Unemployment is one of the most important issues in all countries around the world. An increase in the number of unemployed in any society will cause a lot of problems. So having deep and appropriate knowledge of the factors affecting unemployment is taken into account to reduce it. In this thesis, we gathered data of Population and Housing census 2016 from the Statistical Center of Iran. These data categorized the active and unemployed population of 15 years old or above, based on gender and different levels of education in the counties of Iran. We edit these data, based on our purpose. Our purpose in the thesis is spatial modeling of the number of unemployed based on gender and education as covariates. To achieve this goal, we use Bayesian approach and a method called “integrated nested Laplace approximation” or INLA for short. For many years, Bayesian inference has relied upon Markov chain Monte Carlo (MCMC) methods. This approach focuses on estimating the joint posterior distribution of model parameters, therefore, it is computationally expensive in high-dimensional spaces. Instead, Inla focuses on estimating marginal posterior distributions, and according to tremendous developments in computational systems in recent years, it is done more quickly. In addition, INLA is expressed in models with GMRF feature and it has some advantages that reduce the time of model fitting calculations. Finally and after appropriate modeling of the data, we interpret the effects of the two variables of gender and education as well as spatial effects of the counties of Iran on the number of unemployed.

   In this paper, the aim is to investigate the dependent competing risk model under middle censoring using some bivariate distributions such as Marshall-olkin bivariable Weibull distribution and Marshall-olkin bivariable Gompertz distribution and to compare the maximum likelihood estimation approach and Bayesian approach. To achieve this, subset of real data as well as simulations using R software are used, and the maximum likelihood estimates and Bayesian estimation are compared with each other.

to the importance of its usage. One of the most important challenges in discussing theprogressive Type-II censored data is to determine the removal scheme. The removal schemecan be fixed or randomly selected according to a discrete probability distribution. Thisthesis considers the estimation problem for the two-parameter Pareto distribution underprogressive Type-II censoring with random removals, where the number of units removedat each failure time has a binomial distribution. The main focus of this study is on theBayesian estimates of Pareto distribution using Jeffery’s non-information and InformativePower Gamma distributions as priors for the unknown parameters under the squared errorand absolute error loss functions. Furthermore, the statistical performances of the obtainedestimators are compared with each other and with the maximum likelihood estimators.The comparisons have been done by Monte Carlo simulation. Finally, the E-Bayesian andhierarchical Bayesian estimations of the parameter derived from Pareto distribution arestudied and compared under different loss functions.  

در مسائل دسته‌بندي، داده‌ها با توجه به وجه اشتراكي كه دارند به چند دسته خاص تقسيم مي‌شوند. دسته‌بندي ابزار مهمي براي تحليل مشكلات آماري است. روش‌هاي متعددي براي دسته‌بندي داده‌ها وجود دارد كه برحسب اينكه متغير پاسخ مشخص و يا نامشخص باشند به ترتيب به دو دسته كلي بانظارت و بدون نظارت تقسيم‌بندي مي‌شوند. از جمله اين روش‌ها مي‌توان به روش‌هاي كلاسيك رگرسيوني مثل رگرسيون با داده‌هاي دودويي (لجستيك، پروبيت و...) اشاره كرد. همچنين روش‌هاي دسته‌بندي براساس آموزش ماشين مثل درخت تصميم، جنگل تصادفي و ... جايگزين‌هاي مناسبي براي روش‌هاي رگرسيون كلاسيك هستند. در اين تحقيق ما به بررسي اين روش‌ها مي‌پردازيم و در نهايت اين روش‌ها، براي مجموعه داده‌هاي بانكي از يك كمپين بازاريابي تلفني به كار برده مي‌شود. روش‌هاي مختلف با استفاده از معيار دقت و منحني ROC مقايسه مي‌گردند.  

In many applications, the data subject to inverstigation are in the form of location or geographical positions of some events in a specific region. In the present thesis, we are facing data related to location of corneal endothelium cells of 153 individual. Here, for proper analysis of this data, we have linked spatial point patterns to these images so that we can classify a group of very similar images into identical clusters based on clustering algorithms related to space point patterns. To investigate the cases of dissimilarity, the nearest neighbor distance function, empty space function, K-reply function, etc, have been used.

