Statistics, Optimization & Information Computing http://iapress.org/index.php/soic <p><em><strong>Statistics, Optimization and Information Computing</strong></em>&nbsp;(SOIC) is an international refereed journal dedicated to the latest advancement of statistics, optimization and applications in information sciences.&nbsp; Topics of interest are (but not limited to):&nbsp;</p> <p>Statistical theory and applications</p> <ul> <li class="show">Statistical computing, Simulation and Monte Carlo methods, Bootstrap,&nbsp;Resampling methods, Spatial Statistics, Survival Analysis, Nonparametric and semiparametric methods, Asymptotics, Bayesian inference and Bayesian optimization</li> <li class="show">Stochastic processes, Probability, Statistics and applications</li> <li class="show">Statistical methods and modeling in life sciences including biomedical sciences, environmental sciences and agriculture</li> <li class="show">Decision Theory, Time series&nbsp;analysis, &nbsp;High-dimensional&nbsp; multivariate integrals,&nbsp;statistical analysis in market, business, finance,&nbsp;insurance, economic and social science, etc</li> </ul> <p>&nbsp;Optimization methods and applications</p> <ul> <li class="show">Linear and nonlinear optimization</li> <li class="show">Stochastic optimization, Statistical optimization and Markov-chain etc.</li> <li class="show">Game theory, Network optimization and combinatorial optimization</li> <li class="show">Variational analysis, Convex optimization and nonsmooth optimization</li> <li class="show">Global optimization and semidefinite programming&nbsp;</li> <li class="show">Complementarity problems and variational inequalities</li> <li class="show"><span lang="EN-US">Optimal control: theory and applications</span></li> <li class="show">Operations research, Optimization and applications in management science and engineering</li> </ul> <p>Information computing and&nbsp;machine intelligence</p> <ul> <li class="show">Machine learning, Statistical learning, Deep learning</li> <li class="show">Artificial intelligence,&nbsp;Intelligence computation, Intelligent control and optimization</li> <li class="show">Data mining, Data&nbsp;analysis, Cluster computing, Classification</li> <li class="show">Pattern recognition, Computer vision</li> <li class="show">Compressive sensing and sparse reconstruction</li> <li class="show">Signal and image processing, Medical imaging and analysis, Inverse problem and imaging sciences</li> <li class="show">Genetic algorithm, Natural language processing, Expert systems, Robotics,&nbsp;Information retrieval and computing</li> <li class="show">Numerical analysis and algorithms with applications in computer science and engineering</li> </ul> International Academic Press en-US Statistics, Optimization & Information Computing 2311-004X <span>Authors who publish with this journal agree to the following terms:</span><br /><br /><ol type="a"><ol type="a"><li>Authors retain copyright and grant the journal right of first publication with the work simultaneously licensed under a <a href="http://creativecommons.org/licenses/by/3.0/" target="_new">Creative Commons Attribution License</a> that allows others to share the work with an acknowledgement of the work's authorship and initial publication in this journal.</li><li>Authors are able to enter into separate, additional contractual arrangements for the non-exclusive distribution of the journal's published version of the work (e.g., post it to an institutional repository or publish it in a book), with an acknowledgement of its initial publication in this journal.</li><li>Authors are permitted and encouraged to post their work online (e.g., in institutional repositories or on their website) prior to and during the submission process, as it can lead to productive exchanges, as well as earlier and greater citation of published work (See <a href="http://opcit.eprints.org/oacitation-biblio.html" target="_new">The Effect of Open Access</a>).