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This paper is devoted to computing the sample size of binomial distribution with Bayesian approach. The quadratic loss function is considered and three criterions are applied to obtain p-tolerance regions with the lowest posterior loss. These criterions are: average length, average coverage and worst outcome.

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In this paper, based on the progressive type II right censored data, we consider estimates of MLE and AMLE of scale and shape parameters of weibull distribution. Also a new type of parameter estimation, named inverse estimation, is introdued for both shape and scale parameters of weibull distribution which is used from order statistics properties in it. We use simulations and study the biases and MSE 's of these three estimation procedures and then compare them with each other. At the end, two numerical examples are used to illustrate the proposed procedures.

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Implementing unequal probability sampling, without replacement, is very complex and several methods have been suggested for its performance, including : Midseno design and systematic design. One of the methods that have been introduced by Devil and Tille (1998) is the splitting design that leads to simple random sampling .in this paper by completely explaining the design, with an example, we have shown, the method to calcculate probability for each possible samples, using R software. it`s good to know that we can implement this design using the program in different communities after defining the ideal probability inclusion.

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In many experiments about lifetime examination, we will faced on restrictions of time and sample size, which this factors cause that the researcher can’t access to all of data. Therefore, it is valuable to study prediction of unobserved values based on information of available data. in this paper we have studied the prediction of unobserved values in two status of one-sample and two-sample, when the parent distribution is the exponential distribution and imposed restriction is double censoring. in each case the interval prediction by given cover will be obtain. Finally, a numerical example is given to illustrate the procedures.

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T2 control charts are used to monitor a process when more than one quality variable associated with process is being observed. Recent studies have shown that using variable sample size (VSS) schemes result in charts with more statistical power when detecting small to moderate shifts in the process mean vector. This paper presents an economic- statistical design of T2 control charts with variable sample size and control limits (VSSC). We build a cost model of a T2-VSSC control chart for the purpose of economic- statistical design using the model of Costa and Rahim (2001).This cost model is constructed that involves the cost of false alarms, the cost of finding and eliminating the assignable cause, the cost associated with production in an out-of-control state, and the cost of sampling and testing. We optimize this model using a genetic algorithm (GA) approach. Furthermore, T2-VSSC and T2-VSS charts are compared with respect to the expect cost per unit time.

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In this paper, we investigate the relation between two variables where the one is measured with the ratio or interval scale and the other with the nominal. In this cases, we use from serial correlation coefficient. Computation of some serial coefficient such as biserial and point-biserial coefficient is carried out with some examples and R program.

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In multivariate cases, the aim of canonical correlation analysis (CCA) for two sets of variables x and y is to obtain linear combinations of them so that they have the largest possible correlation. However, when x and y are continouse functions of another variable (generally time) in nature, these two functions belong to function spaces which are of infinite dimension, and CCA for them should be carried out by using some tools provided by functional data analysis. In this paper we first review definitions and concepts of CCA for multivariate data, and then express those of CCA for functional data with considering the problems occur when generalizing the concepts from multivariate to functional cases. We have also treated a real functional data set and interpreted the obtained results.

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Numerical techniques are too often designed to yield specific answers to rigidly defined questions. Graphical techniques are less confining. They aid in understanding the numerous relationships reflected in the data. They help reveal the existence of peculiar looking observations or subsets of the data. It is difficult to obtain similar information from numerical procedures. In this article, by a real data, some types of displaying bivariate data are introduced.

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‎This papers considers the Benford distribution as one the interesting rules of probability theory‎. ‎This rule shows that‎, ‎despite of usual underestanding about the uniform distribution of digites‎ ‎for lieing on different positions in numbers‎, ‎digits are distributed according to an non uniform distributions for numbers araising from many natural phonemena‎. ‎Benford distribution proposes a discrete and asymetric distribution for observations resulted from counting or natural events‎. ‎This rule is used in vorious applicatins in different fields‎.

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So far many confidence intervals were introduced for the binomial proportion. In this paper, our purpose is comparing five well known based on their exact confidence coefficient and average coverage probability.

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For computing different point estimates such as method of moment and maximum like-lihood estimates and different interval estimates (classical confidence interval, unbi-ased confidence interval, HPD interval), we may deal with the equations which need be solved numerically. In this paper, some numerical methods for solving these type of equations are reviewed in S-PLUS package. Various examples are presented to illus-trate the methods described.

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Meta-Analysis means a statistical analysis on the results of their findings is to combine a large number of independent studies. Meta-Analysis software is needed to be done for convenience, Statistical Software for Meta-Analysis is available in many statistical packages available in the present study provide software R is for Meta-Analysis. First, a brief description of the Meta-Analysis, Statistical methods used in the software and can be used to do it, then the software packages R introduced rmeta functions in the package are described for each of the an example will be given functions.

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In previous studies on fitting non-linear regression models with the symmetric structure the normality is usually assumed in the analysis of data. This choice may be inappropriate when the distribution of residual terms is asymmetric. Recently, the family of scale-mixture of skew-normal distributions is the main concern of many researchers. This family includes several skewed and heavy-tailed distributions, such as the skew-t and the skew slash, as special cases and is recommended as an alternative to the normal distribution. The statistical inference based on the maximization of marginal likelihoods is complicated, in general, for non-linear regression models and thus we implement the MCMC approach to obtain Bayes estimates. Finally, we fit a non-linear regression model using proposed distributions for a real data set to show the importance of the recommended model.

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Mathematical methods and statistical distributions present exact results in the climate calculations and hydrological processes. Awareness of the rainfall probability distribution provides the appropriate conditions for water resource planning. Many studies have been done to estimate probability of rainfall by various methods due to the importance of rainfall distribution in the economic, social and particularly agriculture studies. In these studies, the various probabilistic models have been used and the results of the most investigations show that the bivariate gamma distribution branches of gamma model are compatible for rainfall data. The bivariate gamma distribution is used in the hydrological processes modeling. In the present paper, supposing that the X and Y follow the crovelli’s bivariate gamma model, at first a brief description was given in the case of the exact distributions of the functions U=X+Y, P=XY and Q=X⁄((X+Y)) as well as their respective moments, then the validity of this model was evaluated for Rasht airport weather station data. The results showed that rainfall data of this region also confirms The suitability of the crovelli’s bivariate gamma model.