In recent years, fuzzy regression has emerged as a powerful tool for modeling relationships between independent and dependent variables under uncertainty. In classical linear regression, significant variations in data can reduce the accuracy and reliability of results. Therefore, optimal design for fuzzy regression models is of great importance. In this regard, this study examines and develops the D-optimal method for fuzzy regression models to improve the accuracy, efficiency, and parameter estimation. The fuzzy regression scheme is chosen from optimal design points. The proposed method is examined in the context of models with three classical techniques, and the results show that the suggested approach can expand the applications of fuzzy regression models under complex conditions with data containing significant uncertainty.

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 In many challenges related to Bayesian inference, we face with some models that have certain complexities and it is necessary to calculate the likelihood function, which is difficult or impossible to calculate. This complexity makes it impossible to get the posterior distribution which is the basis of Bayesian inferences; so, as a solution, simulation methods can be used to estimate the model. One of the methods used in this field is the Approximate Bayesian Computation via >Key­words: Approximate­BayesianComputation, Kullback- Leibler (K-L) divergence, Bayesian inference,likelihood function, summary statistics,      

   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.

One of the topics of interest in statistics is the time of occurrence of a particular event. Therefore, a sub-field called survival analysis has been created in statistics. In general, survival analysis is a set of statistical methods for analyzing data in which the outcome variable is the time until the occurrence of a specific event. In survival analysis, time variable usually is called survival time. Because this variable determines how long a person "survived" during the follow-up period. Also, because usually in this type of analysis, the desired events are death, illness or other individual experiences, desired event usually called failure. However, failure does not necessarily have a negative meaning, for example, it can be the time until the birth of the first child after marriage (as the moment of starting the study). Many survival analyses are faced with a fundamental problem called censoring. Censoring occurs when we have partial survival time information but do not know the exact survival time.\\\\ With the expansion of science and the progress of various data analysis methods, survival data analysis methods are also progressing, and the application of this science in medical data and other fields is increasing.\\\\ One of the common statistical methods for analyzing survival data is Cox proportional hazard regression, this model does not have the optimal performance when we are faced with the problem of high dimensions, an alternative method that is introduced in this thesis is the use of support vector machine, which is one of the techniques in machine learning and it can work well with high-dimensional problems, and it also does not need to hold the usual regression assumptions that we have in classical statistics.\\\\ The original version of the support vector machine does not have the ability to deal with survival data due to the presence of censors. A naive idea is to exclude the censored samples from the study, as a large amount of information will be lost. In this thesis, by making changes on the constraints of the support vector machine optimization problem, we arrive at a version of this method that is suitable for the analysis of survival data and uses the information of censors.This version is called survival support vector machine. Finally, for a case study, we will use the survival support vector machine method to analyze it and compare it with classical methods in statistics such as Cox proportional hazards regression.  

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.

  Regression in Statistics means returning to an average or a verage value, Statisticians have always examined the relation ship between Variables, One of the most common models that fit data, Are regression models. Regression analysis is a Statistical method for analyzing and modeling multivariate data. Aspecial type of regression model is the high dimensional regression model in Which the Volume of Variables independent of the sample size is greater, that is, when is p > n, in these models, because the matrix X is not, complete column rank, therefore estimating the least squares ?ˆOLS is not obtained uniquely and estimating the parameters will not be a good predictor. for this reason, in recent years, methods called penalty regression or contraction methods have been used. such as ridge, lasso, group lasso and elastic net, that in this thesis, the lasso convex function is used. lasso is defind as the L1 norm of the parameters, that ? is the vector of regression coefficients and ? is the penalizing parameter. larger value of ? exerts higher penalty on regression coefficients, resulting in the inclusion of fewer variables in the model. and conversely commonly, a sequence of ? value are generated, and then variables are detected for each value of the series. Thereafter, a value of ? is chosen by k-fold cross-validation, and corresponding set of predictors are included in the model. also for simulation results in this Thesis, InfTh and BIC have been used, and we discuss all these issues in R software. Keywords Weibull regression, Penalty methods, Shrinkage methods, Lasso, Criteria of information theory, Bayesian information criteria

