Statistics, Optimization & Information Computing

Prediction of Censored Weibull Lifetimes in a Simple Step-Stress Plan With Khamis-Higgins Model

Mohammad Amleh — 2021-08-17

In this paper, we discuss the prediction of the lifetimes to failure of censored units from Weibull distribution for a simple step-stress plan under Khamis-Higgins model. Different methods of prediction are considered including maximum likelihood predictor, modifified maximum likelihood predictor, conditional median predictor, and best unbiased predictor. Another aspect of prediction is constructing prediction limits for future lifetimes of the censored units. The pivotal quantity, highest conditional density, and shortest-length based methods are discussed in this paper. Monte Carlo simulations are performed to compare all the prediction methods developed here and one real data set is analyzed for illustrative purposes.

Bivariate Weibull-G Family Based on Copula Function: Properties, Bayesian and non-Bayesian Estimation and Applications

El-Sayed A. El-Sherpieny — 2021-07-12

This paper aims to obtain a new flexible bivariate generalized family of distributions based on FGM copula, which is called bivariate FGM Weibull-G family. Some of its statistical properties are studied as marginal distributions, product moments, and moment generating functions. Some dependence measures as Kendall’s tau and median regression model are discussed. After introducing the general class, four special sub models of the new family are introduced by taking the baseline distributions as Pareto, inverted Topp-Leone, exponential, and Rayleigh distributions. Maximum likelihood and Bayesian approaches are used to estimate the model unknown parameters. Further, percentile bootstrap confidence interval and bootstrap-t confidence interval are estimated for the model’s parameters. A Monte-Carlo simulation study is carried out of the maximum likelihood and Bayesian estimators. Finally, we illustrate the importance of the proposed bivariate family using two real data sets in medical field.

Exponentiated Extended Chen Distribution: Regression Model and Estimations

Mohammad Rea Kazemi — 2021-08-17

In this paper, we introduce a new four-parameter generalized version of the Chen model called the exponentiated extended Chen distribution. Some results about the reliability characteristics of hazard rate function as well as some mathematical properties are provided. The maximum likelihood estimators and five approaches based on the concept of minimum spacing distance estimators are given for estimation of the model parameters and their performances in estimating of parameters are compared by means of Monte Carlo simulations. Also, a multiple regression model with the censored data based on proposed distribution is introduced.

A Novel Two-parameter Nadarajah-Haghighi Extension: Properties, Copulas, Modeling Real Data and Different Estimation Methods

Wahid Shehata — 2021-07-30

A new two-parameter lifetime distribution is proposed and numerically studied. The new model has a flflexible failure rate shapes such as “monotonically increasing” , “monotonically decreasing” , “bathtub” , “constant” , “upside down” and “J-shape” . Various of its statistical properties are derived. A numerical analysis of skewness and kurtosis are presented. Many bivariate and multivariate extensions are also presented via Farlie Gumbel Morgenstern copula, Renyi entropy copula, modifified Farlie Gumbel Morgenstern copula and Clayton copula. Several estimation methods such as the maximum likelihood, Cramer-von-Mises, L-moment estimation, Anderson Darling, right Tail-Anderson Darling estimation and left tail-Anderson Darling are presented and considered. Numerical simulations are performed to assess the performance of estimation methods. An environmental data set is employed to measure flflexibility of the new model also to compare the estimation methods.

A New Two-parameter Estimator for the Gamma Regression Model

YASIN ASAR — 2022-01-11

In this paper, we propose a new two-parameter biased estimator in gamma regression models when there is collinearity among the regressors. We investigate the mean squared error (MSE) properties of the newly proposed estimator. Moreover, we provide some theorems to compare the new estimators to the existing ones. We conduct a Monte Carlo simulation study to compare the estimators under different designs of collinearity in the sense of MSE. Moreover, we provide a real data application to show the usefulness of the new estimator.The simulations and real data results show that the proposed estimator beats other competitor estimators.

