پرویز نصیری

Evaluation of production products is a process of necessity to check product quality. One of the criteria for evaluating the quality of the manufactured product is the quality characteristic of the process performance index, which has recently considered a number of researchers in statistical articles. Estimation of process performance index can be done according to the type of statistical distribution of product quality by different methods, including the maximum likelihood method, the least error squared method, the maximum product of distances and quantization. In this article, the estimation of the process performance index is presented using the gamma distribution using method of estimation, moment, maximum likelihood and interval shrinkage estimator. To provide the interval contraction estimator, after proving the unbiasedness of the torque estimators asymptotically, it is shown that the performance index estimator is also unbiased. Next, the efficiency of the estimators is compared using the square error criterion.

As application of compound distributions in the study of longevity data, in this paper the compound distribution of inverse Weibull Geometric is investigated. The presence of parameters of scale, shape and failure rate in this distribution, their study in terms of estimation and hypothesis testing is of particular importance. However, since the phenomenon of censorship is also considered in the study of lifetime data, so the parameters under the type-II of censorship are estimated using the maximum likelihood and Bayesian estimation. In Bayesian estimation, the parameters under different loss functions are estimated based on appropriate prior distributions, then the symmetric confidence interval and HPD are presented by simulation and the estimators are compared using statistical criteria. Finally, the goodness of fit of model is presented by the real data.

The two parameter exponential distribution is particularly important among statistical distributions due to its constant failure rate and has applications in the fields of medicine, biology, clinical trials, public health, engineering, economics, demographics, and life span data, and reliability. Due to the importance of life span data, two parameter exponential distribution with censored data has recently attracted the attention of many researchers, but so far the inference about the location parameter with random censored data in the presence of outlier data has not been discussed. In this article, the location and scale parameters of two parameter exponential distribution under random censoring with the presence of k outliers are estimated by Bayesian and classical methods. Due to the importance of the spatial parameter, when censoring the two parameter exponential distribution with the presence of outlier data, the spatial parameter is considered the same but the scale parameter is different. In the Bayesian estimation of parameters, the is checked using Gibbs sampling under the error squared loss function. We recommend used the Bayesian estimation.The generalized variance is given according to the dimensions of the parameters using the maximum likelihood method.

The Singular Spectrum Analysis (SSA) method is a powerful non-parametric method in the field of time series analysis and has been considered due to its features such as no need to stationarity assumptions or a limit on the number of collected observations. The main purpose of the SSA method is to decompose time series into interpretable components such as trend, oscillating component, and unstructured noise. In recent years, continuous efforts have been made by researchers in various fields of research to improve this method, especially in the field of time series prediction. In this paper, a new method for improving the prediction of singular spectrum analysis using Kalman filter algorithm in structural models is introduced. Then, the performance of this method and some generalized methods of SSA are compared with the basic SSA   using the root mean square error criterion. For this comparison, simulated data from structural models and real data of gas consumption in the UK have been used. The results of this study show that the newly introduced method is more accurate than other methods.