</li></ol></ol> Integral stochastic ordering of the multivariate normal mean-variance and the skew-normal scale-shape mixture models http://iapress.org/index.php/soic/article/view/863 <p>‎In this paper‎, ‎we introduce integral stochastic ordering of two‎ most important classes of distributions that are commonly used to fit data possessing high values of skewness and (or)‎ ‎kurtosis‎. ‎The first one is based on the selection distributions started by the univariate skew-normal distribution‎. ‎A broad‎, ‎flexible and newest class in this area is the scale and shape mixture of multivariate skew-normal distributions‎. ‎The second one is the general class of Normal Mean-Variance Mixture distributions‎. ‎We then derive necessary and sufficient conditions for comparing the random vectors from these two classes of distributions‎. ‎The integral orders considered here are the usual‎, ‎concordance‎, ‎supermodular‎, ‎convex‎, ‎increasing convex and directionally convex stochastic orders‎. ‎Moreover‎, ‎for bivariate random vectors‎, ‎in the sense of stop-loss and bivariate concordance stochastic orders‎, ‎the dependence strength of random portfolios is characterized in terms of order of correlations‎.</p> Dariush Jamali Mehdi Amiri Ahad Jamalizadeh N. Balakrishnan Copyright (c) 2020 Statistics, Optimization & Information Computing 2020-02-17 2020-02-17 8 1 1 16 10.19139/soic-2310-5070-863 The Ristic-Balakrishnan odd log-logistic family of distributions: Properties and Applications http://iapress.org/index.php/soic/article/view/715 <p>This paper investigates general mathematical properties of a new generator of continuous distributions with two extra parameter called the Ristic-Balakrishnan odd log-logistic family of distributions. We present some special models and investigate the asymptotes. The new density function can be expressed as a linear combination of exponentiated densities based on the same baseline distribution. Explicit expressions for the ordinary and incomplete moments, generating functions and order statistics, which hold for any baseline model, are determined. Further, we discuss the estimation of the model parameters by maximum likelihood and present a simulation study based on maximum likelihood estimation. A regression model based on proposed model was introduced. Finally, three applications to real data were provided to illustrate the potentiality of the family of distributions.</p> Hamid Esmaeili Fazlollah Lak Emrah Altun Copyright (c) 2020 Statistics, Optimization & Information Computing 2020-02-17 2020-02-17 8 1 17 35 10.19139/soic-2310-5070-715 A weighted transmuted exponential distributions with environmental applications http://iapress.org/index.php/soic/article/view/785 <p>In this paper, we introduce a new three-parameter distribution. It is based on the combination of a re-parametrization of a general family of distributions (known as the EGNB2 distribution) and the so-called quadratic rank transmutation map defined with the exponential distribution as baseline. We explore some mathematical properties of this distribution including the hazard rate function, moments, the moment generating function, the quantile function, various entropy measures and (reversed) residual life functions. A statistical study investigates estimation of the parameters using the method of maximum likelihood. The distribution along with other existing distributions are fitted to two environmental data sets and its superior performance is assessed by using some goodness-of-fit tests. As a result, some environmental measures associated with these data are obtained such as the return level and mean deviation about this level.</p> Christophe Chesneau Hassan S Bakouch Muhammad Nauman Khan Copyright (c) 2020 Statistics, Optimization & Information Computing 2020-02-17 2020-02-17 8 1 36 53 10.19139/soic-2310-5070-785 An Alternative Diagnostic Procedure for Meta-Regression http://iapress.org/index.php/soic/article/view/864 <p>This paper proposes an alternative procedure for detecting outliers in meta-regression using the penalized maximum likelihood with smoothly clipped absolute deviation penalty function. The coordinate descent algorithm is implemented to estimate the parameters where the cross-validation criterion is used to determine the tuning parameter. Extensive simulation experiments demonstrate the usefulness of our proposed procedure as well as its improved power performance compared to previous procedures. Simulation results demonstrate that the performance has a direct relationship with the number of studies and an inverse relationship with the heterogeneity between studies. An illustrative application with real data, implementing the proposed procedure and others, is given.