International Journal of Statistics and Probability

Many clinical trials fall short of their accrual goals. This can be avoided with accurate accrual prediction tools. Past researchers provide important methodological alternative models for predicting accrual in clinical trials. One model allows for slow accrual at the start of the study, which eventually reaches a threshold. A simpler model assumes a constant rate of accrual. A comparison has been attempted but we wish to point out some important considerations when comparing these two models. In fact, we can examine the reasonableness of a constant accrual assumption (simpler model) which had data 239 days into a three-year study. We can now update that and report accumulated from the full three years of accrual data and we can demonstrate that constant accrual rate assumption was met in this particular study. We will use this report to frame future research in the area of accrual prediction.

To assess validity of a low-intensity measure of fitness (X) in a population of older adults as a proxy measure for the original, high-intensity measure (Y), we used ordinary least square regression with the new, potential proxy measure (X) as the sole explanatory variable for Y. A perfect proxy measure would be unbiased (i.e., result in a regression line with a y-intercept of zero and a slope of one) with no error (variance equal to zero). We evaluated the properties of potential biases of proxy measures. A two degree-of-freedom approach using a contrast matrix in the setting of simple linear ordinary least squares regression was compared to a one degree-of-freedom paired t test alternative approach. We found that substantial improvements in power could be gained through use of the two degree-of-freedom approach in many settings, while scenarios where no linear bias was present there could be modest gains from the paired t test approach. In general, the advantages of the two degree-of-freedom approach outweighed the benefits of the one degree-of-freedom approach. Using the two degree-of-freedom approach, we assessed the data from our motivating example and found that the low-intensity fitness measure was biased, and thus was not a good proxy for the original, high-intensity measure of fitness in older adults.

In this article we find exponential good approximation of the empirical neigbourhood distribution of symbolled random graphs conditioned to a given empirical symbol distribution and empirical pair distribution. Using this approximation we shorten or simplify the proof of (Doku-Amponsah \& Morters, 2010, Theorem~2.5); the large deviation principle (LDP) for empirical neigbourhood distribution of symbolled random graphs. We also show that the LDP for the empirical degree measure of the classical Erd\H{o}s-R\'{e}nyi graph is a special case of (Doku-Amponsah \& Moerters, 2010, Theorem~2.5). From the LDP for the empirical degree measure, we derive an LDP for the the proportion of isolated vertices in the classical Erd\H{o}s-R\'{e}nyi graph.

We consider preferential attachment random graphs which may be obtained as follows: It starts with a single node. If a new node appears, it is linked by an edge to one or more existing node(s) with a probability proportional to function of their degree. For a class of linear preferential attachment random graphs we find a large deviation principle (LDP) for the empirical degree measure. In the course of the prove this LDP we establish an LDP for the empirical degree and pair distribution see Theorem 2.3, of the fitness preferential attachment model of random graphs.

To extend the deterministic compartments pharmacokinetics models as diffusions seems not realistic on the biological side because the paths of these stochastic processes are not smooth enough. In order to extend the one compartment intra-veinous bolus models, this paper suggests to model the concentration process $C$ by a class of stochastic differential equations driven by a fractional Brownian motion of Hurst parameter belonging to $]1/2,1[$. The first part of the paper provides probabilistic and statistical results on the concentration process $C$ : the distribution of $C$, a control of the uniform distance between $C$ and the solution of the associated ordinary differential equation, and consistent estimators of the elimination constant, of the Hurst parameter of the driving signal, and of the volatility constant. The second part of the paper provides applications of these theoretical results on simulated concentrations : a method to choose the parameters on small sets of observations, and simulations of the estimators of the elimination constant and of the Hurst parameter of the driving signal. The relationship between the quality of the estimations and the size/length of the sample is discussed.

We study the relation between CKLS model and CIR model. We prove that under a suitable transformation, any CKLS model of order $\frac{1}{2}<\gamma<1$ or $\gamma> 1$ corresponds to a CIR model under a new probability space. Moreover, we get the explicit solution and the precise distribution of the CKLS model at any time $t$ under the new probability measure. We also give the moment estimation of CKLS model.

In the framework of Cramer's probabilistic model of primes, we explore the exact and asymptotic distributions of maximal prime gaps. We show that the Gumbel extreme value distribution exp(-exp(-x)) is the limit law for maximal gaps between Cramer's random primes. The result can be derived from a general theorem about intervals between discrete random events occurring with slowly varying probability monotonically decreasing to zero. A straightforward generalization extends the Gumbel limit law to maximal gaps between prime constellations in Cramer's model.