Predicting the quantity and quality of climate change is one of the complex issues that has occupied the minds of climatologists. Now, with the help of access to new technologies and having multiple series of necessary data from climate variables and with the help of knowledge of understanding the relationships between these variables, basic steps in understanding and predicting climate trends have emerged. As now, computer models all respond to climate prediction issues and factors affecting climate change to the best of their ability. Completely accurate predictions with zero error, regardless of the field and subject matter, are very difficult and almost impossible, especially since the prediction process is in a very complex environment and in a dense cloud of uncertainties and actors and drivers. Numerous and effective effects on the environment and the data and information used in forecasting also have vague and gray features . Among climatic elements, temperature and precipitation are of special importance due to their wide effect on other factors and especially the effects they have on human activities. because human systems are dependent on climatic elements. Like agriculture, industries and the like are designed and operate on the basis of climate stability.Time series models are experimental models and a powerful tool for simulating and predicting the behavior of climatic and hydrological systems such as temperature and precipitation. The classical approach in terms of time series modeling depends on the static and non-static time series according to the application of the Jenkins box approach. If such series show long-term memory properties, the prediction value based on the moving average self-regression (ARMA) and stacked moving average (ARIMA) models will not be valid. If there is long-term memory in time series, there will be a significant correlation between series observations at very long distances, apart and far from each other, which indicates that observations are not independent of each other, there is a correlation between them and past observations. They will help to predict the data. With these descriptions, the existence of long-term memory in atmospheric parameters weakly violates market efficiency, and then changes in the capital market will not be accidental and will be predictable. In the early 1980s, Granger and Jokes proposed an alternative approach to long-term memory modeling by creating their own model of partial stack moving average (ARFIMA), since the ARFIMA model between the short-term memory process and the long-term memory process in series. When differentiated, it creates a distinct advantage over classical S / R analysis, which has a very high tendency to accept the assumption of zero long-term memory despite the short-term memory process .The data required in this article include the average monthly temperature and precipitation in the last half century (1969-2018), which was prepared by the Meteorological Organization. In time series data analysis, time series models including ARFIMA model have been used for modeling and simulation of the mentioned parameters.Changes in temperature and precipitation time series are among the most important climatic parameters in studying hydrological, agricultural, environmental, health, industrial, and economic processes. Assessing and forecasting temperature and precipitation will be of great help to managers and planners of agriculture and water resources. One way to examine time-series data is to use statistical models. Due to the importance of the subject, in this article, the amount of temperature and monthly rainfall in the last half-century (1969-2018) of Tabriz Synoptic Meteorological Station is examined using the ARFIMA model, and to fit the model, R / S and GPH models have been used. To investigate the statics of the model, autocorrelation (ADF), partial autocorrelation (PACF) functions, and differentiation methods have been used. However, since the synoptic meteorological station data is evaluated for the first time, the evaluation is based on the ARFIMA model, the Bayesian Information Criteria (BIC), root-mean-square error (RMSE), and the Akaike information criterion (AIC). The results of R/S and GPH tests show that the model with long-term memory of Tabriz temperature and precipitation time series is approved at a 95% level. The only difference is that in the case of precipitation, this act seems fragile. In addition, the analysis of different structures showed that the temperature and precipitation data have the best fit or performance using the ARFIMA (3,0.2,1) and the ARFIMA (1,0.0004,4), respectively. It should be noted that the RMSE value of the fitting models between the observed values and the simulation of temperature and precipitation was equal to 2.2 and 38.4, respectively, indicating the appropriate accuracy of the model and its applicability for forecasting.

This paper presents the inverse Weibull-Poisson distribution to fit censored lifetime data. The parameters of scale, shape and failure rate are considered in terms of estimation and hypothesis testing, so the parameters are estimated under the type-II of censorship using the maximum likelihood and Bayesian methods. In Bayesian analysis, the parameters are estimated under different loss functions. The simulation section presents the symmetric confidence interval and HPD, and the estimators are compared using statistical criteria. Finally, the model's goodness of fit is evaluated using an actual data set.

 The reliability System plays an important role in the reliability of power play models. Reliability System in Stress-Strengths models is a measure of component reliability. This model was first introduced by Birnbaum in 1956. As we know, the Lindley distribution is widely used in reliability theory and many researchers are used this distribution to calculate Stress-Strengths. In 2013 Al Mutairi and Kundu work out on stress-strength reliability for Lindley distribution. In 2017 Rezaei, et al. estimate the stress-strength parameter R=P(Y<X), when the variables X and Y are from General Lindley distribution. There are different methods to estimate R=P(Y<X) such as maximum likelihood, method of moments, Bayesian, and shrinkage estimation. Recently, many researchers consider the interval shrinkage estimation to estimate parameters of statistical distribution. Here, for the first time, we estimate the R=P(X<Y) by using the interval shrinkage estimation in two parameter Lindley distribution. Ghitany et al. in 2008 showed that the behavior of this distribution in data analysis of life data and reliability is better than the exponential distribution. So, we estimate the parameters of Lindley and R=P(X<Y) by using the interval shrinkage and method of moments estimation. In 2013 Shanker, et al. considers two parameter Lindley distribution for modeling waiting and survival time data. [ Downloaded from mmr.khu.ac.ir on 2022-10-03 ] .

Material and methods:

 In statistical inference, choosing the methods of estimation is very essential in the process of it. The interval shrinkage and method of moments estimation for Lindley distribution is obtained. For interval shrinkage estimation, we consider as an interval for parameter.

Results and discussion:

 To compare the estimators, samples with different sizes and values of parameters are generated from two parameter Lindley distribution by applying R software. Consequently, comparison of the estimators, the estimation of parameters and mean square errors of them are accomplished.