</p> Ali Hassan Abuzaid Enass Abed Abdu Atta Esam Mahdi Copyright (c) 2020 Statistics, Optimization & Information Computing 2020-02-17 2020-02-17 8 1 54 65 10.19139/soic-2310-5070-864 A Density-Based Empirical Likelihood Ratio Approach for Goodness-of-fit Tests in Decreasing Densities http://iapress.org/index.php/soic/article/view/707 <p><span style="background-color: #ffffff;">In this paper, we propose a test for the null hypothesis that a decreasing density function belongs to a given<br>parametric family of distribution functions against the non-parametric alternative. This method, which is based on an empirical likelihood (EL) ratio statistic, is similar to the test introduced by Vexler and Gurevich [23]. The consistency of the test statistic proposed is derived under the null and alternative hypotheses. A simulation study is conducted to inspect the power of the proposed test under various decreasing alternatives. In each scenario, the critical region of the test is obtained using a Monte Carlo technique. The applicability of the proposed test in practice is demonstrated through a few real data examples.</span></p> <p>&nbsp;</p> Vahid Fakoor Masoud Ajami Seyed Mahdi Amir Jahanshahi Ali Shariati Copyright (c) 2020 Statistics, Optimization & Information Computing 2020-02-17 2020-02-17 8 1 66 79 10.19139/soic-2310-5070-707 Estimation of Parameters and Reliability Characteristics in Lindley Distribution Using Randomly Censored Data http://iapress.org/index.php/soic/article/view/692 <p><span style="background-color: #ffffff;">This article deals with the estimation of parameters and reliability characteristics of Lindley distribution under<br>random censoring. Expected time on test based on randomly censored data is obtained. The maximum likelihood estimators of the unknown parameters and reliability characteristics are derived. The asymptotic, bootstrap p and bootstrap t confidence intervals of the parameters are constructed. The Bayes estimators of the parameters and reliability characteristics under squared error loss function using non-informative and gamma informative priors are obtained. For computing of Bayes estimates, Lindley approximation and MCMC methods are considered. Highest posterior density (HPD) credible intervals of the parameters are obtained using MCMC method. Various estimation procedures are compared using a Monte Carlo simulation study. Finally, a real data set is analyzed for illustration purposes.</span></p> Renu Garg Madhulika Dube Hare Krishna Copyright (c) 2020 Statistics, Optimization & Information Computing 2020-02-17 2020-02-17 8 1 80 97 10.19139/soic-2310-5070-692 Improved Estimator of the Conditional Tail Expectation in the case of heavy-tailed losses http://iapress.org/index.php/soic/article/view/665 <p>In this paper, we investigate the extreme-value methodology, to propose an improved estimator of the conditional tail expectation (CTE) for a loss distribution with a finite mean but infinite variance.<br>The present work introduces a new estimator of the CTE based on the bias-reduced estimators of high quantile for heavy-tailed distributions. The asymptotic normality of the proposed estimator is established and checked, in a simulation study. Moreover, we compare, in terms of bias and mean squared error, our estimator with the known old estimator.</p> Mohamed Laidi Abdelaziz Rassoul Hamid Ould Rouis Copyright (c) 2020 Statistics, Optimization & Information Computing 2020-02-17 2020-02-17 8 1 98 109 10.19139/soic-2310-5070-665 Weighted Cumulative Residual (Past) Inaccuracy For Minimum (Maximum) of Order Statistics http://iapress.org/index.php/soic/article/view/695 <p>In this paper, we propose a measure of weighted cumulative residual inaccuracy between survival function of the first-order statistic and parent survival function $\bar{F}$. We also consider weighted cumulative inaccuracy measure between distribution of the last- order statistic and parent distribution $F$. For these concepts, we obtain some reliability properties and characterization results&nbsp; such as relationships with other functions, bounds, stochastic ordering and effect of linear transformation. Dynamic versions of these weighted measures are considered.</p> Safeih Daneshi Ahmad Nezakati Saeid Tahmasebi Copyright (c) 2020 Statistics, Optimization & Information Computing 2020-02-17 2020-02-17 8 1 110 126 10.19139/soic-2310-5070-695 The accuracy of modeling of Gaussian stochastic process in some Orlicz spaces http://iapress.org/index.php/soic/article/view/670 <p><span style="background-color: #ffffff;">The main purpose of this study is the construction of a model of a Gaussian stochastic process with given reliability and accuracy in some Orlicz spaces. In the paper, a suitable model is presented, conditions for the model parameters are derived, and some examples of their calculations are given.