Optimal designs have an important role in many applied areas such as medical, engineering, pharmaceutical and marketing studies. Using such as categories of designs designs can considerably reduce the cost of experiment. Finding an optimal design requires pre-specifying a criterion which needs to be optimized. For samples, these criteriaare chosen as functions of Fisher information matrix. The most popular criterion is D-optimal criterion which is determinant of Fisher information matrix. In a nonlinear model, dependency of this matrix onunknown parameters in an optimal design problem. A number of approaches such as Bayesian, Locally and Minimax optimal designs are suggested in order to solve dependency on the parameters.\\\\In this thesis we study the effect of the choice of different a priori distributions, such as the Uniform, Gamma and Lognormal distributions in obtaining the D-optimal designs for a non-linear model, when the errors present different correlation structures. we study the effect of the choice of different a priori distributions, such as the Uniform, Gamma and Lognormal distributions in obtaining the D-optimal designs for a non-linear model, when the errors present different correlation structures. In order to calculate these designs the Monte Carlo method is used and a general methodology is proposed that allows to find D-optimal designs for any type of non-linear model in the presence of correlated observations, later the designs found are compared by calculating the efficiencies taking as a reference design the one obtained with the a priori Uniform distribution, evidencing that depending on the selected correlation structure there is an a priori effect and finally through the information criteria AIC and BIC the best correlation structure is selected among the structures chosen for then make a simulation study with the purpose of checking and verifying from the point of view of the proposed statisticians.

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.  

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.   

  reast cancer is one of the most common cancers in women today. Although men also get this cancer, the risk is more serious in women. Sometimes a misdiagnosis of cancer can lead to the death of a human being, and this should be considered a serious risk. Breast cancer tumors have two types, malignant and benign. Identifying the right type of these tumors will prevent unnecessary treatments and reduce mortality.The aim of this dissertation is to compare five methods of classification, naive Bayes, support vector machine, artificial neural network, logistic regression and random forest on breast cancer data to diagnose benign and malignant cancer tumors to determine the best method according to evaluation criteria. Choose binary, accuracy, precision, sensitivity, specificity, F1 score and Matthews correlation coefficient. The main criterion is to compare the accuracy of the model, then other criteria will be considered.

Diagonal quasi-Newton method 

   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.

  In this thesis, we develop simple, yet efficient, procedures for sampling approximations of the two-Parameter Poisson-Dirichlet Process and the normalized inverse- Gaussian process. We compare the efficiency of the new approximations to the corresponding stick-breaking approximations of the two-parameter Poisson-Dirichlet Process and the normalized inverse-Gaussian process, in which we demonstrate a substantial improvement.

Estimation of the survival function by using the copula for the inverse Rayleigh distribution.

گاهي اوقات ممكن است نمونه اي كه مشاهده مي كنيم نمونه اي اريب از جامعه باشد. به اين معنا كه تمام اعضا از شانس برابري براي انتخاب شدن در نمونه برخوردار نيستند. براي حل اين مشكل از نسخه اريب-طول كه نسخه ي وزني شده از متغير تصادفي اصلي جامعه است، استفاده مي شود. در نمونه گيري اريب-طول شانس حذف شدن هر واحد از نمونه نااريب، متناسب با طول عمر آن واحد مي باشد. حال آن كه در برخي حالات ممكن است شانس حذف شدن متناسب با طول عمر واحد تحت مطالعه نباشد، از اين رو براي حل اين مشكل مي توان از توزيع هاي وزني استفاده كرد. در اين پايان نامه توزيع اصلي جامعه را گسسته در نظر گرفتيم و سپس با استفاده از تابع ميانگين مانده عمر، توزيع پواسون بريده شده وزني شده و توزيع پواسون آماسيده در صفر بريده شده وزني شده را معرفي كرديم و ويژگي هاي آن ها را مورد بررسي قرار داديم، همچنين نشان داديم مشاهداتي كه ميانگين مانده عمر بزرگ تري دارند شانس بيشتري براي انتخاب شدن در نمونه را دارند. توزيع هاي وزني شده داراي كاربردهاي فراواني در مبحث تحليل بقا و قابليت اعتماد مي باشند، به همين دليل علاوه بر روش شبيه سازي، برخي موارد كاربرد آن با استفاده از داده هاي واقعي نيز تشريح شده است. 