Conclusion:

 Simulation and real data methods are used to compare the method of moments and interval shrinkage estimation for estimating parameters of two parameter Lindley distribution. The results show that the interval shrinkage estimator is better than the method of moment estimator. Material and methods In statistical inference, choosing the methods of estimation is very essential in the process of it. The interval shrinkage and method of moments estimation for Lindley distribution is obtained. For interval shrinkage estimation, we consider as an interval for parameter. Results and discussion To compare the estimators, samples with different sizes and values of parameters are generated from two parameter Lindley distribution by applying R software. Consequently, comparison of the estimators, the estimation of parameters and mean square errors of them are accomplished. Conclusion Simulation and real data methods are used to compare the method of moments and interval shrinkage estimation for estimating parameters of two parameter Lindley distribution. The results show that the interval shrinkage estimator is better than the method of moment estimator.

The empirical Bayes estimation of the exponential distribution parameter under squared error and LINEX loss functions is investigated when the record collects the data ranked set sampling scheme method. Then, point and interval predictions for future record values are studied. The results of this sampling scheme are compared with the products of the inverse sampling scheme. To compare the accuracy of estimators, Bayes risk and posterior risk criteria are used. These point predictors are compared in the sense of their mean squared prediction errors. To evaluate the prediction intervals for both the sampling schemes, the average interval length and coverage probability are computed and compared. In the present study, the hyperparameters are estimated in two methods. By studying the simulation and presenting real data, the estimation methods are compared, and the performance of the introduced schemes is evaluated.

In the analysis of Bernoulli's variables, an investigation of the their dependence is of the prime importance. In this paper, the distribution of the Markov logarithmic series is introduced by the execution of the first-order dependence among Bernoulli variables. In order to estimate the parameters of this distribution, maximum likelihood, moment, Bayesian and also a new method which called the expected Bayesian method (E-Bayesian) are employed. In continuation, using a simulation study, it is shown that the expected Bayesian estimator out performed over the other estimators.

Length of stay in hospital is one of the effective factors in determining the cost of hospitalized patients and one of the high-cost departments is the pediatric intensive care unit (PICU). Knowing how long patients stay in hospital beds can be effective. The purpose of this study was to provide the most appropriate statistical distribution of patients 'stay in PICU wards to predict patients' hospital stay.

In this paper, in addition to investigating the diagnoses presented to patients admitted to the PICU ward, it has been attempted to use the best statistical models in survival studies such as the inverse Weibull distribution family or its combinations to determine the best statistical model for pediatric hospitalization. To determine the pediatric intensive care unit of three hospitals in Mashhad in 2018 based on these
distributions, the first, second and third quartiles of survival time are identified and the best statistical distribution is determined for patients' residence time. R statistical software version 3.5.2 was also used for data analysis and statistical modeling of the population. Finally, maximum likelihood, Akaike Information Criteria (AIC) and Bayesian Information Criteria (BIC) were used to identify the appropriate model.

Based on the data from these three hospitals, several statistical distributions suitable for survival data were fitted to patients' survival times in the PICU wards studied, and the distribution parameters along with intermediate indices and first and third quartiles were reported. After fitting the composite statistical Weibull and Generalized Reverse Weibull statistical distributions to the length of hospital stay in the PICU ward, the best distribution was the logistic regression Weibull series distribution with the highest likelihood.

Generalized inverse Weibull logarithmic series and Inverse Weibull Geometric distribution had a good fit for patients’ bed time in PICU department of reviewed hospitals.

The non-homogeneous bivariate compound Poisson process with short term periodic intensity function is used for modeling the events with seasonal patterns or periodic trends. In this paper, this process is carefully introduced. In order to characterize the dependence structure between jumps, the Levy copula function is provided. For estimating the parameters of the model, the inference for margins method is used. As an application, this model is fitted to an automobile insurance dataset with inference for margins method and its accuracy is compared with the full maximum likelihood method. By using the goodness of fit test, it is confirmed that this model is appropriate for describing the data.