</span></p> YU. V. Kozachenko Antonina Tegza N. V.Troshki Copyright (c) 2020 Statistics, Optimization & Information Computing 2020-02-17 2020-02-17 8 1 127 135 10.19139/soic-2310-5070-670 Stochastic models to estimate population dynamics http://iapress.org/index.php/soic/article/view/488 <p>The growth dynamics that a population follows is mainly due to births, deaths or migrations, each of these<br>phenomena is affected by other factors such as public health, birth control, work sources, economy, safety and conditions of quality of life in neighboring countries, among many others. In this paper is proposed two statistical models based on a system of stochastic differential equations (SDE) that model the dynamics of population growth, and three computational algorithms that allow the generation of probability distribution samples in high dimensions, in models that have non-linear structures and that are useful for making inferences. The algorithms allow to estimate simultaneously states solutions and parameters in SDE models. The interpretation of the parameters is important because they are related to the variables of growth, mortality, migration, physical-chemical conditions of the environment, among other factors. The algorithms are illustrated using real data from a sector of the population of the Republic of Ecuador, and are compared with the results obtained with the models used by theWorld Bank for the same data, which shows that stochastic models Proposals based on an SDE more adequately and reliably adjust the dynamics of demographic randomness, sampling errors and environmental randomness in comparison with the deterministic models used by the World Bank. It is observed that the population grows year by year and seems to have a definite tendency; that is, a clearly growing behavior is seen. To measure the relative success of the algorithms, the relative error was estimated, obtaining small percentage errors.</p> Saba Infante luis sanchez Aracelis Hernandez Copyright (c) 2020 Statistics, Optimization & Information Computing 2020-02-17 2020-02-17 8 1 136 152 On Distributions of One Class of Random Sums and their Applications http://iapress.org/index.php/soic/article/view/698 <p><span style="background-color: #ffffff;">We propose results of the investigation of properties of the random sums of random variables. We consider the case, where the number of summands is the first moment of an event occurrence. An integral equation is presented that determines distributions of random sums. With the help of the obtained results we analyse the distribution function of the time during which the Geiger-Muller counter will not lose any particles, the distribution function of the busy period of a redundant system with renewal, and the distribution function of the sojourn times of a single-server queueing system.</span></p> Ivan Matsak Mikhail Moklyachuk Copyright (c) 2020 Statistics, Optimization & Information Computing 2020-02-18 2020-02-18 8 1 153 164 10.19139/soic-2310-5070-698 Inexact Double Step Length Method For Solving Systems Of Nonlinear Equations http://iapress.org/index.php/soic/article/view/532 <p>In this paper, a single direction with double step length method for solving systems of nonlinear equations is presented. Main idea used in the algorithm is to approximate the Jacobian via acceleration parameter. Furthermore, the two step lengths are calculated using inexact line search procedure. This method is matrix-free, and so is advantageous when solving large-scale problems. The proposed method is proven to be globally convergent under appropriate conditions. The preliminary numerical results reported in this paper using a large-scale benchmark test problems show that the proposed method is practically quite effective.