آمده را با ساير روش‌ها مقايسه و مورد ارزيابي قرار مي‌دهيم.

A time series is a set of data recorded over time. For example, we can refer to the time series of the price of a share in the stock market, the amount of rain in an area, etc. One of the most important goals of time series analysis is to predict its future values. Several statistical methods for predicting time series, such as the method of using time series analysis models of Autoregressive integrated moving average model and Seasonal autoregressive integrated moving average model, wavelet analysis methods have been in-troduced. Along with statistical methods, neural networks are also a powerful tool for predicting time series, due to the ability of neural networks to model relationships and complex patterns in data, predicting time series using it has attracted the attention of researchers in various fields and is a research topic. It has become popular. The use of convolutional neural networks to predict time series is known as an e?ective method for analyzing and predicting repetitive patterns in time data. These networks are designed to recognize di?erent patterns in temporal data and can make accurate predictions for future data values using these patterns. Long Short Term Memory (LSTM) Recurrent Neural Networks and Gate Recurrent Neural Networks (GRU) are two types of neural networks used for time series forecasting. LSTM and GRU networks are useful for time series forecasting due to their ability to retain memory over time. These networks, using a memory unit, keep the previous information and make the next prediction according to this information. In this thesis, time series forecasting with convolutional neural network and LSTM and GRU neural networks is investigated. The performance of these networks in prediction accuracy is compared. Also, their performance is compared with statistical methods such as SARIMA.Key ords. Forecasting time series, Neural networks, Recurrent neural networks, Long short-term memory, Gated recurrent unit, Convolutional neural networks.

   Abstract The problem of variable selection is a crucial and difficult aspect of statisticai modeling. Choosing the wrong predictor variables for the final model can result in either underfitting or overfitting. It is crucial to control the rate of false discovery during the inference stage, in variable selection methods. A false discovery rate is said in proportion to auxiliary variables that are improperly chosen among all selected variables. False discovery rate control has been studied for a long time, and several approaches have been developed to achieve an optimal solution. Recently, a new family of FDR control methods called “Knockoff filters” has been introduced. This thesis addresses the issue of variable selection in regression models error false discovery rate control whit various knockoff versions, including fixed-X knockoffs and X-model knockoffs. These knockoff methods can be suitable structures to imitate the existing variables and control the false discovery rate to acceptable limits. The performance of each type of knockoff method will be reviewed in comparison whit each other and some common methods to control the false discovery rate. The efficiency of the presented models has been studied using the data obtained from the simulation.       Keywords: variable selection, sparse regression, knockoff filter, false discovery rate.   

   Diabetes is a   endocrine disorder characterized by chronic hyperglycemia as a result of insulin resistance or deficiency. Diabetes is one of the most common matebolic diseases in the world and one the challenging problems of the present centary, which is the result of interactions between genetic and behavioral predisposition and environmental factors. Considering the prevalence of type 2 diabetes around the world, it is useful for doctors to identify connections and discore new rules, and for this reason, doctors and researchers analyzed and investigated the cause of the growing increase of this disease by using artificial intelligence and its subset. In this thesis, by using machine learning, including decision tree, random forest, logistic regression and neural network, we analyze and investigate the diagnosis and prognosis of type 2 diabetes by using the data if Ravansar cohort, which includes 10047 people and 137 variables, we understand that the main factors affecting this disease are age, fasting blood sugar level, manganese, selenium, etc. Also, people who are involved with this disease   should change their lifestyle according to the doctor's advice so that they don't face more problems in the rest of their lives. Keywords: Type 2 diabetes, Artificial Intelligenece, Machine Learning, Decision Tree, Random Forest, Logistic Regression, Neural Network.

يكي از عوامل مهم در بررسي آموزش، پيش‌بيني پيشرفت ‌تحصيلي است و استفاده از فنون داده‌كاوي يكي از راه‌كار‌هاي نوين پيش‌بيني پيشرفت ‌تحصيلي است. در اين پايان‌نامه، فنون داده‌كاوي در دو بخش روش‌هاي ساده شامل درخت‌ تصميم، جنگل تصادفي، $K$-نزديك‌ترين همسايه و بخش روش‌هاي پيچيده‌تر شامل ماشين ‌بردار ‌پشتيبان و شبكه عصبي مورد مطالعه قرار گرفته‌اند. همچنين دقت اين روش‌ها بر روي مجموعه داده‌هاي مربوط به دانشجويان دانشگاه رازي از سال 1375 تا 1401 در مقطع كارداني و كارشناسي مورد بررسي و مقايسه قرار گرفته است. از روش‌هاي بررسي شده جنگل تصادفي بيشترين دقت پيش‌بيني را نتيجه داده است اما از لحاظ سرعت پاسخ‌دهي هزينه محاسباتي بالايي دارد. روش $K$-نزديك‌ترين همسايه از لحاظ دقت خيلي نزديك به روش جنگل تصادفي است با اين تفاوت كه زمان اندكي لازم است تا خروجي‌ها حاصل شوند.   