For the decomposability property is very a practical one in Welfare analysis, most researchers and users favor decomposable poverty indices such as the Foster-Greer-Thorbeck poverty index. This may lead to neglect the so important weighted indices like the Kakwani and Shorrocks ones which have interesting other properties in Welfare analysis. To face up to this problem, we give in this paper, statistical estimations of the gap of decomposability of a large class of such indices using the General Poverty Indice (GPI) and of a new asymptotic representation Theorem for it, in terms of functional empirical processes theory. The results then enable independent handling of targeted groups and next global reporting with significant confidence intervals. Data-driven examples are given with real data.

In this article for a finite typed random geometric graph we define the empirical locality distribution, which records the number of nodes of a given type linked to a given number of nodes of each type. We find large deviation principle (LDP) for the empirical locality measure given the empirical pair measure and the empirical type measure of the typed random geometric graphs. From this LDP, we derive large deviation principles for the degree measure and the proportion of detached nodes in the classical Erdos-Renyi graph defined on [0, 1]^d. This graphs have been suggested by (Canning and Penman, 2003) as a possible extension to the randomly typed random graphs.

We consider the variable selection problem in linear regression. Suppose that we have a set of random variables $X_1,...,X_m,Y,\epsilon$ such that $Y=\sum_{k\in \pi}\alpha_kX_k+\epsilon$ with $\pi\subseteq \{1,...,m\}$ and $\alpha_k\in {\mathbb R}$ unknown, and $\epsilon$ is independent of any linear combination of $X_1,...,X_m$. Given actually emitted $n$ examples $\{(x_{i,1}...,x_{i,m},y_i)\}_{i=1}^n$ emitted from $(X_1,...,X_m, Y)$, we wish to estimate the true $\pi$ using information criteria in the form of $H+(k/2)d_n$, where $H$ is the likelihood with respect to $\pi$ multiplied by -1, and $\{d_n\}$ is a positive real sequence. If $d_n$ is too small, we cannot obtain consistency because of overestimation. For autoregression, Hannan-Quinn proved that, in their setting of $H$ and $k$, the rate $d_n=2\log\log n$ is the minimum satisfying strong consistency. This paper solves the statement affirmative for linear regression as well which has a completely different setting.

Variance is very important in test statistics as it measures the degree of reliability of estimates. It depends not only on the sample size but also on other factors such as population size, type of data and its distribution, and method of sampling or experiments. But here, we assume that these other fasctors are fixed, and that the test statistic depends only on the sample size. When the sample size is larger, the variance will be smaller. Smaller variance makes test statistics larger or gives more significant results in testing a hypothesis. Whatever the hypothesis is, it does not matter. Thus, the test result is often misleading because much of it reflects the sample size. Therefore, we discuss the large sample problem in performing traditional tests and show how to fix this problem.

Reviewer Acknowledgements for International Journal of Statistics and Probability, Vol. 11, No. 6

Reviewer Acknowledgements for International Journal of Statistics and Probability, Vol. 11, No. 6

Reviewer Acknowledgements for International Journal of Statistics and Probability, Vol. 11, No. 5

Reviewer Acknowledgements for International Journal of Statistics and Probability, Vol. 11, No. 3

Reviewer Acknowledgements for International Journal of Statistics and Probability, Vol. 11, No. 4

Reviewer Acknowledgements for International Journal of Statistics and Probability, Vol. 11, No. 2

Reviewer Acknowledgements for International Journal of Statistics and Probability, Vol. 11, No. 1

Dependent and independent variables may appear uncorrelated when analyzed in full range in medical data. However, when an independent variable is divided by the cutoff value, the dependent and independent variables may become correlated in each group. Furthermore, researchers often convert independent variables of quantitative data into binary data by cutoff value and perform statistical analysis with the data. Therefore, it is important to select the optimum cutoff value since performing statistical analysis depends on the cutoff value. Our study determines the optimal cutoff value when the data of dependent and independent variables are quantitative. The piecewise linear regression analysis divides an independent variable into two by the cutoff value, and linear regression analysis is performed in each group. However, the piecewise linear regression analysis may not obtain the optimal cutoff value when data follow a non-normal distribution. Unfortunately, medical data often follows a non-normal distribution. We, therefore, performed theWilcoxon-Mann-Whitney (WMW) test with two-sided for all potential cutoff values and adopted the cutoff value that minimizes the P-value (called minimum P-value approach). Calculating the cutoff value using the minimum P-value approach is often used in the log-rank and chi-squared test but not the WMW test. First, using Monte Carlo simulations at various settings, we verified the performance of the cutoff value for the WMW test by the minimum P-value approach. Then, COVID-19 data were analyzed to demonstrate the practical applicability of the cutoff value.