  The subject of classification is the one of the important issues indifferent sciences. The logistic regression is the one of the statistical methods to classify data in which the underlying distribution of the data is assumed to be known. Today, researchers in addition to statistical methods use other methods such as machine learning to classify data.  In this thesis, the decision trees C4.5, C5, CART, CHAID, and QUEST  are introduced,  and each of them is completely studied. Some ensemble learning algorithms such as random forest, Bagging, and Boosting in the field of supervised learning are also explained. Finally,  using five data sets, we compare the performance of these algorithms with respect to the accuracy measure.

   One of the fundamental issues in statistics is the modeling of random phenomena. Generally, statistical models are used to represent random structures, predicting future behavior of variables, deduction and extraction of information from data. In the meantime, the copula function as a model for multivariate and dependent observations has attracted the attention of many users in recent studies. In fact, an alternative way to model the dependency structure between multivariate data without imposing any assumptions on the marginal distributions based on the structure of the copula functions has been proposed which considers defects such as linear correlation coefficient, asymmetry and sequence dependence. Copula functions are functions to create a multivariate common distribution. Or, in other words, it establishes relationship between multivariate distribution functions and one-dimensional marginal distribution functions. These functions of the marginal distributions have a continuous uniform distribution over interval (0,1). In addition, copula functions are useful in obtaining dependency on both sides of the distribution by using the tail dependence. In this thesis, the selection of copula functions is performed using maximum likelihood method and prediction method. And the appropriate copula function on the Automotive and Metal Industry Stock Exchange data for years 88-96 based on the maximum likelihood estimation method and the Akaike information criterion as well as on the prediction method has been determined and used to provide optimal forecasts on the data.

Gaussian time-series models are often specified through their spectral density. Such models pose several computational challenges, in particular because of the non-sparse nature of the covariance matrix. We derive a fast approximation of the likelihood for such models. We use importance sampling to correct for the approximation error. We show that the variance of the importance sampling weights vanishes as the sample size goes to infinity. We show that the posterior is typically multi-modal, and derive a Sequential Monte Carlo sampler based on an annealing sequence in order to sample from the approximate posterior. Performance of the overall approach is evaluated on simulated and real datasets.

   Normal 0 false false false EN-US X-NONE FA The weighted k out of n system is a one with n components that each component has a specific weight and it works if sum of its active components be at least k. A lot of researches and studies have been carried out around the properties of k out of n systems. This thesis investigates the reliability and some properties of these systems. One of these properties is the redundancy allocation that its result has been presented in the first part of this thesis. In the next part, the result of a weighted k out of n system with dependent components have been studied. Finally, k out of n system generalized to the weighted (k1, k2, …, km) out of n system and its result have been presented.

Our research is applied in terms of purpose. Because the proposed model lays solutions to improve the premium determination and generally improve the performance of insurance companies.We offer model forecasting methods to determine the premium rate,That detects data exploration and modeling. Among these methods, the accelerated gradient is a method in composite Poisson model. Since the main variables and interaction effects used in the models are, therefore, a tree accelerated gradient algorithm with the name TDboost offer visited. Also for data with a large zero accumulation The methods will be provided to make the premium forecast possible . First, we will discuss the definitions and concepts required in insurance science . So we introduce and examine the accelerated gradient tree model .In the third chapter, we implement a model for the survey of the database composite Poisson with insurance studies data.In the fourth chapter, we will analyze and compare non-parametric models using data sets, And finally, we will conclude our suggestions and conclusions.  

  ‏در آمار يكي از ابزار مهم براي تحليل داده ها در مدل هاي آماري برآورد پارامترها و انتخاب متغير مناسب است و روش هاي مختلفي براي آن وجود دارد. دو مورد از معروف ترين آن ها در حالت كلاسيك روش كمترين مربعات معمولي و روش بر‎‏آورد درستنمايي ماكسيمم است. اما در رگرسيون با بعد بالا‏، به علت وقوع مشكل بيش برآورد نمي توان از اين روش ها استفاده كرد‏، پس محقق سعي مي كند با كمك روش هاي انقباضي مانند رگرسيون جريمه دار اين مشكل را حل كند. در حالي كه آمار بيزي براي برآورد پارامترها از برآورد حالت پسين استفاده مي كند. زماني كه با رگرسيون با بعد بالا مواجه مي شود‏، تلاش مي كند كه اين مشكل را با استفاده از روش هاي   تنظيم بيزي (انقباضي بيزي) حل كند. اين روش ها تعداد متغيرهاي پيش بيني كننده و پيچيدگي مدل را كاهش مي دهند و برآورد پارامترها و انتخاب متغير ها را ساده تر مي كنند. بنابراين در اين پايان نامه اين روش ها را مورد بحث و بررسي قرار مي دهيم