</p> Abubakar Sani Halilu Mohammed Yusuf Waziri Yau Balarabe Musa Copyright (c) 2020 Statistics, Optimization & Information Computing 2020-02-18 2020-02-18 8 1 165 174 10.19139/soic-2310-5070-532 On the Distributed Order Fractional Multi-Strain Tuberculosis Model: a Numerical Study http://iapress.org/index.php/soic/article/view/621 <p>In this paper, a novel mathematical distributed order fractional model of multistrain Tuberculosis is presented. The proposed model is governed by a system of distributed order fractional differential equations, where the distributed order fractional derivative is defined in the sense of the Grünwald-Letinkov definition. A nonstandard finite difference method is proposed to study the resulting system. The stability analysis of the proposed model is discussed. Numerical simulations show that the nonstandard finite difference method can be applied to solve such distributed order fractional differential equations simply and eectively.</p> Nasser Sweilam S. M. AL-Mekhlafi A. O. Albalawi Copyright (c) 2020 Statistics, Optimization & Information Computing 2020-02-18 2020-02-18 8 1 175 186 10.19139/soic-2310-5070-621 Higher-order symmetric duality in nondifferentiable multiobjective fractional programming problem over cone contraints http://iapress.org/index.php/soic/article/view/601 <p>In this paper, we introduce the definition of higher-order K-(C, α, ρ, d)-convexity/pseudoconvexity over cone and discuss a nontrivial numerical examples for existing such type of functions. The purpose of the paper is to study higher order fractional symmetric duality over arbitrary cones for nondifferentiable Mond-Weir type programs under higher- order K-(C, α, ρ, d)-convexity/pseudoconvexity assumptions. Next, we prove appropriate duality relations under aforesaid assumptions.</p> Ramu Dubey Deepmala Vishnu Narayan Mishra Copyright (c) 2020 Statistics, Optimization & Information Computing 2020-02-18 2020-02-18 8 1 187 205 10.19139/soic-2310-5070-601 Vector-valued nonuniform multiresolution analysis related to Walsh function http://iapress.org/index.php/soic/article/view/681 <p>In this paper, we introduce vector-valued nonuniform multiresolution analysis on positive half-line related to Walsh function. We obtain the necessary and sufficient condition for the existence of associated wavelets.</p> Abdullah Copyright (c) 2020 Statistics, Optimization & Information Computing 2020-02-18 2020-02-18 8 1 206 219 10.19139/soic-2310-5070-681 Informational Energy and Entropy Applied to Testing Exponentiality http://iapress.org/index.php/soic/article/view/616 <p>The exponential distribution is widely used in reliability and life testing analysis. In this paper, two tests of fit for the exponential distribution based on Informational Energy and entropy are constructed. Consistency and other properties of the tests are proved. Using a simulation study, critical values of the proposed tests are obtained and then power values of tests are computed and compared with each other against various alternatives. Finally, we apply the tests for time between failures of secondary reactor pumps and waiting times for fatal plane accidents in the USA from 1983 to 1998.</p> Hadi Alizadeh Noughabi Havva Alizadeh Noughabi Jalil Jarrahiferiz Copyright (c) 2020 Statistics, Optimization & Information Computing 2020-02-18 2020-02-18 8 1 220 228 10.19139/soic-2310-5070-616 Improving firefly-based multi-objective optimization based on attraction law and crowding distance http://iapress.org/index.php/soic/article/view/382 <p>Multi-objective optimization problems are so designed that they simultaneously minimize several objectives functions (which are sometimes contradictory). In most cases, the objectives are in conflict with each other such that optimization of one objective does not lead to the optimization of another ones. Therefore, we should achieve a certain balance of goals to solve these problems, which usually requires the application of an intelligent method. In this regard, use of meta-heuristic algorithms will be associated with resolved problems. In this paper, we propose a new multi-objective firefly optimization method which is designed based on the law of attraction and crowding distance. The proposed methods efficiency has been evaluated by three valid test functions containing convex, nonconvex and multi discontinuous convex Pareto fronts. Simulation results confirm the significant accuracy of proposed method in defining the Pareto front for all three test functions. In addition, the simulation results indicates that proposed algorithm has higher accuracy and greater convergence speed, compared to other well known multi-objective algorithms such as non-dominated sorting genetic algorithm, Bees algorithm, Differential Evolution algorithm and Strong Pareto Evolutionary Algorithm.