The objective of this work is to predict the risk of contracting Covid - 19 in the Mexican population, by means of the construction of a multilogistical model, based on the Ministry of Health applied to patients who presented with the symptoms that encompass the disease. With this probabilistic model, it was possible to estimate the degree of contracting Covid -19, taking as a reference the health conditions of the patients, and with it, medically influence to counteract the disease.

In the midst of the global outbreak with over 300,000 worldwide death cases of COVID-19, Canada has reported 79,101 confirmed cases of the novel coronavirus (COVID-19) as of May 19, 2020, in which the severity differs from region to region. To provide a timely view and understanding of the evolving pandemic in Canada, we develop a real time interactive web-based platform which primarily includes data visualization and statistical analysis. The website highlights real time tracking of the development of COVID-19 with visualized graphs and forecasts future trends with applications of different statistical predictive models. By providing research-based statistical analysis, we are able to shed the light on the epidemiological characteristics of COVID-19. We also provide timely social news and preventive measures from the government on the website.

The whole world has been affected by the COVID-19 pandemic. It has changed life drastically, affecting both social and business behavior and causing major economic distress throughout the world. The disease is often denominated a “novel coronavirus,” meaning that it is a new strain, that none of us carry antibodies to it and that there is much to be learned about its pathology. This obviously makes it hard to control. While several countries seem to have grasped ways to contain the virus, the United States (the “U.S.”) has seen steady growth in the number of cases and deaths. This paper uses multiple regression models to examine the differences among the several U.S. states in the numbers of cases and deaths and investigates several possible contributing factors to these totals.

This paper aims at assessing agricultural eco-efficiency of 40 European countries, including non-European Union and ex-USSR ones, in the period 1990–2019 (30 years). A stochastic frontier model with a panel translog specification is employed to allow technology to change in time and across countries, and both output elasticities and returns to scale to vary with input levels and time. Our study is original compared to existing ones in the literature because it considers the almost totality of European countries and focuses on a long and recent period. As such, it is able to draw an exhaustive and updated picture of agricultural eco-efficiency in Europe that fills both temporal and spatial information gaps left by existing studies. In our results, countries with a definitely increasing eco-efficiency in the period 1990–2019 are Albania, Croatia, Iceland, Lithuania, North Macedonia, Portugal and Ukraine, while countries with a definitely decreasing eco-efficiency are Cyprus, Czechia, France, Greece, Hungary, Malta, Romania and Slovakia. All other countries have an approximately constant eco-efficiency in the period 1990–2019, ranging, in average, between 0.93 and 0.95, with the exception of two groups of countries: (i) Denmark, Italy, Serbia-Montenegro, Slovenia and Switzerland, which show a decline of eco-efficiency in recent years; (ii) Ireland and Latvia, which exhibit an upward inversion of the trend in the penultimate decade. These two groups of countries should be monitored in the near future to better establish whether the decline or the increase in eco-efficiency is temporary or permanent. Our study also provides, for the first time, evidence on agricultural eco-efficiency in non-European Union transition economies, specifically it emphasizes the promising performance of Albania, North Macedonia and Ukraine.

In this research acute malnutrition (AM) and household income (HI) are investigated. Historically, governorates of Iraq suffered inequality in AM and HI for several reasons, such as government's focus on heart of city in specific governorates; like Baghdad, Basra, and Nineveh. Question is raised whether the spatial patterns of AM and HI are existed in Iraq? If so, can the pattern of HI explain the pattern of AM? The present paper investigates the spatial structure of AM across different governorates in Iraq and its spatial correlation to HI. This investigation will provide implications for policy makers, finding local clusters and showing visual picture for each of AM and HI. The study utilizes a cross-sectional survey data collected in 2004 for 18 governorates. Mapping is used as the first step to conduct visual inspection for AM and HI using quartiles. Several spatial econometric techniques are available in the literature, which deal with the spatial autocorrelation in geographically referenced data. Two statistics of spatial autocorrelation, based on sharing boundary neighbours, known as global and local Moran's I, are carried out. Wartenberg's measure is used to detect bivariate spatial correlation. In conclusion, based on visual inspection of mapping, global clustering in high level of AM and low level of HI were in general concentrated in western-southern governorates. This global clustering for AM was confirmed by significant global Moran's I statistic, but was not confirmed for HI. Out of 18 governorates, three and one governorates were found as local clusters in AM and HI respectively based on local Moran's I i. Bivariate spatial correlation between AM and HI was not found significant.