   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.  

The intuition of risk is based on two main concepts: the possibility of a negative outcome, i.e. a lo   and the variability in terms of an expected result, i.e. a deviation. Since the time when the modern theory of finance was accepted, the role of risk measurement has attracted attention. Initially, it was predominantly used as a dispersion measure, such as variance, which contemplates the second pillar of the intuition. More recently, the occurrence of critical events has turned the attention to tail-risk measurement, as is the case of well known Value at Risk (VaR) and Expected Shortfall (ES)measures, which contemplate the first pillar. In this Thesis, a risk measure is considered which contemplate both pillars of intuition on risk. These pillars include the possibility of negative results and variability over an expected result, as a single measure. This resulting composition, based on properties of the two components, is a coherent risk measure. Similar results for the cases of convex and co-monotone risk measures are exposed. Then, the eleven well-known risk measures consider from different classes. Finally, the empirical values of corresponding to loss, deviation and loss-deviation risk measures are obtained and compared using Monte Carlo and real data.   

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.

همه ي ما ناراحتي انتظاركشيدن درصف را تجربه كرده ايم.علت اصلي تشكيل صف اين است كه تقاضا براي سرويس بيش ازامكانات سرويس دهي است. در دنياي امروز با توجه به پيشرفت تكنولوژي، سازمان ها در تلاش هستند كه از رقبا پيشي بگيرند و اين جز با برنامه ريزي دقيق و به كارگيري صحيح منابع و امكانات امكان پذير نيست. بنابراين مديران با توجه به پيچيدگي سيستم ها، بايد با استفاده از ابزارهاي مناسب مانند برنامه ريزي خطي، برنامه ريزي پويا، برنامه ريزي اعداد صحيح، شبيه سازي، تئوري صف و ... كه براي تحليل سيستم هاي وجود دارند، برنامه‌ريزي صحيحي انجام داده و از به هدر رفتن منابع جلوگيري كنند. . دراين تحقيق مفاهيم لازم براي يادگيري صف وصف بندي ونيز شيوه ي شبيه سازي مدل هايي ازصف بندي ارائه گرديده است.كليد واژه: سيستم صف بندي، تئوري صف، الگوي ورود متقاضيان،الگوي سرويس،نظم صف،ظرفيت يا گنجايش سيستم،تعدادمتقاضيان درسيستم،شبيه سازي   

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.

  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.

   Variable selection is one of the most important topics in statistical modeling which is widely used in statistical applications. In this thesis, penalized regression models are used for selection important variables and in order to accelerate the estimation procedure of regression coefficients from partial likelihood of recurrent event data, the coordinate descent algorithm is applied. Using real longitudinal data from 230 patients with schizophrenia admitted to Farabi Hospital in Kermanshah from 01/01/1395 to 12/12/1397, each experienced more than one recurrence was able to select important variables. We have differentiated from the large number of covariate variables included in this data and finally fitted the models. Keywords: Longitudinal Data, penalty Regression, Partial Likelihood, Recurrent Event Data, Coordinate   Descent Algorithm

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

  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

  در اين رساله، انواعي از سياست نگهداري براي پيشگيري خسارت­هاي(گاهاً جبران­ناپذير) ناشي از خرابي قطعات در حين كار كردن، مطالعه مي­شود. همانطور كه بيان شد شكست واحدها در زمان كار كردن ممكن است گران تمام شود. در مواردي كه با افزايش عمر، نرخ شكست افزايش مي­يابد، براي جلوگيري از خسارات، واحد را بايد قبل از آنكه خراب شود تعويض كنيم. سياست تعويض عمر، از پايه­هاي اصلي سياست نگهداري است كه براي جلوگيري از شكست يك واحد در زمان كار كردن است. در سياست تعويض عمر، قطعه در زمان شكست و يا زمان مشخص t تعويض مي شود اگر قطعه در زمان t در حال كار كردن باشد.مشخص است كه تعيين زمان t يكي از مسايل بسيار مهم در بحث سياست جايگذاري است.بارلو و پروشان(1965) ميانگين زمان شكست تحت سياست جايگذاري را به عنوان معياري از تاثير t معرفي نمودند.

  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.  

Financial institutions are always exposed to investment risk.

  Determining the suitable premium for an insurer is one of the most important categories in the insurance industry. Inmostbonus-malussystems premiumbasedonthenumberofclaims Theclaimamountsarenot taken into accont. In this case, policyholders who had accidents with small or large claims are penalized unfairlyinthesameway. Ateventhepolicyholdersmayleavetheinsurancecompanytogetridoftheirbad history claims. In this thesis, in addition to the number of claims, the amount of claim is also considered. Also, in the malus zone, relative premiums softened by introducing and applying deductible  

  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    

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.

برآورد تابع بقا و عوامل موثر بر بيماران مبتلا به سرطان پستان در عراق از سال 2014 تا 2016  

  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.