  در آمار يكي از مهم ترين ابزارها براي تجزيه و تحليل داده ها ، به دست آوردن برآورد مناسب يك تابع است كه روش هاي مختلفي براي آن به وجود آمده است. يكي از معروف ترين و ساده ترين روش هاي برآورد، روش كمترين مربعات معمولي است كه در شرايط مطلوب مزيت هاي فراواني دارد. اين روش در رگرسيون بعد بالا كاربردي ندارد و دليل اين مساله هم اين است كه در رگرسيون بعد بالا به علت زياد بودن متغير هاي پيشگو، سبب دشوار شدن تفسير مدل و كاهش دقت در برآورد مي شود. در چنين شرايطي محقق مي تواند با كاهش متغير هاي پيشگو و درواقع حذف متغير هاي كم اثر با استفاده از روش هاي خاصي كه بيان مي گردند، سبب بهتر شدن تفسير اين مدل ها شود. دراين پايان نامه ابتدا ضمن معرفي روش هايي كه به روش هاي انقباضي معروف هستند، روش هايي همانند لاسو ، لاسو گروهي، ريج، بريج و الاستيك نت مورد بررسي قرار مي گيرند. از طرف ديگر   مدل هاي با ضرايب متغير نيز از جمله مهم ترين ابزارها براي كشف الگوهاي حركتي در بسياري از علوم از جمله: سرمايه گذاري مالي، اپيدميولوژي، علوم سياسي،علوم پزشكي، اكولوژي و غيره هستند. اين مدل ها بسط طبيعي مدل هاي كلاسيك پارامتري هستند كه با تفسير پذيري خوب، محبوبيت زيادي در تجزيه و تحليل داده ها به دست آورده اند. انعطاف پذيري و تفسير پذيري بالاي اين مدل ها در دهه اخيرسبب شده كه تحولات شگرف و جالبي در روش شناسي، نظري و كاربردي در اين زمينه پديد آيد. در ادامه ضمن معرفي مدل هاي با ضرايب متغير به بررسي مهم ترين روش برآورد پارامتر در اين مدل ها كه روش استفاده از تابع هسته است پرداخته مي شود. همچنين مدل هاي با ضرايب متغير تعميم يافته را معرفي خواهيم كرد و با استفاده از روش رگرسيون بريج در مدل هاي بعد بالا، برآورد پارامتر ها در اين حالت را نيز مورد بحث و بررسي قرار خواهيم داد. در نهايت انتخاب متغير براي مدل هاي با ضريب متغير تعميم يافته بعد بالا را مورد بررسي قرار مي دهيم كه از روش انقباضي لاسو گروهي در اين بحث استفاده مي كنيم ، همچنين براي انتخاب بهترين زير مجموعه از متغير هاي موجود از روش اطلاع بيزي تعميم يافته استفاده مي كنيم و تمام اين مسائل را در نرم افزار R مورد بحث و بررسي قرار خواهيم داد.

Waiting lines and service efficiency are the important elements for any bank. Queuing theory has been fairly a successful tool in the performance analysis of waiting lines. In this paper, an optimized model is proposed to improve the bank queuing system based on queuing theory. This method can optimize the number of server and improve the service efficiency that could effectively cut down service costs and customer’s waiting time  

In many environmental applications involving spacial and spatio-temporal data, covariance functions are the fundamental tools for modeling dependent data which observed over space and (or) time. Constructing nonseparable spatio-temporal variogram and covariance functions is one of the issues related to spatio-temporal geostatistics for space-time data. Limitations on the number of locations and high values of parameters motivate the need for practical and efficient method to estimate the parameters of covariance models for spatial interpolation, or kriging. In this paper, we discuss different types of spatio-temporal data, also we combine these methods with Bees algorithm (BA) to explore the spatiotemporal correlation structure of monthly ground-water data in Ilam city. Finally, we predict the level of some spacial stations using spatio-temporal kriging which the efficiency of model was assessed by Mean of Kriging Standard Deviations (MKSD). Keywords: Kriging, Spatio-temporal data, Bee Algorithm