This paper presents the elements entailing the building of a panel data model on the basis of both cross-sectional and time series dimensions, as well as the assumptions implemented for the model application; this, with the objective of focusing on the main elements of the panel data modelling, its way of building, the estimation of parameters and their ratification. On the basis of the methodology of operations research, a practical application exercise is made to estimate the number of kidnapping cases in Mexico based on several economic indicators, finding that from the two types of panel data analyzed in this research, the best adjustment is obtained through the random-effects model, and the most meaningful variables are the Gross domestic product growth and the informal employment rate from the period 2010 to 2019 in each of the states. Thus, it is illustrated that panel data modelling present a better adjustment of data than any other type of models such as linear regression and time series analysis.

The aim of the study is to analyze the pattern of Gross domestic product (GDP) according to Human development index (HDI) for 184 countries of the world. GDP per capita indicates only economic prosperity but not the overall development of the citizens of a country. This research tries to find out the beneath relationship of the financial state and human development of countries using the data of 2018. For demonstrating this analysis several parametric and non-parametric regression methods subject to shape restriction have been used. The study targets to shed light on comparative performance of shape constrained regression with cone projection, polynomial regression, LOESS, Istonic regression with pooled adjacent violators algorithm, Kernel regression, smoothing spline and generalized additive model in convex situation.

In this paper, we proposed a bootstrap approach to construct the confidence interval of quantiles for current status data, which is computationally simple and efficient without estimating nuisance parameters. The reasonability of the proposed method is verified by the well performance presented in the extensive simulation study. We also analyzed a real data set as illustration.

In this paper, we shall discuss negatively dependent fuzzy set-valued random variables. And at last, we shall prove the limit theorems for rowwise negatively dependent fuzzy set-valued random variables in the sense of $d_H^\infty$, which is the extension of (Guan \& Sun, 2014) and (Guan \& Wan, 2016).

In this paper, we study the simple convergence and the uniform convergence of the Nelson-Aalen nonparametric estimator studied in Njamen $\&$ Ngatchou (Njamen $\&$ Ngatchou, 2014) in a contest of competiting risks.

Absenteeism is a national crisis in the United States, and must be addressed adequately at the early stages or at its onset, to prevent consequential disaster and burden due to absenteeism. A pervasive and persuasive nonchronic absenteeism results in chronic absenteeism, and causes severe damage to students’ life, schools and societies. While a good number of articles address various issues relating to chronic absenteeism, no evidence of research exists investigating nonchronic absenteeism. The aim of this article is to investigate factors affecting nonchronic absenteeism in K-8 students in the United States by applying discrete regression models. Initially, we investigate K-8 students nonchronic absenteeism discrepancies due to socio-demographic and parental involvement factors via descriptive analysis and then employ Poisson and negative binomial regression models for exploring significant factors of K-8 nonchronic absenteeism. The findings of this study will be of great use to stakeholders in developing appropriate incentive measures for reducing nonchronic absenteeism early and thereby reducing chronic absenteeism.

When estimating an unknown function from a data set of n observations, the function is often known to be convex. For example, the long-run average waiting time of a customer in a single server queue is known to be convex in the service rate (Weber 1983) even though there is no closed-form formula for the mean waiting time, and hence, it needs to be estimated from a data set. A computationally efficient way of finding the best fit of the convex function to the data set is to compute the least absolute deviations estimator minimizing the sum of absolute deviations over the set of convex functions. This estimator exhibits numerically preferred behavior since it can be computed faster and for a larger data sets compared to other existing methods (Lim & Luo 2014). In this paper, we establish the validity of the least absolute deviations estimator by proving that the least absolute deviations estimator converges almost surely to the true function as n increases to infinity under modest assumptions.