   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

  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.

In this thesis, we give a new distribution of a new >- F(HCF) distribution. Since the Burr distribution of the most special case of this family is theHyperbolic Cosine New Burr distribution. We also discuss simulation method , also maximumlikelihood minimum spaccing estimators of the parameters of the distribution . The new distributioncan be use effectively in the analysis of survival data .Show that the distribution of (HCB)Compared to distributions New Burr (NB), Weibull distribution (W), Log normal(LN) is flexibieto fit the data.  

در اين پايان ­نامه، كاربرد مدل­ هايبيز ناپارامتري در وظايف پردازش زبان طبيعي مورد مطالعه قرار داده شده­ اند. ابتدا روش ­هايبيز ناپارامتري براساس رايج ­ترين توزيع پيشين يعني فرايند ديريكله مورد مطالعهقرار گرفته­ اند. سپس نمايش­ هاي متفاوت از فرايند ديريكله مانند طرح كيسه پوليا،فرايند رستوران چيني و ساختار استيك بريكينگ معرفي شده ­اند. در ادامه به معرفي دو فرايند توليد شده توسط فرايند­هاي ديريكلهيعني فرايند­هايديريكله­ سلسله مراتبي و فرايند­هاي پيتمن يور پرداخته شده است. در پايان 4 راه­ حلپيشنهادي بيز ناپارامتري در وظايف پردازش زبان طبيعي از جمله تقسيم­ بندي كلمه،استخراج عبارت و صف­ بندي، تجزيه­ مستقل از متن و مدل­سازي زبان ارائه شده ­اند.

  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.

  چكيدهپديده انتظار كشيدن در صف با افزايش تراكم جمعيت و شهري شدن جامعه ، بيش از پيش گسترش يافته است هدف از اين پايان نامه،پيش بيني زمان انتظار هر مشتري در مدل صف M/M/S   است .در اين سيستم، تصميم گيرنده گان قصد دارند نتايج مفيدي را با ارائه دانش كافي در مورد سيستم صف بدست آورند.در اين پايان نامه براي مدلسازي صف M/M/S فرآيند زاد و مرگ ماركوفي را در نظر مي گيريم، نرخ   ورود ? و داراي توزيع پواسون و فاصله زماني بين دو ورود متوالي داراي توزيع نمايي و همچنين نرخ سرويس ? و داراي توزيع نمايي است .ما يكي از بانك هاي شهر كرمانشاه (بانك ملي) را انتخاب كرده تا عملكرد رفتار بانك با چند سرويس دهنده (باجه ) را مورد ارزيابي قرار دهيم . داده هاي مربوط به ورود و زمان سرويس هر مشتري در طول يك روز كاري بانك ( 6:30 صبح لغايت 12:30 بعد از ظهر ) يادداشت شده ، سپس پارامترهاي مدل صف M/M/S با محاسبات رياضي و نرم افزاري بدست آمد و با يكديگر مقايسه شدند و سپس تأييد مي شوند كه از دو روش نتايج بدست آمده برابرند.در پايان نيز به كمك شبيه سازي(فصل چهارم)پارامترهايي كه از مدل واقعي بدست آمده اند،برآورد مي شوند و مورد مقايسه قرار مي گيرند و نتايج حاصل به بانك داده شده و با ارائه راهكار مناسب به كاهش طول صف و زمان انتظار مشتريان در صف و سيستم مي پردازيم.كليد واژه ها : تئوري صف بندي در مدل M/M/S ، بانك ملي ايران ، توزيع احتمال ، شبيه سازي  

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.

  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

  When determining the locating of the units with the largest number of variables studied (Hot spots), determining the most efficient  sampling method is important. Some ofthe methods employed in spatial communities are systematic sampling, stratifiedsampling method, and adaptive sampling method. In this thesis, theeffectiveness of various sampling methods including simple random sampling, systematicsampling, stratified sampling and cluster adaptive sampling for locating Hot spots have been studied.  

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

 for analyises emax model can that baysian D-optimal desition for E-max model

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.