An Integer Optimal Control Model of Production-Inventory System

Ali Khaleel Dhaiban — 2020-12-27

The optimal control model of the production-inventory system has investigated in several past studies, but without taking into account the integer condition. This study suggested a new approach to find the integer solution of production-inventory control model under periodic review policy. A new approach is based on the modified some equations of Pontryagin maximum principle that used to find the solution of the non-integer model. Our numerical results showed the efficiency of the new approach by saving the paths of inventory level and production rate up to reach its goals over time. The total penalty costs of the model were the same, despite a difference in the values of initial inventory level. Also, we testified a new approach by formulating the quadratic programming problem of the production-inventory system. The solution was the same for the two problems; quadratic programming and new approach.

Penalty ADM Algorithm for Cardinality Constrained Mean-Absolute Deviation Portfolio Optimization

Temadher AlMaadeed — 2022-02-03

In this paper, we study the cardinality constrained mean-absolute deviation portfolio optimization problem with risk-neutral interest rate and short-selling. We enhance the model by adding extra constraints to avoid investing in those stocks without short-selling positions. Also, we further enhance the model by determining the short rebate based on the return. The penalty alternating direction method is used to solve the mixed integer linear model. Finally, numerical experiments are provided to compare all models in terms of Sharpe ratios and CPU times using the data set of the NASDAQ and S&P indexes.

Statistical Inference for Multivariate Conditional Cumulative Distribution Function Estimation By Stochastic Approximation Method

Sahar Slama — 2022-03-24

This paper handles non-parametric estimation of a conditional cumulative distribution function (CCDF). Using a recursive approach, we set forward a multivariate recursive estimator defifined by stochastic approximation algorithm. Our basic objective is to investigate the statistical inference of our estimator and compare it with that of non-recursive Nadaraya-Watson’s estimator. From this perspective, we fifirst derive the asymptotic properties of the proposed estimator which highly depend on the choice of two parameters, the stepsize (γn) as well as the bandwidth (hn). The second generation plug-in method, a method of bandwidth selection minimizing the Mean Weighted Integrated Squared Error (MW ISE) of the estimator in reference, entails the optimal choice of the bandwidth and therefore maintains an appropriate choice of the stepsize parameter. Basically, we demonstrate that, under some conditions, the Mean Squared Error (MSE) of the proposed estimator can be smaller than the one of Nadaraya Watson’s estimator. We corroborate our theoretical results through simulation studies and two real dataset applications, namely the Insurance Company Benchmark (COIL 2000) dataset as well as the French Hospital Data of COVID-19 epidemic.

On Accelerated Failure Time Models Performance Under Progressive Type-II Censoring

Amal Helu — 2022-04-26

Accelerated failure time (AFT) models have intensive applications in many research areas, including but not limited to behavioral, chronic (e.g., cancer), and infectious diseases (e.g., HIV) research. In this paper, we investigate the performance of the AFT models when Progressive Type-II censoring schemes are performed. We demonstrate the usefulness of using these schemes. We discuss their testing procedure power, $Bias$, and $MSE$ of the hazard ratio estimates compared to the same sample size of the uncensored data. Theoretically, we derive the models, the $MLE$ scores, and the Fisher information matrix. A comparison between these estimators is provided by using extensive simulation. A real-life data example is provided to illustrate our proposed estimators.

Bayesian Disease Mapping: A Literature Review With an Application, Using WinBugs Software

Lizanne Raubenheimer — 2022-04-09

In this paper we review the improper and proper conditional autoregressive (CAR) models. A set of spatially correlated Gaussian random effects are assumed. The CAR model which contains components from both the uncorrelated heterogeneity (UH) and correlated heterogeneity (CH) models, have been applied to the South African acute pericarditis 2014 data set, where a Poisson model is used. Acute pericarditis is caused by an inflammation of the pericardium in the heart. The data set has been used to examine whether there is a significant difference between the proper conditional autoregressive prior and the intrinsic conditional autoregressive prior for the correlated heterogeneity component in a convolution model. Both the hyperpriors of the precision for the uncorrelated heterogeneity components were modelled by using the Jeffreys’ prior. The sensitivity of the hyperprior has also been investigated. The deaths from this disease in 2014 in South Africa have been considered, where disease maps and the relative risk of acquiring and dying from acute pericarditis have been investigated, as well as the standardised mortality ratio (SMR). The convergence and burn-in period of the models were assessed by the Brook-Gelman-Rubin (BGR) diagnostic. The deviance information criterion (DIC) was used to assess the models.