The control limits derived for the Median Absolute Deviation (MAD) based Standard deviation (S) control chart proposed by Abu-Shawiesh was for monitoring quality characteristics when a standard value of sigma (σ) is known or given by the management/ engineers. When sigma (σ) is unknown and we are interested in monitoring past/non-normal data, then there is the need to modify the simple robust control limits. In this paper, the control limits for the Shewhart ¯ X and S control chart based on median absolute deviation were modified using the concept of three sigma (3σ) limits. An evaluation performance tool was also developed to evaluate the efficiency of the modified control chart. An algorithm implemented on S-Plus programming language was developed to compute the two evaluation parameters used in this study. The results show that the control limits interval and the average run length for the modified control charts is smaller than that of the existing control charts. Therefore, the modified control limits is more efficient than the existing control limits. It is recommended that the modified control limits be used when monitoring past/non-normal data or when there is no standard value of sigma specify by the process engineer/ management.

A closed form formula is provided for the probability, in a closed time interval, that an arithmetic Brownian motion remains under or above a sequence of three affine, one-sided boundaries (equivalently, for the probability that a geometric Brownian motion remains under or above a sequence of three exponential, one-sided boundaries). The numerical evaluation of this formula can be done instantly and with the accuracy required for all practical purposes. The method followed can be extended to sequences of absorbing boundaries of higher dimension. It is also applied to sequences of two-sided boundaries.

In this article, we present a Bayesian analysis with convex tent priors for step-stress accelerated life testing (SSALT) using a proportional hazard (PH) model. As flexible as the cumulative exposure (CE) model in fitting step-stress data and its attractive mathematical properties, the PH model makes Bayesian inference much more accessible than the CE model. Two sampling methods through Markov chain Monte Carlo algorithms are employed for posterior inference of parameters. The performance of the methodology is investigated using both simulated and real data sets.

This paper investigates the design of accelerated life test (ALT) sampling plans under progressive Type II interval censoring with random removals. For ALT sampling plans with two over-stress levels, the optimal stress levels and the allocation proportions to them are obtained by minimizing the asymptotic generalized variance of the maximum likelihood estimation of model parameters. The required sample size and the acceptability constant which satisfy given levels of producer’s risk and consumer’s risk are found. ALT sampling plans with three over-stress levels are also considered under some specific settings. The properties of the derived ALT sampling plans under different parameter values are investigated by a numerical study. Some interesting patterns, which can provide useful insight to practitioners in related areas, are found. The true acceptance probabilities are computed using a Monte Carlo simulation and the results show that the accuracy of the derived ALT sampling plans is satisfactory. A numerical example is also provided for illustrative purpose.

Obstetric Fistula is a medical condition that involves an opening or perforation between the vagina and the bladder or the vagina and the rectum. It is a serious, life threatening and often debilitating medical condition that affects thousands of women in developing countries.The study consists of 270 obstetric fistula patients having all required information who were taking treatment at Jimma University Specialized Hospital in south west Ethiopia from January, 2011 to January ,2017. The log-rank and generalized wilcoxon test were used to explore the association between the recovery time and different independent categorical covariates. Then using different baseline distribution parametric models were employed to have an appropriate model for the recovery time/status of the patients based on Akaike information criteria (AIC) of the model. Result of Both log-rank and generalized wilcoxon test showed that there were significant differences among obstetric fistula patients in survival experience of weight , marital status, Residence, Incontinence, Antenatal care, mode of delivery, status of urethra and types of fistula of patients at 5% level of significance. Based on AIC log-normal gamma shared frailty model is an appropriate model and there is heterogeneity between patients with zone. The final model showed that marital status, Residence, Incontinence, Antenatal care, status of urethra and types of fistula were the determinants of recovery status of the patients at 5% level of significance. In Conclusion, the result showed that married women, rural residence, incontinence of urine more than 3 months, hadn’t antenatal care and completely damaged urethra were prolonged time recovery time of patients whereas having recto-vaginal-fistula shorten recovery status than vesico-vaginal fistula group of patients.

In insurance loss reserving, a large portion of zeros are expected at the later development periods of an incremental loss triangle. Negative losses occur frequently in the incremental loss triangle due to actuarial practices such as subrogation and salvation. The nature of the distributions assumed by most stochastic models, such as the lognormal and over-dispersed Poisson distributions, brings restrictions on the zeros and negatives appearing in the loss triangle. In this paper, we propose a Bayesian mixture model for stochastic reserving under the situation where there are both zeros and negatives in the incremental loss triangle. A multinomial regression model will be applied to model the sign of the loss data, while the lognormal distribution is assumed for the loss magnitudes of negatives and positives. Bayesian generalized linear models will be fitted for both the mixture and magnitude models. The model will be implemented using the Markov chain Monte Carlo (MCMC) techniques in BUGS. Our model provides a realistic tool for stochastic reserving in the cases of zeros and negatives.