</p> Farid shayesteh Reihaneh Kardehi Moghaddam Copyright (c) 2020 Statistics, Optimization & Information Computing 2020-02-18 2020-02-18 8 1 229 241 10.19139/soic-2310-5070-382 An itertive algorithm with error terms for solving a system of implicit n-variational inclusions http://iapress.org/index.php/soic/article/view/705 <p>A new system of implicit n-variational inclusions is considered. We propose a new algorithm with error terms for computing the approximate solutions of our system. The convergence of the iterative sequences generated by the iterative algorithm is also discussed. Some special cases are also discussed.</p> Zubair Khan Syed Shakaib Irfan M. Firdosh Khan P. Shukla Copyright (c) 2020 Statistics, Optimization & Information Computing 2020-02-18 2020-02-18 8 1 242 253 10.19139/soic-2310-5070-705 A Consensus Clustering Method for Clustering Social Networks http://iapress.org/index.php/soic/article/view/716 <p>Detecting Communities in networks is one of the appealing fields in computer science. A wide range of methods are proposed for this problem. These methods employ different strategies and optimization functions to detect communities (or clusters). Therefore, it seems a good idea to combine these strategies to take advantage of the strengths of the methods and overcome their problems. This is the idea behind consensus clustering technique which combines several clustering results into one. In this paper, we propose a very good-performing method based on consensus clustering to detect communities of a network. Our method, called “Azar”, employed several community detection methods as base methods. Then Azar generates a new compressed network based on the common views of the used base methods and, gives this new compressed network to the last community detection method to find the final partition. We evaluate our approach by employing real and artificial datasets. The implementation results compare the base methods with Azar according to accuracy measures such as modularity and Normalized Mutual Information (NMI). The results show the good-performing behavior of Azar even for the most difficult networks. The results show the brilliant power of Azar in comparison with all the other methods.</p> Masoumeh Kheirkhahzadeh Morteza Analoui Copyright (c) 2020 Statistics, Optimization & Information Computing 2020-02-18 2020-02-18 8 1 254 271 10.19139/soic-2310-5070-716 Business Analytics using Dynamic Pricing based on Customer Entry-Exit Rates Tradeoff http://iapress.org/index.php/soic/article/view/551 <p>This paper concerns with an integrated business process to be applied as a decision support for market analysis and decision making. The proposed business intelligence and analytics system makes use of an extract, transform and load mechanism for data collection and purification. As a mathematical decision optimization, dynamic pricing is formulated based on customer entry-exit rates in a history-based pricing model. The optimal prices for products are obtained so that aggregated profit is maximized. A case study is reported to show the effectiveness of the approach. Also, analytical investigations on the impacts of the sensitive parameters of the pricing model are given.</p> Hamed Fazlollahtabar Minoo Talebi Ashoori Copyright (c) 2020 Statistics, Optimization & Information Computing 2020-02-18 2020-02-18 8 1 272 280 10.19139/soic-2310-5070-551 Optimal control of a rectilinear motion of a rocket http://iapress.org/index.php/soic/article/view/741 <p>In this work, we have modelled the problem of maximizing the velocity of a rocket moving with a rectilinear motion by a linear optimal control problem, where the control represents the action of the pilot on the rocket. In order to solve the obtained model, we applied both analytical and numerical methods. The analytical solution is calculated using the Pontryagin maximum principle while the approximate solution of the problem is found using the shooting method as well as two techniques of discretization: the technique using the Cauchy formula and the one using the Euler formula. In order to compare the different methods, we developed an implementation with MATLAB and presented some simulation results.