimate, a sample generation algorithm is supplied, as well as a Monte Carlo simulation analysis. We can see from the simulation research that as the censoring level is increased, the mean squared error of parameter estimates decrease’s for all given values. With increasing sample size, the mean squared error and average length of parameter estimates decrease. The estimates get increasingly accurate as the sample size grows higher, suggesting that its asymptotically unbiased. Furthermore, in all cases, the mean squared error diminishes as the sample size grows, indicating that the estimates of parameter are consistent. Modelling to medical data and the percentage of household spending on education out of total household expenditure from the household income, expenditure and consumption survey (HIECS) data are used to show the importance of the new model. The Kumaraswamy, beta, truncated power Lomax, truncated Weibull, and one parameter-beta distributions perform poorly in comparison to the suggested distribution.

A New Group Acceptance Sampling Plans based on Percentiles for the Weibull Fréchet Model

Basma Ahmed, Haitham Yousof — Thu, 17 Mar 2022 00:00:00 +0800

When the life test is truncated at a pre-determined duration, group acceptance sampling plans for the Weibull
Frchet distribution percentiles are introduced in this article. Under a given group size, acceptance limit, and customer risk, the minimum number of groups needed to guarantee the specified life percentile is calculated. The operating characteristic values are discovered, additionally the producer’s risk. To illustrate the process mentioned here, two experimental are given. Also, real data set is used to demonstrate the flexibility of the Weibull Frchet model.

Comparison of Subspace Dimension Reduction Methods in Logistic Regression

Saeed Heydari, Mahmoud Afshari, Saeed Tahmasbi, Morad Alizadeh — Thu, 23 Sep 2021 00:00:00 +0800

Regression models are very useful in describing and predicting real world phenomena. The Logistic regression is an extremely robust and flexible method for dichotomous classification prediction. This model is a classification model rather than regression model. When the number of predictors in regression models is high, data analysis is difficult. Dimension reduction has become one of the most important issues in regression analysis because of its importance in dealing with problems with high-dimensional data. In this paper, the methods of diminishing the dimension of variables in logistic regression, which include the estimation of central subspace based on the inverse regression, the likelihood acquisition method and principal component analysis are considered. Using a real data associated with the dental problems the Logistic regression is fitted and the correct classification of the data computed. At the end, The simulation study is presented to compare the sufficient dimension reduction methods with each other. In the simulation, MATLAB software is used and the Programs are attached at the end of the article in appendix.

A Bayesian Semi-parametric Quantile Regression Approach for Joint Modeling of Longitudinal Ordinal and Continuous Responses

Omid Khazaei, Mojtaba Ganjali, Mojtaba Khazaei — Mon, 13 Mar 2023 00:00:00 +0800

Quantile regression (QR) models are one of the methods for longitudinal data analysis. When responses seem
to be skew and asymmetric due to outliers and heavy-tails, QR models may work suitably. This paper developes the semi-parametric quantile regression model for analyzing longitudinal continuous and ordinal mixed responses. The latent variable model and some threshold parameters are used to perform the quantile regression model’s ordinal part. The error of the latent variable model has Asymmetric Laplace (AL) distribution. The error term’s distribution is assumed to be AL distribution to model the continuous responses. The correlations of longitudinal responses belong to the same individual and those of mixed continuous and ordinal responses are considered using a random-effects approach. The regression spline is used to approximate the non-parametric part of the model. The parameter estimation procedure is performed under a
Bayesian paradigm using the Gibbs sampling method. A simulation study is performed to demonstrate the proposed model’s performance where the relative biases, standard errors, and root of MSEs of estimated parameters are decreased in the semi- parametric QR joint model when the number of subjects is increased. In our application, it was found that the mother’s age and her child’s age have significant effects on reading ability, and antisocial behavior depends on the child’s gender.