When private or stigmatizing characteristics are included in sample surveys, direct questions result in low cooperation of the respondents. To increase cooperation, indirect questioning procedures have been established in the literature. Nonrandomized response methods are one group of such procedures and have attracted much attention in recent years. In this article, we consider four popular nonrandomized response schemes and present a possibility to improve the estimation precision of these schemes. The basic idea is to require multiple indirect answers from each respondent. We develop a Fisher scoring algorithm for the maximum likelihood estimation in the presented new schemes and show the better efficiency of the new schemes compared with the original designs.

When private or stigmatizing characteristics are included in sample surveys, direct questions result in low cooperation of the respondents. To increase cooperation, indirect questioning procedures have been established in the literature. Nonrandomized response methods are one group of such procedures and have attracted much attention in recent years. In this article, we consider four popular nonrandomized response schemes and present a possibility to improve the estimation precision of these schemes. The basic idea is to require multiple indirect answers from each respondent. We develop a Fisher scoring algorithm for the maximum likelihood estimation in the presented new schemes and show the better efficiency of the new schemes compared with the original designs.

The paper reports on the comparison of models of measurement with constrained and free factor loadings as part of confirmatory factor analysis in a simulation study. The comparison was conducted in order to find out whether constrained factor loadings that cause a reduced degree of adaptability to specificities of data mean a disadvantage in comparison to factor loadings that are freely estimated. Furthermore, the way of conducting the link transformation, the sample size and the number of variables were varied. The simulated data were dichotomous and constructed to conform to one underlying source of responding. The investigation of model fit and accuracy in estimating factor loadings yielded similar results for constrained and free factor loadings in confirmatory factor analysis. Furthermore, there were effects due to the type of link transformation and sample size.

International Journal of Statistics and Probability wishes to acknowledge the following individuals for their assistance with peer review of manuscripts for this issue. Their help and contributions in maintaining the quality of the journal is greatly appreciated. Many authors, regardless of whether International Journal of Statistics and Probability publishes their work, appreciate the helpful feedback provided by the reviewers. Reviewers for Volume 8, Number 5 Abdullah A. Smadi, Yarmouk University, Jordan Carla J. Thompson, University of West Florida, USA Chin-Shang Li, School of Nursing, USA Encarnación Alvarez-Verdejo, University of Granada, Spain Felix Almendra-Arao, UPIITA del Instituto Politécnico Nacional , México Gabriel A. Okyere, Kwame Nkrumah University of Science and Technology, Ghana Gane Samb Lo, University Gaston Berger, SENEGAL Gennaro Punzo, University of Naples Parthenope, Italy Gerardo Febres, Universidad Simón Bolívar, Venezuela Ivair R. Silva, Federal University of Ouro Preto – UFOP, Brazil Mingao Yuan, North Dakota State University, USA Philip Westgate, University of Kentucky, USA Qingyang Zhang, University of Arkansas, USA Sajid Ali, Quaid-i-Azam University, Pakistan Sohair F. Higazi, University of Tanta, Egypt Subhradev Sen, Alliance University, India Vyacheslav Abramov, Swinburne University of Technology, Australia Wei Zhang, The George Washington University, USA Yuvraj Sunecher, University of Technology Mauritius, Mauritius Zaixing Li, China University of Mining and Technology (Beijing), China Wendy Smith On behalf of, The Editorial Board of International Journal of Statistics and Probability Canadian Center of Science and Education

International Journal of Statistics and Probability wishes to acknowledge the following individuals for their assistance with peer review of manuscripts for this issue. Their help and contributions in maintaining the quality of the journal is greatly appreciated. Many authors, regardless of whether International Journal of Statistics and Probability publishes their work, appreciate the helpful feedback provided by the reviewers. Reviewers for Volume 9, Number 1 Chin-Shang Li, School of Nursing, USA Faisal Khamis, Al Ain University of Science and Technology, Canada Felix Almendra-Arao, UPIITA del Instituto Politécnico Nacional, México Gabriel A. Okyere, Kwame Nkrumah University of Science and Technology, Ghana Gerardo Febres, Universidad Simón Bolívar, Venezuela Mohieddine Rahmouni, University of Tunis, Tunisia Noha Youssef, American University in Cairo, Egypt Philip Westgate, University of Kentucky, USA Qingyang Zhang, University of Arkansas, USA Shatrunjai Pratap Singh, John Hancock Financial Services, USA Weizhong Tian, Eastern New Mexico University, USA Zaixing Li, China University of Mining and Technology (Beijing), China Wendy Smith On behalf of, The Editorial Board of International Journal of Statistics and Probability Canadian Center of Science and Education