In some situations, considering a suitable sampling scheme, to reduce the cost and increase efficiency is crucial. In this study, based on a record ranked set sampling scheme, the likelihood and Bayesian prediction of upper record values from a future sequence are discussed in the exponential model. To this end, under an upper record ranked set sample (RRSS) as an informative sample, the maximum likelihood as well as the Bayes point predictors for future upper record values under squared error (SE) and linear-exponential (LINEX) loss functions are obtained. Furthermore, based on a RRSS scheme, two Bayesian prediction intervals are presented. Prediction intervals are compared in terms of coverage probability and expected length. The results of the RRSS scheme are compared with the one based on ordinary records. Finally, a real data set concerning the daily heat degree is used to evaluate the theoretical results obtained. The results show that، in most of the situations, the RRSS scheme performs better.

Estimation of statistical distribution parameter is one of the important subject of statistical inference. Due to the applications of Lomax distribution in business, economy, statistical science, queue theory, internet traffic modeling and so on, in this paper, the parameters of Lomax distribution under type II censored samples using maximum likelihood and Bayesian methods are estimated. Whereas, selection of prior distribution and loss function plays an important role in Bayesian estimation, therefore the Bayesian estimations are presented by appropriate prior distribution under loss functions, mean square error, Linex and entropy. Whereas the normal equation obtained from estimation methods are not distinct function of parameters, they are estimated using error methods such as EM algorithm and Lindley approximation. At the end, using mean square error criteria, the estimators are compared and the result shows that the Bayesian estimator is better than the maximum likelihood estimator and the accuracy of estimator improves by increasing the sample number while the number of failure is fixed.

Historically, various methods were suggested for the estimation of Bernoulli and Binomial distributions parameter. One of the suggested methods is the Bayesian method, which is based on employing prior distribution. Their sound selection on parameter space play a crucial role in reducing posterior Bayesian estimator error. At times, large scale of the parametric changes on parameter space brings about an increase in error rate and enlargement of the comparison criteria .therefore, determining appropriate prior distribution on parameter space plays a key part in reducing comparison criteria. Accordingly, in this paper appropriately modified prior distribution was considered for Binomial distribution parameter and then, while extending certain conditions on prior distribution hyperparameters, an effective estimate under the title Expected Bayesian Estimate (AKA E-Bayes) would be proposed. At last, to evaluate the measurement methodologies utilized in this paper, under MSE criteria , extensive simulation studies were conducted, and the results were analyzed and above mentioned methods will be applied in a real example.