Bootstrap Confidence Intervals for Common Signal-to-noise Ratio of Two-parameter Exponential Distributions

Warisa Thangjai — 2022-05-04

Signal-to-noise ratio (SNR) is a reciprocal of coefffficient of variation. The SNR is a measure of mean relative to the variability. Confidence procedures for common SNR of two-parameter exponential distributions were developed using generalized confidence interval (GCI) approach, large sample (LS) approach, adjusted method of variance estimates recovery (Adjusted MOVER) approach, and bootstrap approaches based on standard bootstrap (SB) and parametric bootstrap (PB). The performances of all approaches are measured by coverage probability and average length. Simulation studies show that all approaches have the coverage probabilities below the nominal confidence level of 0.95 when the common SNR is negative value. However, the coverage probabilities of all approaches are greater than the nominal confidence level of 0.95 when the common SNR is positive value. Moreover, the LS and AM approaches are the conservative confidence intervals. In addition, the GCI and PB approaches provide the confidence intervals with coverage probabilities close to the nominal confidence level of 0.95 when the sample sizes are large and the common SNR is positive value. The GCI and PB approaches are recommended to estimate the confidence intervals for the common SNR of two-parameter exponential distributions. Finally, all proposed approaches are employed in the data of the survival days of lung cancer patients for a demonstration.

A Weighted-path Following Interior-point Algorithm for Convex Quadratic Optimization Based on Modified Search Directions

Nouha Moussaoui — 2022-06-25

Getting a perfectly centered initial point for feasible path-following interior-point algorithms is a hard practical task. Therefore, it is worth to analyze other cases when the starting point is not necessarily centered. In this paper, we propose a short-step weighted-path following interior-point algorithm (IPA) for solving convex quadratic optimization (CQO). The latter is based on a modified search direction which is obtained by the technique of algebraically equivalent transformation (AET) introduced by a new univariate function to the Newton system which defines the weighted-path. At each iteration, the algorithm uses only full-Newton steps and the strategy of the central-path for tracing approximately the weighted-path. We show that the algorithm is well-defined and converges locally quadratically to an optimal solution of CQO. Moreover, we obtain the currently best known iteration bound, namely, $\mathcal{O}\left(\sqrt{n}\log \dfrac{n}{\epsilon}\right)$ which is as good as the bound for linear optimization analogue. Some numerical results are given to evaluate the efffficiency of the algorithm.

The Functional Regression With Reconstructed Functions From Hybrid Principal Components Analysis: With EEG-fMRI Application

Mohammad Fayaz — 2022-06-25

Objective: In this article, we reconstruct the hybrid data with hybrid principal component analysis (HPCA) as a feature extraction step and model them with functional regression as a modeling step, and comparing models and choose the best number of HPCA based on the prediction accuracy as an evaluation step. Method: We decompose the hybrid data to the eigencomponents with HPCA. The reconstructed data from HPCA were divided into the training and testing dataset. The function-on-function signal compression and scalar-on-function regressions were used. Three simulation scenarios and their applications in the neuroimaging datasets (EEG-fMRI) were studied. The number of HPCA was selected with the mean squared prediction error (MSPE). Result: The simulation shows that the raw data, reconstructed from the first and all HPCAs for the training dataset has median MSPE 0.1001, 0.0028, and 0.0174 respectively, and for the testing, the dataset has 0.3207, 0.1118, and 0.2484 respectively. The EEG-fMRI suggests that in both auditory and visual tasks and standard and target stimuli for different regions of the brain the first HPCA has the smallest MSPE. Conclusions: We conclude this method improves the prediction accuracy of the experiments with the EEG datasets. And we recommend that instead of using the functional PCA on the desired dimension, reconstruct the data with HPCA and average it on the other two dimensions for functional regression models.