Reviewer Acknowledgements for International Journal of Statistics and Probability, Vol. 10, No. 2, 2021

International Journal of Statistics and Probability wishes to acknowledge the following individuals for their assistance with peer review of manuscripts for this issue. Their help and contributions in maintaining the quality of the journal is greatly appreciated.Many authors, regardless of whether International Journal of Statistics and Probability publishes their work, appreciate the helpful feedback provided by the reviewers.Reviewers for Volume 7, Number 4Afsin Sahin, Gazi University, TurkeyCarla J. Thompson, University of West Florida, USAEncarnación Alvarez-Verdejo, University of Granada, SpainFelix Almendra-Arao, UPIITA del Instituto Politécnico Nacional, MéxicoHui Zhang, St. Jude Children’s Research Hospital, USALuiz Ricardo Nakamura, University of Sao Paulo, BrazilMohieddine Rahmouni, University of Tunis, TunisiaPhilip Westgate, University of Kentucky, USASajid Ali, Quaid-i-Azam University, PakistanSohair F. Higazi, University of Tanta, EgyptVilda Purutcuoglu, Middle East Technical University (METU), TurkeyVyacheslav Abramov, Swinburne University of Technology, AustraliaWei Zhang, The George Washington University, USAWojciech Gamrot, University of Economics, Poland Wendy SmithOn behalf of,The Editorial Board of International Journal of Statistics and ProbabilityCanadian Center of Science and Education

International Journal of Statistics and Probability wishes to acknowledge the following individuals for their assistance with peer review of manuscripts for this issue. Their help and contributions in maintaining the quality of the journal is greatly appreciated.Many authors, regardless of whether International Journal of Statistics and Probability publishes their work, appreciate the helpful feedback provided by the reviewers.Reviewers for Volume 6, Number 3 Ali Reza Fotouhi, University of the Fraser Valley, CanadaChin-Shang Li, University of California, USADouglas Lorenz, University of Louisville, USAFarida Kachapova, The Auckland University of Technology, New ZealandFelix Almendra-Arao, UPIITA del Instituto Politécnico Nacional, MéxicoGane Samb Lo, University Gaston Berger, SenegalGerardo Febres, Universidad Simón Bolívar, VenezuelaHaiming Zhou, Northern Illinois University, USAHui Zhang, St. Jude Children’s Research Hospital, USAJacek Białek, University of Lodz, PolandLuiz Ricardo Nakamura, University of Sao Paulo, BrazilMarcelo Bourguignon, Universidade Federal de Pernambuco, BrazilMaryam Eskandarzadeh, Persion Gulf Boshehr University, IranNahid Sanjari Farsipour, Alzahra University, IranPhilip Westgate, University of Kentucky, USARebecca Bendayan, University College London, UKSajid Ali, Bocconi University, ItalyShatrunjai Pratap Singh, John Hancock Financial Services, USAShuling Liu, Yale University, USASohair F. Higazi, University of Tanta, EgyptSubhradev Sen, Alliance University, IndiaTomás R. Cotos-Yáñez, University of Vigo, SpainVyacheslav Abramov, Swinburne University of Technology, AustraliaZaixing Li, China University of Mining and Technology (Beijing), China Wendy SmithOn behalf of,The Editorial Board of International Journal of Statistics and ProbabilityCanadian Center of Science and Education

International Journal of Statistics and Probability wishes to acknowledge the following individuals for their assistance with peer review of manuscripts for this issue. Their help and contributions in maintaining the quality of the journal is greatly appreciated.Many authors, regardless of whether International Journal of Statistics and Probability publishes their work, appreciate the helpful feedback provided by the reviewers.Reviewers for Volume 7, Number 5Jacek Białek, University of Lodz, PolandJingwei Meng, Indiana University, USALuiz Ricardo Nakamura, University of Sao Paulo, BrazilPablo José Moya Fernández, Universidad de Granada, SpainRebecca Bendayan, University College London, UKSajid Ali, Quaid-i-Azam University, PakistanSubhradev Sen, Alliance University, India Wendy SmithOn behalf of,The Editorial Board of International Journal of Statistics and ProbabilityCanadian Center of Science and Education