This article intends to study the phenomenon of diglossia in the formal and informal domain and also the study of age, gender, level of education and job on the application of the two languages of Persian and Turkish in Ardabil city. The research is a descriptive-survey from the viewpoint of methodology. 400 research statistical sample people were selected out of the statistical population (Ardabil city population) in form of stage sampling and based on Morgan Table .For data collection, the research questionnaire of Parasher used and for the analysis of findings, the paired samples T test and one way ANOWA were employed. The comparison of the application of Persian and Turkish in Ardabil city showed that the youth as compared with the aged, the women as compared with men, the holders of higher education as compared with those with lower higher education and the educational and administrative domains as compared with other domains have had a greater use of the Persian language accordingly.
1- Sociolinguists are interested in studying to see how the members of each society are able to display their own identity through language and how they show a suitable response vis-à-vis delicate differences of lingual applications related to social, economic, political, religious and cultural variables of the society (Spolsky, 2008). Due to the different diversity among the humans in the society, language becomes a function of these diversities with specific social species. These factors include: education, job, profession domain, age, gender, social class, register, style and media (Zandi, 2014:7-8).
Social multilingualism is a prevailing phenomenon and in the world scale, it is considered an ordinary position rather than exceptional one. In fact, in most of the countries in the world, there is more than one indigenous language is prevailing and rarely, we can find a single language country and the number of multilingual countries are much more (Trudgill, 1984).
2- Theoretical Framework: Sociolinguists have evaluated the phenomenon of lingual encounter in different societies. One of the most important subjects under discussion in this research is also the issue of lingual encounter. The phenomenon of lingual encounter leads to the formation of cases such as bilingualism, multilingualism and Diglossia in human societies. In the classic viewpoint taken from Fergusson (1959:233), diglossia phenomenon is a specific type of standard building which the two varieties of a language live together beside each other and throughout the society and each undertakes a certain role. These two varieties are called low and high varieties. One of the most important features of diglossia is the specialization of the low and high role of the standard. High varieties are used in formal textures and low varieties are used in informal textures.
Fesold (1984:40-52) also terms diglossia as jumping from one style to another style. In his view, diglossia is the feature of the societies rather than individuals. Individuals might be bilingual but societies are diglossia. In other words, the term diglossia, describes the social or formalized social bilingualism.
However, Nersesians (1995:73-80) classifies diglossia in contemporary Iran into three groups: The first group is the concurrent presence of literary Persian with verbal Persian. In her view, the second group is the most obvious and old sample of diglossia in Iran. In the article of Ferguson (1972), it has been stated as an example that in fact, there is concurrent presence of standard Persian with a local variety in the lingual set of individuals. Many Iranian still in their daily talks with their family members speak in local dialects whereas the same individuals in their own conversations with other individuals in the alleys and streets, working place etc., use the standard Persian (literary or verbal). Pursuing the expanded view of Fishman (1967:29),Nersesians believes in the presence of the diglossia phenomenon as the third type too and that is the concurrent presence of Persian language with other ethnic languages. In Iran, in addition to the Persian speaking population, there are other ethnic groups who speak their ethnic languages in their local conversations. As a result of increase of communications and conversation of Persian language into the common language of different tribes, these types of individuals are bilingual or multilingual. From the viewpoint of the situation of bilingualism, most of these efforts have passed the incomplete bilingualism and single literacy bilingualism stages and in particular have reached to the full bilingualism of the new generation. However, the bilingualism of these people even more than the condition of concurrent presence of standard Persian with a variety or a local language, has found the diglossia aspect, whereas mother tongue is used in domains such as house, friendly conversations with individuals belonging to their own lingual and tribal groups. Persian language is also employed in domains such as administrative and educational positions. In this article, we will deal with the study of the phenomenon of diglossia from the third type which was introduced in Nersesians theory.
In addition to placing the expanded theory of diglossia of Fishman to regulate a part of research data, his domain analysis has also been used. Fishman (1967) is the first person who presented the term of the domain of languages application and then Fesold(1984:183) expanded this concept and introduced the domains of language application including family, neighborhood, friendship, business, school, working environment, public affairs and religious affairs. In this research, using the Fesold viewpoint, the phenomenon of diglossia will be studied in two domains of informal (family, friendship and neighborhood) and formal domain (administrative, business and education) with the inclusion of the impact factors of age, gender, level of education and job on the application of the two languages of Persian and Turkish in Ardabil city.
3- Research The research is applied from the viewpoint of objective and survey as far as method is concerned. 400 research statistical sample has been selected out of the statistical population (Ardabil population) based on Morgan Table.
The most basic instrument used in this research was questionnaire. The questionnaire has been selected based on the questionnaire of research model of Parasher(1980) and of course with some amendments in it. In order to analyze the data and testing the hypotheses, also paired-samples T test and One-way ANOWA test have been employed in the research.
4- Conclusion and In summary, the results of hypotheses test showed the followings:• In Ardabil, in formal positions and in encountering with Persian speaking people, the Persian language and in the informal positions and in encountering with Turkish speaking people, the Turkish language is used accordingly.
• In comparing the age groups, the younger individuals use Persian more than other groups.
• In Ardabil city, children use Persian language more than other groups.
• In comparison of gender groups, girls use Persian language more than boys.
• In a comparison on rate of education, the literate people use Persian language more than illiterate people.
• In the comparison of job groups, people with a greater educational jobs use Persian more than other job groups.
The comparison of the application of Persian language and Turkish language in six social domains, family, friendship, neighborhood, business, educational and administrative affairs in Ardabil city showed the followings: - There is a significant difference between the application of Persian language and Turkish language in the respondents in each of the social domains.
- In the domain of the family (informal position), the application of Persian language (formal language) is less and vice versa, the application of the Turkish language (mother lounge) was more than other social domains.
- In the educational domain (formal position), the application of Persian language was more and vice versa, the application of Turkish language was less than other social domains. However, the dominant language in all other social domains of Turkish language was observed. The result is in agreement with the research findings of Fishman and Cooper(1971), Parasher (1980), Fereidouni (1998), Sanaei Moghadam(1998) and Imani (2004).
Comparing the averages of the application of two languages of Persian and Turkish by the examinees of Ardabil city in eight academic groups, it is concluded that Turkish is used by illiterate individuals greater and the least application of this language belongs to the level of primary school and associate in art/science degree programs. The greatest application of the Persian language belongs to the individuals with the education at the level of guidance schools. The results obtained in the part 4 and 5 ( impact of educational level on language application) is in agreement with the research findings of David (2003), Fereidouni (1998), Sanaei Moghadam (1999), Bashirnejad (2000) and Mashayekh(2004).
The comparison of the averages obtained from the rate of application of the two languages by the respondents in Ardabil city on two gender group showed that Turkish is used greater by the men. As for the Persian language, also the application of this language has been reported to be greater among women as compared with men. The results obtained (the impact of gender on language application) is in agreement with the results of the research by Bashir Nejad (2000) and Imani (2004).