  Today, Copula’s use of the statistical functions which has increased dramatically. Although Copula functions have good advantages in statistical inferences, but when more than bivariate face, there are many computational problems. Therefore, using graphicmodels, wecananalysisthestructureofmulti-dimensionalCopula’swiththe dependenceofMarkovtreestructures. Butbecausethesizeofthevariablesincreases the structure of these graphical models are complex and time-consuming. Therefore, we can consider the conditions of models in a fully Bayesian framework contract. So that the tree and other tree-dependent parameters can be defined by the prior,and then get their posterior distributions. Because tree structures are related to each other variables, in this thesis using Markov Chain Monte Carlo simulation methods to compare the proposals of tree structures is investigated.

The data of most real-world optimization problems (OPs) are often not known exactly at the same time the problem is being solved‎. ‎The reasons for data uncertainty contain measurement errors‎, ‎imprecise data‎, ‎future developments‎, ‎environmental conditions‎. ‎Thus‎, ‎using uncertain robust optimization for optimization problems with uncertain data is essential‎. ‎In robust optimization‎, ‎the uncertain parameters are assumed to belong to a set that is known prior‎, ‎and the focus lies on the worst case‎. ‎The goal is to ensure that the solution is feasible and works well in every possible future scenario‎. ‎An uncertain problem can be solved using the scalarization methods (Benson’s method and elastic constraint method) in multi objective optimization‎. ‎This thesis also focuses on a unified approach to characterizing different kinds of multi objective robustness concepts‎. ‎Based on linear and nonlinear scalarization results for several set order relations‎, ‎together with the help of image space analysis‎, ‎some suitable subsets of scalarization image space are introduced to make equivalent characterizations for upper set (lower set‎, ‎set‎, ‎certainly‎, ‎respectively) less ordered robustness for uncertain multi objective optimization problems‎. ‎In the sequel‎, ‎by virtue of scalar robust optimization and using a deterministic robust counterpart‎, ‎a more general form of the robust optimization is considered in which the objective function and constraints contains uncertain data‎. ‎Moreover‎, ‎the relation between uncertain optimization and the image set is analyzed‎. ‎This idea leads to solve a min-max problem‎. ‎Moreover‎, ‎several necessary and sufficient optimality conditions‎, ‎especially saddle point sufficient optimality conditions for scalar robust optimization problems‎, ‎are obtained‎. ‎Finally‎, ‎a simple example for finding a shortest path is included‎.

  Adaptive web sampling design is a flexible >In these designs, an initial sample is first taken, then the selection of the next units is based on thecompound distribution: that is, with a predetermined probability, the units are selected through thelinks that are connected to the previous sample, or a unit is selected randomly. In this thesis, this

  In this distribution after introducing the concept of expected shortfall (ES) as a financial risk measure we briefly discuss the coherence properties of this measure. This statistic risk measure arises in a natural way from the estimation of the average of the 100p percent worst losses in a sample of returns to a portfolio where p is some fixed confidence level. Then we comprehensively review several know parametric method for estimating expected shortfall.  

  In this thesis, using variational methods and Critical Point Theory, we will investigate the existence and the multiplicity of solutions to   boundary value problems, including Neumannand Dirichlet problems, impulsive problems, fractional differential equations, vaiableexponent equations and etc. Moreover, in some of the results, the positivity and non-triviality of the solutiond will be discussed. Regarding the problems under study, we consider the nonlinear parts as continuous or Carathéodory functions. Then we build the related functionals and discuss the multiplicity of their critical points, obtaining multiple solutions which are the already obtained critical points. Finally, we illuminate the obtained results by presenting various examples.

Financial institutions are always exposed to investment risk.

  Optimal designs have an important role in designing the experiments and help the experimenter to do the experiment in a shorter time and with lower costs. In order to find the optimal designs, one has to consider the optimality criteria which is usually a function of Fisher Information Matrix. In the present thesis, the optimal designs for regression models with interval-valued data are obtained. These data are in fact, observations that are not accurately measurable and are reported as intervals. In this thesis, linear regression models fit these data and an optimal design for them is obtained.