International Journal of Statistics and Probability wishes to acknowledge the following individuals for their assistance with peer review of manuscripts for this issue. Their help and contributions in maintaining the quality of the journal is greatly appreciated.Many authors, regardless of whether International Journal of Statistics and Probability publishes their work, appreciate the helpful feedback provided by the reviewers.Reviewers for Volume 6, Number 2 Bibi Abdelouahab, University Mentouri Constantine, AlgeriaCarla J. Thompson, University of West Florida, USAChin-Shang Li (Editor-in-Chief), University of California, USADouglas Lorenz, University of Louisville, USAFarida Kachapova, The Auckland University of Technology, New ZealandGabriel A. Okyere, Kwame Nkrumah University of Science and Technology, GhanaGane Samb Lo, University Gaston Berger, SENEGALGennaro Punzo, University of Naples Parthenope, ItalyGerardo Febres, Universidad Simon Bolívar, VenezuelaHui Zhang, St. Jude Children’s Research Hospital, USAJacek Białek, University of Lodz, PolandJorge M. Mendes, NOVA University of Lisbon, PortugalKassim S. Mwitondi, Sheffield Hallam University, UKKrishna K. Saha, Central Connecticut State University, USAMan Fung LO, Hong Kong Polytechnic University, Hong KongNahid Sanjari Farsipour, Alzahra University, IranNicolas MARIE, ESME Sudria Paris, FrancePhilip Westgate, University of Kentucky, USASajid Ali, Bocconi University, ItalyShatrunjai Pratap Singh, John Hancock Financial Services, USASohair F. Higazi, University of Tanta, EgyptSubhradev Sen, Alliance University, IndiaTewfik Kernane, University of Sciences and Technology USTHB, AlgeriaZaixing Li, China University of Mining and Technology (Beijing), China Wendy SmithOn behalf of,The Editorial Board of International Journal of Statistics and ProbabilityCanadian Center of Science and Education

International Journal of Statistics and Probability wishes to acknowledge the following individuals for their assistance with peer review of manuscripts for this issue. Their help and contributions in maintaining the quality of the journal is greatly appreciated. Many authors, regardless of whether International Journal of Statistics and Probability publishes their work, appreciate the helpful feedback provided by the reviewers. Reviewers for Volume 8, Number 2 Abdullah A. Smadi, Yarmouk University, Jordan Afsin Sahin, Gazi University, Turkey Carla J. Thompson, University of West Florida, USA Chin-Shang Li, School of Nursing, USA Gabriel A. Okyere, Kwame Nkrumah University of Science and Technology, Ghana Hui Zhang, St. Jude Children’s Research Hospital, USA Nahid Sanjari Farsipour, Alzahra University, Iran Philip Westgate, University of Kentucky, USA Sajid Ali, Quaid-i-Azam University, Pakistan Shatrunjai Pratap Singh, John Hancock Financial Services, USA Wei Zhang, The George Washington University, USA Weizhong Tian, Eastern New Mexico University, USA Wojciech Gamrot, University of Economics, Poland Zaixing Li, China University of Mining and Technology (Beijing), China Wendy Smith On behalf of, The Editorial Board of International Journal of Statistics and Probability Canadian Center of Science and Education

International Journal of Statistics and Probability wishes to acknowledge the following individuals for their assistance with peer review of manuscripts for this issue. Their help and contributions in maintaining the quality of the journal is greatly appreciated. Many authors, regardless of whether International Journal of Statistics and Probability publishes their work, appreciate the helpful feedback provided by the reviewers. Reviewers for Volume 3, Number 4 Abdullah A. SMADI Anna Grana' Bibi Abdelouahab Carla J. Thompson Carolyn Huston Chin-Shang Li Ehsan Karim Enayetur Raheem Ivair R. Silva Jacek Bialek Jorge M. Mendes Kouji Yamamoto Lishu Li Michela Ottobre Philip Westgate Sajid Ali Sohair F. Higazi Vyacheslav Abramov Yichuan Zhao Zaixing Li Wendy Smith On behalf of, The Editorial Board of International Journal of Statistics and Probability Canadian Center of Science and Education