</p> Mohamed Aliane Nacima Moussouni Mohand Bentobache Copyright (c) 2020 Statistics, Optimization & Information Computing 2020-02-18 2020-02-18 8 1 281 295 10.19139/soic-2310-5070-741 Probability Model Based on Cluster Analysis to Classify Sequences of Observations for Small Training Sets http://iapress.org/index.php/soic/article/view/690 <p>The problem of recognizing patterns, when there are few training data available, is particularly relevant and arises in cases when collection of training data is expensive or essentially impossible. The work proposes a new probability model MC&amp;CL (Markov Chain and Clusters) based on a combination of markov chain and algorithm of clustering (self-organizing map of Kohonen, k-means method), to solve a problem of classifying sequences of observations, when the amount of training dataset is low. An original experimental comparison is made between the developed model (MC&amp;CL) and a number of the other popular models to classify sequences: HMM (Hidden Markov Model), HCRF (Hidden Conditional Random Fields),LSTM (Long Short-Term Memory), kNN+DTW (k-Nearest Neighbors algorithm + Dynamic Time Warping algorithm). A comparison is made using synthetic random sequences, generated from the hidden markov model, with noise added to training specimens. The best accuracy of classifying the suggested model is shown, as compared to those under review, when the amount of training data is low.</p> Sergey S Yulin Irina N Palamar Copyright (c) 2020 Statistics, Optimization & Information Computing 2020-02-18 2020-02-18 8 1 296 303 10.19139/soic-2310-5070-690 The Alpha-Beta Skew Logistic Distribution: Properties and Applications http://iapress.org/index.php/soic/article/view/706 <p><span style="font-family: CMR10; font-size: 9pt; color: #000000; font-style: normal; font-variant: normal;">A new family of skew distributions is introduced by extending the alpha skew logistic distribution proposed by Hazarika-Chakraborty [9]. This family of distributions is called the alpha-beta skew logistic (ABSLG) distribution.Density function, moments, skewness and kurtosis coefficients are derived. The parameters of the new family are estimated by maximum likelihood and moments methods. The performance of the obtained estimators examined via a Monte carlo simulation. Flexibility, usefulness and suitability of ABSLG is illustrated by analyzing two real data sets.</span></p> Hamid Esmaeili Fazlollah Lak Morad Alizadeh Mohammad esmail Dehghan monfared Copyright (c) 2020 Statistics, Optimization & Information Computing 2020-02-18 2020-02-18 8 1 304 317 10.19139/soic-2310-5070-706 A Robust Statistical method to Estimate the Intervention Effect with Longitudinal Data http://iapress.org/index.php/soic/article/view/811 <p>Segmented regression is a standard statistical procedure used to estimate the effect of a policy intervention on time series outcomes. This statistical method assumes the normality of the outcome variable, a large sample size, no autocorrelation in the observations, and a linear trend over time. Also, segmented regression is very sensitive to outliers. In a small sample study, if the outcome variable does not follow a Gaussian distribution, then using segmented regression to estimate the intervention effect leads to incorrect inferences. To address the small sample problem and non-normality in the outcome variable, including outliers, we describe and develop a robust statistical method to estimate the policy intervention effect in a series of longitudinal data. A simulation study is conducted to demonstrate the effect of outliers and non-normality in the outcomes by calculating the power of the test statistics with the segmented regression and the proposed robust statistical methods. Moreover, since finding the sampling distribution of the proposed robust statistic is analytically difficult, we use a nonparametric bootstrap technique to study the properties of the sampling distribution and make statistical inferences. Simulation studies show that the proposed method has more power than the standard t-test used in segmented regression analysis under the non-normality error distribution. Finally, we use the developed technique to estimate the intervention effect of the Istanbul Declaration on illegal organ activities. The robust method detected more significant effects compared to the standard method and provided shorter confidence intervals.</p> Mohammad M Islam Erik L Heiny Copyright (c) 2020 Statistics, Optimization & Information Computing 2020-02-17 2020-02-17 8 1 318 327 10.19139/soic-2310-5070-811