  AbstractDiseasemapping refers to a set of statistical methods in which the incidence orprevalenceof a type of disease or death due to a specific cause within a geographicrangeis investigated . Consider the spatial area that has been compiled into severalsubsurfaceareas and the number of incidents occurring in the area under studyThederived spatial data is called spatial counting data The purpose of the diseasemappingis to estimate the relative risk of the incident in each of the sub-areas basedonthe data collected One of the most common models in disease mapping is theBYMmodel, which uses a randomized Gaussian mapping field (GMRF) to modeltherandom effects of sub-regions and correlations between space between sub-areaInthis thesis, the BYM model and Bayesian inference are described with the aid ofthe null cluster approximation method of the inla integral packet In the end,this modelis used to determine therelative risk of death from driving accidents in Kermanshah province  Keywords: diseasesmapping, spatial models, method using integratated nestedLaplace approximations(INLA), model BYM    

  We all have experienced the discomfort of waiting the queue.traffic or for paying tolls and ... .Themain reason for queuing is that demand for service is more than the service facilitties. Queuetheory is linked to factors such as queuing time,queue length,etc.With the expected properties ofthe flow of input to the system and service practices,it proposes an optimal system to reduce thedamage caused by queuing.In this thesis,after presenting the introduction and initial concepts, an invistigation of an unlimitedsource system and its prominent features,including the number of applicants in queue andsystem,waiting time,and so on will be done.In this model inputs have poisson distribution and servicetime exponential distribution.We then examine the bayesian queues M/M/1 and M/M/s,andwe see that there are some queuing features that are not mathematical expectation for them.Thenwe obtain the point estimate,distance and hypothesis test for Bayes systems and finally,we willsimulate what we have been studying at the end.

  Regression is used to predict and express variations of a variable based on other variables. In fact, statistical regression analysis and statistical techniques are used to examine and model the relationship between variables. Linear regression is one of the most widely used statistical tools. Modern regression applications for large data sets have created new challenges. when the number of variables approaches or exceeds the number of samples, We will consider a new method in this thesis that applies to many genomic databases. This method is called the Ising Bayesian Approximation (BIA). This method is used to quickly calculate the latent probabilities for the fit of the characteristic in the linear regression L2 compensated. From a practical point of view, BIA provides an algorithm for computing effective Bayesian paths for regression compensated L2. Using this method, it is possible to calcugate the latent likelihood of fit for a collection of dataset data, as is commonly found in genomic studies. The importance of this study is to consider the relationship between the features when evaluating meaningful statistics in the large data set. When the number of properties is high, even low correlations can lead to a decrease in the characteristics of the later probabilities. In this thesis, We also show that choosing a probability threshold for examining the importance of high-demention issues is usually not logical. Instead, BIA can be used as part of a two-step process in which BIA is used to quickly eliminate inappropriate variables, that is, variables that have a lower rating in the later probability before a rigorous validation process, from the computational point for the deduction of coefficients regression to be used the computational influence of BIA and the existence of a natural threshold for the penalized parameter are used, the two-step process is appropriate

  The research on optimal reinsurance design has a long history for academicians and practitioners. Because it is an effective risk management tool for insurers. Depending on the chosen objective and constraints , there are many ways for optimal design of reinsurance.The primary objective of the thesis is to examine theoretically sound and yet practical solution in the quest for optimal reinsurance designs. In order to achieve such an objective, this thesis is divided into two parts. In the first part, a numberof reinsurance models are examined and their optimal reinsurance treaties are derived. This part focuses on the risk measure minimization reinsurance models and discusses the optimal reinsurance treaties by exploiting two of the mostcommon risk measures known as the Value-at-Risk (VaR) and the Conditional Tail Expectation (CTE). Some additional important economic factors such as the reinsurance premium budget, the insurer’s profitability are also considered. The second part proposes an innovative method in formulating the reinsurance models, which we refer as the empirical approach since it exploits explicitly the insurer’s empirical loss data. The empirical approach has the advantage that it is practical and intuitively appealing. This approach is motivated by the difficulty that the reinsurance models are often infinite dimensional optimization problems and hence the explicit solutions are achievable only in some special cases. The empirical approach effectively reformulates the optimal reinsurance problem into a finite dimensional optimization problem. Furthermore, we demonstrate that the second-order conic programming can be used to obtain the optimal solutions for a wide range of reinsurance models formulated by the empirical approach.