Dynamics of the Predator-Prey Model with Beddington-DeAngelis Functional Response Perturbed by Lévy Noise

Olga Borysenko, Oleksandr Borysenko — Mon, 28 Nov 2022 00:00:00 +0800

We study the non-autonomous stochastic predator-prey model with Beddington-DeAngelies functional response driven by the system of stochastic differential equations with white noise, centered and non-centered Poisson noises. It is proved the existence and uniqueness of the global positive solution of considered system. We obtain sufficient conditions of stochastic ultimate boundedness, stochastic permanence, non-persistence in the mean, weak and strong persistence in the mean and extinction of the population densities in the considered stochastic predator-prey model.

The Marshall-Olkin Odd Exponential Half Logistic-G Family of Distributions: Properties and Applications

Broderick Oluyede, Fastel Chipepa — Wed, 15 Dec 2021 00:00:00 +0800

We develop a new family of distributions, referred to as the Marshall-Olkin odd exponential half logistic-G, which is a linear combination of the exponential-G family of distributions. The family of distributions can handle heavy-tailed data and has non-monotonic hazard rate functions. We also conducted a simulation study to assess the performance of the proposed model. Real data examples are provided to demonstrate the usefulness of the proposed model in comparison with several other existing models.

Simultaneous Test for Means: An Unblind Way to the F-test in One-way Analysis of Variance

Elsayed A. H Elamir — Wed, 11 Aug 2021 00:00:00 +0800

After rejecting the null hypothesis in the analysis of variance, the next step is to make the pairwise comparisons to find out differences in means. The purpose of this paper is threefold. The foremost aim is to suggest expression for calculating decision limit that enables us to collect the test and pairwise comparisons in one step. This expression is proposed as the ratio of between square for each treatment and within sum of squares for all treatments. The second aim is to obtain the sampling distribution of the proposed ratio under the null hypothesis. This sampling distribution is derived exactly as the beta distribution of the second type. The third aim is to use beta distribution of second type and adjusted p-values to create adjusted points and decision limit. Therefore, reject the null hypothesis of equal means if any adjusted point falls outside the decision limit. Simulation study is conducted to compute type I error. The results show that the proposed method controls the type I error near the nominal values using Benjamini-Hochberg’adjusted p-values. Two applications are given to show the benefits of the proposed method.

Selecting Key Features of Online Behaviour on South African Informative Websites Prior to Unsupervised Machine Learning

Judah Soobramoney, Retius Chifurira, Temesgen Zewotir — Fri, 21 Oct 2022 00:00:00 +0800

The main aim of the study was to explore the feature selection process of online web data prior to unsupervised machine learning models. At the time of writing, no such literature could be found reporting the use of feature selection in this context. Feature selection was determined by inspecting the variability and association between features. The variability of numeric features were quantified using the variance, mean absolute difference and dispersion ratio metrics whilst the coefficient of unalikeability was employed for categorical features. To quantify association, correlation matrices were used for numeric features, chi-squared independence tests between categorical features and box-and-whisker plots between mixed features. The main findings showed the variance, mean absolute difference, dispersion ratio and coefficient of unalikeability metrics have successfully highlighted features with very low variability within the observed data. Whilst the correlation matrix, chi-squared test for independence and box-and-whisker plots highlighted possible redundancy, natural relationships and insightful relationships between the features thereby suggesting features to be considered for omission prior to unsupervised modelling. The proposed methods and findings can be applied to various other applications of feature selection and exploration.

On a Closed-Loop Supply Chain with Graded Returns

Najeeb Al-Matar, Lotfi Tadj — Sat, 18 Mar 2023 00:00:00 +0800

We use optimal control theory to determine the optimal manufacturing, remanufacturing, and disposal rates in a closed-loop supply chain. The returned items are of different quality levels. The firm grades the returned items according to their quality. Each class of returned items is remanufactured and stocked separately. Also, all items are subject to deterioration and the deterioration rate depends on the class. Finally, each class of items is sold to a different segment of customers. An illustrative example is presented along with a sensitivity analysis on some of the system parameters.