  A special category of nonparametric inference includes types of hypothesis tests in the commu-nity under study. The basis of the methods of testing the classical nonparametric hypothesisis that the data, the hypotheses and the method of obtaining the test are crisp and Withoutimprecise . But in practice and in the real world, there are many situations that the exact andconsistency of the above are unrealistic. In these cases, the methods of testing the statisticalhypothesis in the classical state of efficiency and credibility are not necessary. The theory offuzzy sets is the perfect way to formulate and analyze issues in these fuzzy states. In generalnon-parametric tests can be carried out in the following three phases

Estimation reliability in some distributions with fuzzy parameter

Optimal ‎designs ‎as a‎ ‎tool, ‎which ‎help ‎researchers ‎to ‎predict ‎more ‎accurate ‎results, ‎has ‎been ‎commonly ‎considered ‎for ‎along ‎time. ‎Most ‎of ‎these ‎researches ‎are ‎based ‎on ‎the ‎Linear ‎models ‎with ‎normal ‎distribution ‎for ‎response ‎variable. ‎Another ‎assumption ‎which ‎has ‎been ‎considered ‎in ‎the ‎regular literatures, ‎is ‎the ‎independency ‎on ‎predictor ‎variables. ‎In ‎the ‎present ‎thesis, ‎we ‎study ‎Poisson ‎regression ‎model ‎as a‎ ‎special ‎case ‎of ‎generalized ‎linear ‎models. ‎Also ‎we ‎consider ‎some ‎cases ‎with ‎dependent‎ ‎predictor ‎variables. ‎‏‎$‎‎‎A-‎$‎optimal ‎designs ‎obtain ‎for ‎Poisson ‎regression ‎model ‎and ‎Poisson ‎ridge ‎regression ‎model. ‎We ‎also ‎calculate ‎ridge ‎parameter ‎based ‎on a‎ ‎new ‎method. ‎The ‎new ‎method ‎to ‎find ‎the ‎new ‎ridge ‎parameter, ‎compare ‎to ‎the ‎some ‎previous ‎methods.

  In this thesis we consier tree concepts of orthogonlity in a Hilbert C?-module V over a C?-algebra A : the Birkhof-James orthogonality ?B , the strong Birkhof-ames orthogonlity ?SB , and the orthogonality with respect to the A-valued inner product on V . We characterize the classes of Hilbert C?-modules in which any two of them coincide .

  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.

  امنيت يكي از اركان موجودات زنده و احساس امنيت يكي از اساسيترين نيازهاي نوع بشر است. امروزه با گستري وسايل ارتباطي و حجم اطلاعات مبادله شده در شبكههاي رايانهاي و همچنين توسعه و پيشرفتهاي صنعت مخابرات ند رسانه اي، مفهوم مخابرات تصويري متحول شده است. امنيت رسانه هاي ديجيتال يكي از مسائل مهم و مطرا جامعه رمزنگاري در دنياي امروز است. با توجه به كاربرد روزافزون رايانه و گستري زيرساخت هاي ارتباطي مثل شبكههاي سيار و اينترنت، حفظ محرمانگي و تاييد صحت تصاوير روز به روز اهميت بيشتري مييابد. با توجه به كاربرد روزافزون اينترنت و افزايش حجم اطلاعات مبادله شده، حفظ امنيت و تاييد صحت مخابره شده كه ميتواند كاربردهايي در امور تجاري، نظامي و حتي پزشكي داشته باشند نيز روز به روز اهميت بيشتري ميابد. در جهان ديجيتال امروزي امنيت تصاوير ديجيتال بيش از پيش اهميت پيدا كرده است. در سالهاي اخير سرعت زيادي در رشد انتقال تصاوير ديجيتال از طريق كامپيوتر بويژه اينترنت صورت گرفته است.به عنوان مثال ما در اين پاياننامه از يك روي رمزنگاري تصوير صحبت ميكنيم كه در امور پزشكي كه مرتبط با عكسبرداري از بيماران ميباشد و همچنين صحت و امنيت اطلاعات بيمار از اهميّت بالايي برخوردار است، استفاده ميشود. اين روي از رمزنگاري مبتني بر ميدان گالواست و ما آن را به طور كامل پيادهسازي كرده و علاوه بر بيان نقاط ضعف آن، راهي براي بهبود كارايي اين روي را بيان ميكنيم

  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