In many practical studies in medical, social and economic studies, the data are collected over time as discrete longitudinal data. One of the important issues in this data is the effect of the previous response on the current response, which can be considered by a transition model. Another important issue in the data set is heterogeneity among individuals which can be covered by adding a random effect to the transition model. Another important problem in longitudinal data is missing values. In this thesis, a non-ignorable missingness mechanism is considered for modeling binary and ordinal longitudinal data by a random effects transition model. Some simulation studies are performed for illustration of the proposed approaches; also, the proposed approaches are used for analyzing a real data set.

  اخيراً‏، مسئله‌ي نقطه‌ي تغيير يكي از موضوعاتي است كه مورد توجه بسياري از آماردانان واقع شده است. نقطه‌ي تغيير‏، مي‌تواند در بسياري از زمينه‌هاي تحقيقاتي و صنعتي مفيد واقع شود و از خسارات جبران‌ناپذير پيشگيري كند. در اين رساله‏، ما به مطالعه‌ي مسئله‌ي نقطه‌ي تغيير و تشخيص آن‏، با استفاده از آزمون فرض پرداخته‌ايم. ابتدا‏، به تعريف نقطه‌ي تغيير و مثال‌هايي از آن مي‌پردازيم‏، سپس تشخيص تك‌نقطه‌ي تغيير در داده‌هاي طول عمر با حجم كم را مورد بررسي قرار مي‌دهيم. در راستاي اجراي اين آزمون فرض‏، از آماره‌هاي متفاوتي استفاده مي‌كنيم كه يكي از آن‌ها‏، آماره‌ي آزمون نسبت درستنمايي تجربي است. بالاكريشنان و همكاران ‎‎‎‎(2016) ‎‏ تشخيص تك‌نقطه‌ي تغيير و بررسي آن را در دو حالت پارامتري و ناپارامتري مورد مطالعه قرار داده‌اند. هدف اين رساله‏، تشخيص نقطه‌ي تغيير و مقايسه‌ي آماره‌هاي متعدد از طريق توان آزمون‌هاست.كليد واژه: آزمون فرض، نقطه‌ي تغيير، نسبت درستنمايي تجربي، داده‌هاي طول عمر

  Measuring and comparing risk in the insurance management process is essential, because of the risk measurement in banks, insurance companies and financial.The basis for desicion making is to allocate their resources.One way, the comparison based on some of the measure of the important risks and compare the risk with the stochastic order.In this dissertation, we propose a generalization of the increasing convex order to the multivariate setting to compare vectors of risks that accounts for both the marginal impacts and the dependence structures ofthe vectors. This generalization is suitable for comparing vectors with heterogeneous components andextends some well-known properties of the univariate increasing convex order. For example, comparisonsof vectors with the same copula can be characterized in terms of the multivariate tail conditionalexpectations introduced by Cousin and Di Bernardino. Also the multivariate extensions of the risk measures, tail conditional expectation and value at risk are presented and their invariance with respect to the univariate case are characterized.

The Study of the spatial pattern of trees in a forest stand has always gained attention among forestry researchers. Data on Spatial location of individual trees in a natural forest can present useful information on the distribution and structure of different forest species, as well as interaction between them. In the paper, data on spatial location of Iranian oak (Quercus brantii) in a 2 hectares plot in the zagros forests, Hasanabad area (west of Iran) were investigated. To this end, statistical methods in spatial point process, particularly widely used summary statistics like the pair correlation function and J function, were employed. Based on the results, there was a significant positive interaction (clustering) within Iranian oak species at spatial distances 2 to 6 meters, while no significant interaction was observed for other species.In addition, there was a significant interaction repulsion Iranian oak and other species.

Efforts to find solutions to prevent the risk and damage caused by accidents have been one of the most overwhelming human issues throughout history. Insurance is one of the most efficient industries or methods that can help them reduce the harmful effects of risk. One of the most important and practical aspects of insurance statistics is the investigation of claims distributions that follow a heavy tail distribution in heavy economic losses that are more economically important. These heavy tailings include Elliptic, Laplace, T-student, Normal, Paratou,Logistic,... distributions. The various risk measures, including tail variance, conditional variance, value at risk, conditional value at risk,... under these distributions, are designed to minimize risk and increase returns. We will benefit from these conditions. In this thesis, we focus more on tail variance and tail conditional expected and their application.