The Odd Log-Logistic Transmuted-G Family of Distributions: Properties, Characterization, Applications and Different Methods of Estimation

Morad Alizadeh — 2022-04-22

In this work, we propose a new class of lifetime distributions called the odd log-logistic transmuted-G family. The proposed family of distributions is constructed by compounding the odd log-logistic distribution with the transmuted distribution. It can provide better fits than some of the known lifetime models and this fact represents a good characterization of this new family. Some characterizations for the new family are presented as well as some of its mathematical properties including. The maximum likelihood, Least squares and weighted least squares, Cram\'{e}r--von--Mises, Anderson-Darling and right-tailed Anderson-Darlingare and maximum product of spacings methods are used for estimating the model parameters. The importance and flexibility of the new family are illustrated by means of an application to a real data set.

Polar Integers and Polar Integer Optimization

Yuly Shipilevsky — 2022-06-25

This is a pioneering work, introducing a special class of complex numbers, wherein their absolute values and arguments given in a Polar coordinate system are integers, which when considered within the complex plane, constitute Unicentered Radial Lattice and similarly for quaternions and Euclidean R²and R³Spaces. The corresponding Optimization Problems are introduced as well.

Detection Model With a Maximum Discounted Effort Reward Search to Maintenance a Best Decision Under the Quality Control Process

Mohamed El-Hadidy — 2022-02-20

This paper aims to get a needed service by making the best decision of choosing one suitable company (queue) from K − independent Markovian queues (companies). The customers arrive at each queue according to a Poisson process. The service time of each customer has an exponential distribution. In a steady-state, the best decision depends on the minimum cost of detecting the suitable company which provides the best service with high speed (maximum service rate). To minimize the detection cost and maximize the probability of detection, we consider the search effort bounded by a Gaussian distribution as a function with a discounted parameter. The effectiveness of this model appears in a simulation study and the comparison with other models.

New Algorithms and Software for Significance Controlled Variable Selection

Adriano Zambom — 2022-05-29

Stepwise regression algorithms have been widely used for a variety of applications and continue to be a fundamental tool in variable selection. Most functions available in statistical software packages deliver models that may contain insignificant predictors because of the criterion of the optimization at each step. Here we introduce an R package that provides the user with several measures of the prospective model at each step of the algorithm. These prospective models are checked with multiple testing p-value corrections such as Bonferroni and False Discovery Rate and hence the algorithm's final model includes only predictors that have their significance controlled by the choice of correction type and alpha level. Moreover, the steps forward or backward can have an entry or drop criterion that is a combination of the p-values of prospective models. We illustrate the functionality of the package with examples and simulations.

A Hybrid Harmony Search and Particle Swarm Optimization Algorithm (HSPSO) for Testing Non-functional Properties in Software System

Nurudeen Muhammad Bala — 2021-01-09

An important aspect of improving software system is testing. However, it is time demanding and sometimes
labour intensive if done manually. In this paper, we developed an automatic search-based approach for testing the nonfunctional properties of a software system using hybrid harmony search and particle swarm optimization algorithms. The approach birthed a new algorithm named HSPSO, which is proposed based on the strength of HS over Genetic algorithm (GA) in terms of less adjustable parameters, quick convergence and smooth implementation. On the other hand, we propose the PSO to complement the drawback of HS in terms of time consumption problem. Besides, we used four programs for the comparative efficiency analysis of the proposed algorithm in relation to competing algorithms based on average branch coverage and execution time. The results from the analysis showed that the HSPSO algorithm was able to achieve 100% average coverage with a fewer number of generated test cases and under limited execution time.

On Sensitivity for Portfolio Optimisation Based on a High-dimensional Jump-diffusion Merton Model

Bahareh Afhami — 2022-06-25

The problem of singularity of the variance-covariance matrix and its impact on the sensitivity of Markowitz portfolio optimization has been extensively studied in the literature when the underlying model does not include jump terms. In this paper, we first use a jump-diffusion multivariate Merton model to evaluate sensitivity of portfolio optimization and apply principal component analysis (PCA) for dimensionality reduction as a solution to singularity of the variance-covariance matrix. Finally, we provide a numerical study based on the adjusted daily closing price of $S\&{P}\, 500$ stocks to explore the impact of the dimension of the reduced space and jump terms on the sensitivity of the portfolio optimization. Empirical experiments confirm that for models without jump terms, the sensitivity analysis may not reflect the correct assessment of the impact of dimensionality reduction on the portfolio optimization.