  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

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.

Recently, one of the subjects that is attractive for statisticians on applied fields, is optimal designs to do the experiments. Optimal designs are obtaind using real-valued function which is call optimal criteria.Statistical models to study the behavior of absorption or Drog release are called statistical models in pharmacokinetic/pharmacodynamics. In this thesis, we consider optimal designs for models in pharmacokinetic/pharmacodynamics studies.Since that information matrixs for these models depend on the unknown parameters, locally optimal designs have been considered to find optimal designs. Numerical results have been obtained for D-, A-, E-optimal designs.

Determination of optimal design for testing procedures is one of the major topics of interest to most statisticians. These designs are commonly obtained by optimizing some functions of information matrix to acquire the most appropriate parameter estimates. But many results on optimal designs of experiments are derived under the assumption that the statistical model is known at the design stage. Thus, the purpose of an experiment should be dual: to determine which of more rival models is the more adequate and then to estimate the parameters of the chosen model. In the present thesis, study DKL and DT optimality

  ‎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.

  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.

 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.

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 many from life ‎testing and reliability ‎studies, the experimenter may not always obtain complete information on failure times for all experimental units. for Example, individuals in a clinical trial may drop out of the study, may have to be terminated for lack of funds or in an industrial experiment, units may break accidentally. ‎Therefore, one has to remove some units prior to failure for saving time and cost associated with testing. Data obtained from such experiments are called censored. The most common censoring schemes are type I and type II. The Type I and Type II censoring schemes have major deficiency in that they only do not allow removal of units at points other than the terminal point of the experiment. Due to experimenter use a versatile scheme of censoring called progressive.‎This thesis has been focused on the scenario of progressive Type II censoring. A problem associated with this scheme is that the total testing duration might be unacceptably long. To address this issue, a hybrid variant of the ‎progressive ‎‎censoring scheme was proposed in which imposing a time limit T on the test. Although this hybrid ‎progressive ‎‎censoring scheme controls the total testing duration not larger than T, it is possible that the effective sample size is very small or even zero in which usual efficient statistical inference may not be feasible. To strike a balance between the ‎total ‎testing ‎time ‎and ‎the ‎efficiency ‎in ‎statistical ‎inference, ‎Ng ‎et.al ‎(2009)‎ proposed an adaptive Type II progressive censoring scheme.In this thesis influential methods for progressive Type II censoring and adaptive Type II progressive censoring under some statistical distributions are studied. We ‏‎obtain‎ both maximum likelihood estimators, approximate maximum likelihood estimators and observed information matrix for the unknown parameters. We simulated values of the estimates parameters, a comparison of the values variance and covariance of the estimators with those obtained from the corresponding observed information matrix and coverage probabilities for pivotal quantities based estimators. Various interval estimation methods for the unknown parameters such as asymptotic confidence intervals with both observed information matrix and fisher information matrix, percentile bootstrap and bootstrap-t confidence intervals are obtained. Then these methods are compared in terms of their expected lengths and coverage probabilities using simulation.

 Comparing risks play an important role in insurance statistics. One of the ways to compare risks is by using the measures of risk. In actuarial literature, considering tail variabilities of risks which are   low frequency and   high severity losses is vital. While in many cases, comparing based on different risk measures will be followed various results as well as using a risk measure in different cases. Furthermore, we cannot also propose an explicit expressions for risk measure under a special statistical distribution.   Because of these limitations, actuaries should use stochastic orders for ordering risks. Therefore, comparison of random risks with using the   functions of probability   distributions as Tail ,   top Loss,   excess-Mean functions and etc is more helpful than comparing based on some   umerical criteria associated distributions. The comparison of the Random risks with using mentioned functions which usually produce partial orders among probability distributions is called “Stochastic Orders.”In this thesis, firstly, The risk concept, some measures of risk and type of stochastic orders are introduced which allow us to compare variabilites between random variables. Then, the relationships between the excess wealth order and other familiar stochastic variability orders (Dispersive Order, Stop Loss, convex, star and mean-excess) has been studied. In the reminder of this thesis, some characterizations of variability stochastic orders are showed by using the usual and distortion risk measures.

  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

  Indubitable, waiting in queue is not gracious experience for customers. Each models of queuing include many various properties will be as arrival pattern and service that influence on their operation. In this thesis, we survey one of the most important queuing models that is M/M/? model. In this model, arrival rate and service rate of customers will be to form of Poisson distribution and also duration time between arrival and service of customers is Exponential distribution. In this thesis, after saying introduction and elemental concepts, we practise to survey Markovian queuing models. Then, we are introduced perfect concepts of Fuzzy sets and finally, whereas arrival rate and service rate are uncertain, parameters of mentioned model have been surveyed for fuzzy in transient and steady-states and calculate the probability that n customers are in the system, the average system length and the average waiting time of a customer in the system with using of related to them ?-cuts

  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.

  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