Estimation reliability in some distributions with fuzzy parameter

  ‎In statistical study of spatial two-dimensional societies‎, ‎one of the purposes of which is preparing different plans‎, ‎collecting data from all area is of great importance‎. Since enumerating‎ all points a ‎wide‎ area is difficult and in some cases impossible‎, ‎then the required data should be collected only for a part of that area as the sample‎. ‎In a conventional and non-spatial population in which the location of the sample unit is not considered‎, ‎the main assessment criterion for sampling is efficiency of the estimator‎. ‎In sampling two-dimensional areas‎, ‎in addition to efficiency and estimators precision‎, ‎well-ballance of all the area is considered as well with due consideration to sampling methods in two-dimensional ‎population‎‎, ‎in this thesis‎, the relate ‎sampling methods are studied‎, also their well-spread‎, ‎and efficiencies are measured.

‎Cox processes appropriate statistical models for cluster point patterns like trees in a forest location‎. ‎In the meantime‎, ‎log-Gaussian Cox processes for high flexibility in modeling and statistical analysis in a forest where trees are of most interest‎. ‎Considering the Bayesian approach can be integrated nested Laplace approximation method (INLA) for estimation and statistical inference about the parameters of a log-Gaussian Cox model was used‎. ‎INLA a quick‎, ‎yet thorough approach to Bayesian estimation of parameters of statistical models with a Latent Gaussian model (LGM)‎, ‎such as log-Gaussian Cox process models‎. ‎The INLA is a promising new technology for Markov chain Monte Carlo Bayesian inference without (MCMC)‎, ‎is also a definite alternative to this approach‎, ‎the main advantage of MCMC method to calculate the INLA is fast‎, ‎because calculations using Markov chain Monte Carlo is time-consuming‎. ‎In this thesis‎, ‎Bayesian inference for log-Gaussian Cox processes with INLA approach to examine and use it for modeling the location of trees in a forest‎.

  Using optimum experimental design to run an experiment is one of the topics in applied statistics which isconsidered by some statisticians. Design of a experiment for statistical regression models is very important.In this thesis and making optimal plans for generalized linear regression model Gompertz model in thefamily has been placed. In order to find optimal designs of optimality criteria shall be used. These criteriaare usually functions of the matrix. Given that in generalized linear models, matrix depends on unknownparameters of the model, so in this thesis using D -Bhyngy Bayesian Criterion, schemeD parser Bayesianregression model Gompertz is calculated.

  Optimal designs play an important role in marketing research, medical and the other sciences.Using of these designs can be reduced the cost of researche and experiments. To calculate theoptimal design need to have an optimality criterion. In this thesis, D-optimal criterion hasbeen considered which is a function of the Fisher information matrix. In the nonlinear models,the Fisher information matrix depends on unknown parameters will cause inconsistenciesin the design. There are some techniques to solve this problem of dependence optimalitycriterion on unknown parameters. In this situation, it can be pointed to three of themas follows: 1- The localy optimal design, 2- Minimax optimal design, 3- Bayesian optimaldesign. In this thesis, Inverse Quadratic Polynomial regression model will be introduced.Then, Bayesian D-optimal design for this model on the based on prior distribution uniformand normal for unknown parameters will be obtained.

  In this thesis, we give a new distribution of a new class of distributions called the Hyperbolic Cosine – F (HCF) distribution.Since the Weibull distribution of the most popular and most widely used distributions in reliability and lifetime data analysis. A special case of this family is the Hyperbolic Cosine Weibull distribution . We also discuss simulation method, also maximum likelihood minimum spaccings estimators of the parameters of the distribution.And continue   we have discussed   with the second type of censorship increasingly on the distribution, to estimate the parameters. The new distribution can be used effectively in the analysis of survival data.

Dynamic formulations of reliability theory are of so considerable interest in the analysis and comparison of working systems in real time. Dynamic signatures, which have been considered by many researchers in the recent years, are useful tools in the studying and comparisons of the lifetimes of used systems.In this thesis, we study the dynamic signatures and its application in reliability theory of coherent systems. In this direction, we first introduce the signature of a coherent system having i.i.d components lifetimes and investigate some their properties and applications in reliability theory of coherent systems. Then, we studythe dynamic signatures under some information about the lifetime of the system. Samaniego et al. (2009) considered a situation that some partial information about the system and its components lifetimes are available and defined the dynamic signatures under such information.The last purpose of this thesis is introducing of such dynamic signatures, which depends only on the system structure, andstudyingtheir applications.