Modeling is one of the most basic methods to explain the statistical variables that by using it we can realize the response variable distribution. Mixture distribution can improve the goodness of fit largely, so, the aim of this study was to introduce the mixture of logarithmic series distribution and modeling of effects of nutrition on complications in diabetic patients by it. This study examined appropriate model fitted related to diabetic patient's data after introducing the mixture of logarithmic series distribution. 32 variables have been considered which related to type and consumption instruction of food as independent variables and complication as dependent variable. The results showed that according to chi-square value of Mixture logarithmic series distribution, fitted model with a mixing ratio of 1/32 to all independent variables are reasonable model.Discussion & given that data of diabetic patient's complications have no zero density and also comparing χ^2 statistic from mixture of logarithmic series distribution combined and mixed Poisson distribution, we find that mixed logarithmic series distribution model gives a better fit to data.

Introduction & Zinc is an essential element for the immune system. This element has different effects on immune system activity. On the other hand, different serum Zn levels also alter normal B-cell line and T-cell line functions. The present study was carried out to assess B cell line and T cell line tolerance to low concentration Zinc Chloride In vitro study. This experimental study was conducted at the Payame Noor University of Tehran in 2010. The B- cell line and T-cell line were exposed to 1, 5, 10, 20, 30, 40, 50, 75, 100,125, 150,175 and 200 μm (λ) of Zinc Chloride followed by incubation at 12, 24, 36, 48, 60 and 72 hrs. Viability of B- cell line (Raji) and T-cell line (molt-4) were evaluated with hemocytometer method and percentage of living cells have been considered as cellular tolerance index to cytotoxic effects of Zinc chloride. The results were analyzed by SPSS software, version 18 using T-test and Kruskal-Wallis test. In this study, the results showed Zinc chloride concentrations up to 40 μm (λ) at different incubation time points (12-72 hrs) had no effects on B cell line and T cell line viability (p> 0.05) With 50-200 μm (λ) concentrations, Zinc at different incubation time points (12-72 hrs) tolerance B cell and T cell line decreased and viability decreased significantly when compared with the control group and test groups up to 40 μm (λ) concentration (p< 0.05). All groups at different after incubation time, Zinc concentrations (50-200 μm) B cell and T cell line tolerance decreased significantly when compared with Zinc chloride concentrations up to 40 μm (λ) (p< 0.05). Zinc is necessary for the normal function of the immune system. A variety of in vitro effects of zinc on B cell line and T cell line depend on the zinc concentration. High dosages of zinc evoke negative effects on B cell line and T cell line. An excess of zinc can inhibit B- cell line and T-cell line function.

What was once identified as communications in military organizations is called ICT in the light of increasing developments of modern technologies in military fields. ICT is as significant in military industry as nervous system in human body. Then it is now feasible at senior managerial level; commanding level, to act decisively so that the most lucrative information (data analyzed in the organization by computerized data analysis systems) can be handled as communicatively as possible in the light of speed, accuracy and security and thereby all available resources can be handled with the highest flexibility. Given the slow trend of development of command and control system (C4I), this article is an attempt to run an analogical survey in the developed countries in order to identify, explore and approve statistically suggested axes and scales as to the system development. It makes both planning for executive measures struggling the challenges and apply the system in strategic planning for the vision document of the organization as to C4I.

Bayesian analysis starts with selection of a prior distribution which represents our prior knowledge about the parameter. A proper distribution on the parameter space is selected and based on this distribution posterior distribution is approximately estimated. In this paper, we will draw large samples from our prior distribution using computers. The prior sample and the likelihood function can then be utilized to generate another sample which can be considered as a sample from the posterior distribution. Gibbs sampler is another computer procedure to provide complete posterior analysis in a variety of situations. Here we briefly review this approximate methods and illustrate them by some examples.