 In this thesis‎, ‎we the first study point process and their models and summary functions‎. ‎Then‎, ‎we discussion global envelope test for spatial processes‎. ‎Finally‎, ‎we compare power of stated test with other test for simulated and real data‎.  In this thesis‎, ‎we the first study point process and their models and summary functions‎. ‎Then‎, ‎we discussion global envelope test for spatial processes‎. ‎Finally‎, ‎we compare power of stated test with other test for simulated and real data‎.

  The allocation of redundant component(s) in a system so as to optimize the lifetime of the system is quite ‌considerable inreliability theory. In engineering systems, the k-out-of-n system is a very important structure, whichworks if and only if at least k components are operating. In this thesis, we consider the problems of optimal allocation of R redundancies to n components of   k-out-of-n systemsand series systems, as particular case of k-out-of-n systems when k=n,with respect to some stochastic orderings.Two commonly used methods to allocate redundancy are active redundancy and standby redundancy. We discuss the allocation of active redundancies to series and k-out-of-n systems in the three cases with i.i.d components and redundancies, i.i.d components and i.i.d redundancies and stochastically ordered components. We also compare the lifetimes of series systems arising out of one standby redundancy. Optimal allocation of redundancies in -out-of-   ystems

  The epidemic type aftershock sequence (ETAS) model of serves as the baseline model for describing the behavior of earthquake clusters. The ETAS model is a space-time point process that is based on the empirical laws driven from the descriptive study of earthquakes statistics. The model assumes that earthquakes are produced by two sources: background seismic activities and clusters of aftershocks that are produced with occurrence of large earthquakes. Parameters of the common ETAS model are fixed and clusters are assumed to be isotropic. Since the earthquake that occurred in past are heterogeneous and clusters of aftershocks are not isotropic, so in the present thesis we study an improved version of the ETAS model which allows the parameters to vary spatial.

  In the recent years, many researches on dynamic measures of uncertainty have been carriedout which indicate their practical importance. One of the related interesting issues is thenonparametric estimation of such measures. Since in the reliability and survival analysis,samples usually contain censored data, so in this thesis, using the kernel density estimation,we investigate the nonparametric estimation of generalized past entropy and Renyi’s residualentropy based on the censored data. Some of the asymptotic properties of the estimators arestudied.

  ‎The locations of trees in a forest form a spatial point pattern‎, ‎which due to spatial correlation between the trees is often clustered‎ . ‎One of the most appropriate models for modeling cluster point patterns is log-Gaussian Cox model‎. ‎In this model‎, ‎it is assumed that a Gaussian random field affects the intensity function of the point process‎. ‎Spatial prediction of the hiden Gaussian random field based on the observed point pattern is very important‎.‎To fit this model and perform spatial prediction of the underlying Gaussian field both Markov Chain Monte Carlo (MCMC) and integrated nested Laplace approximation (INLA) methods can be used‎.‎In this thesis‎, ‎we use these methods to fit a log-Gaussian Cox process to a tree species the tropical rain forest of Barro Colorado Island‎.

  We all have experienced the discomfort of waiting in queue, or to pay the toll roads in traffic, sitting in the car waiting; to pay for items bought in stores and we will remain in government offices’ queue. We, as customers, generally do not like this kind of waiting and managers also do not like seeing us waiting in the queue, because these queues may have cost for them.The main reason of forming queue is that the demand for service is more than service’sfacilities. Queuing theory by linking factors such as waiting time in the queue, queue length and etc. considering the given properties login and service practices,formsan optimized designsystem to reduce the damage caused by queues. In this thesis, after the introduction and basic concepts, we study queuing model Mb / M / 1 withreviewPoisson arrival rate that is fixed with customers to bulk the distribution server is exponential. And then non-Markov model M / G / 1 that is the customer’s time service overall distribution function.Then study such components such as queue length, number of customers in the system and the system busy period. At last, we study   Mx/ G / 1 queue model to conclude and waiting time in the system and period of unemployment and employment, and in steady state in the queue. And finally, we study their generating functionin a steady state.Keywords:   Bulk Queue, Steady State, entropy, Breakdown, Supplementary, Unreliable, Queue Size