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According to the first nth observations of the upper record from exponential distribution, in this article, we can compute maximum likelihood estimation of this distribution parameter. We, then, concentrate on point prediction of the future upper record values in exponential distribution based both on classic and Bayes approaches and second degree and linex loss functions.We, ultimately, deal with numerical comparison available point predictions through Monte Carlo simulation.

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In this article study summery of reversed hazard rate and mixture distributons then introduce reversed hazard rate mixture and waiting times of failure also introduce mixture reversed hazard rate additive modele and multiplicative and introduce behavioure mixture of k increasing reversed hazard rate (IRFR) Increasing(IRFR).

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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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Recently several control charts have been introduced in the  statistical process control  literature which are based on the idea of Bayesian Predictive Density (BPD).  Among these charts is the variation control chart which we refer to it as VBPD chart.

In this paper we add the idea of Moving Average to VBPD chart and introduce a new variation control chart which has all advantages of the original VBPD chart and in addition has a new advantage which is its sensitivity to small changes in process variance. We refer to this new chart as MAVBPD chart.

In both VBPD and MAVBP charts , the parameters are assumed unknown but the control statistic has a known F distribution which means that, the control limits can be obtained  without simulation.

 

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Statistical models are utilized to learn about the mechanism that the data are generating from it. Often it is assumed that the random variables y_i,i=1,…,n ,are samples from the probability distribution F which is belong to a parametric distributions class. However, in practice, a parametric model may be inappropriate to describe the data. In this settings, the parametric assumption could be relaxed and more flexible models could be used analysis of data. In the nonparametric Bayes approach, a prior distributions is defined over the whole space of probability distributions for random variable distribution. Due to the Dirichlet process (DP) has interesting properties, it is thus used extensively. In this paper, we introduce DP and its features.

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In this paper, we obtain unbiased estimators of e using stopping time random variables and simulation.

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Beliefs are the result of uncertainty. Sometimes uncertainty is because of a random process and sometimes the result of lack of information. In the past, the only solution in situations of uncertainty has been the probability theory. But the past few decades, various theories of other variables and systems are put forward for the systems with no adequate and accurate information. One of these approaches is the theory of evidence. In recent years, the theory Dempster-Shafer or the theory of belief functions as a generalization of the probability theory, which makes the display of different levels of information, from complete certainty to total ignorance. According to the theory of belief, the belief function presents a mathematical probability for the use of mental judgments.A model for persenting belief functions is the transferable belief model. This model is basically similar to the Bayesian model. In this model, beliefs are at two levels, one credal level in which beliefs are accepted by belief functions that are quantified, and other is the pignistic level in which beliefs can be used for decision making and quantified by probability functions. This model differs the Bayesian model regarding creedal level the Bayesian model does not have this level.

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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.

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This article describes the limiting distribution of the degrees of nodes has been derived for a kind of random tree named

k-minimal label random recursive tree, as the size of the tree goes to infinity. The outdegree of the tree is equal to the number of customers in a pyramid marketing agency immediatly alluring

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In this article introduce the sequential order statistics. Therefore based on multiply Type-II censored sample of sequential order statistics, Bayesian estimators are derived for the parameters of one- and two- parameter exponential distributions under the assumption that the prior distribution is given by an inverse gamma distribution and the Bayes estimator with respect to squared error loss is calculated. Moreover, prediction of future failure time is considered. Finally in example Bayesian estimator and non-bayesian estimatores, namely the Best Linear Unbiased Estimator (BLUE) and Approximate Maximum Likelihood Estimator (AMLE) are derived.

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Bayesian networks (BNs) are modern tools for modeling phenomena in dynamic and static systems and are used in different subjects such as disease diagnosis, weather forecasting, decision making and clustering. A BN is a graphical-probabilistic model which represents causal relations among random variables and consists of a directed acyclic graph and a set of conditional probabilities. Structure learning and parameter learning are two main subjects in BNs. In this paper, we consider a BN with a known structure and then, by simulate some data, we try to learn structure of the network using two well-known algorithms, namely, PC and $ K_{2} $ algorithms. Then, we learn parameters of the network and derive the maximum likelihood, maximum a posteriori and posterior mean estimates of the corresponding parameters. Furthermore, we compare performance of the estimates using the Kullback-Leibler divergence criteria and finally, utilizing a real data set, we consider the structure and parameter learning tasks to illustrate practical utility of the proposed methods.

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‎The equilibrium distributions have many applications in reliability theory, stochastic orderings and random processes. ‎The purpose of this paper is to introduce the equilibrium distributions and presents some results related to this issue. Some results are based on order statistics. ‎In this paper, ‎the generalized Pareto distributions are also analyzed and some basic relationships between the equilibrium distributions are presented.

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The two-parameter Birnbaum–Saunders (BS) distribution was originally proposed as a failure time distribution
for fatigue failure caused under cyclic loading. BS model is a positively skewed statistical distribution which has
received great attention in recent decades. Several extensions of this distribution with various degrees of skewness,
kurtosis and modality are considered. In particular, a generalized version of this model was derived based on symmetrical
distributions in the real line named the generalized BS (GBS) distribution. In this article, we propose a
new family of life distributions, generated from elliptically contoured distributions, and the density and some of its
properties are obtained. Explicit expressions for the density of a number of specific elliptical distributions, such as
Pearson type VII, t, Cauchy, Kotz type, normal, Laplace and logistic are found. Another generalization of the BS
distribution is also presented using skew-elliptical distribution which makes its symmetry more flexible. Finally,
some examples are provided to illustrate application of the distribution.

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In many diverse scientific fields, the measurements are directions. For instance, a biologist may be measuring the
direction of flight of a bird or the orientation of an animal. A series of such observations is called ”directional
data”. Since a direction has no magnitude, these can be conveniently represented as points on the circumference of
a unit circle centered at the origin or as unit vectors connecting the origin to these points. Because of this circular
representation, such observations are also called circular data. In this paper, circular data will be introduced at first
and then it is explained how to calculate the mean direction, dispersion and higher moments. The solutions to many
directional data problems are often not obtainable in simple closed analytical forms. Therefore, computer softwares
is essential to use these methods. At the end of this paper, the CircStat’s package has been used to analyze data sets
in R and Matlab softwares.

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In many quality control applications, the necessary distributional assumptions to correctly apply the traditional parametric control charts are either not met or there is simply not enough information or evidence to verify the assumptions. It is well known that performance of many parametric control charts can be seriously degraded in situations like this. Thus, control charts that do not require a specific distributional assumption to be valid, so-called nonparametric or distribution-free charts, are desirable in practice. In this paper, a simple to use multivariate nonparametric control chart is introduced. The chart is based on the multivariate two sample Mann-Withney Wilcoxon test for equality of location vectors of two populations. Using simulated data we show that there are situations in which the Mann-Withney multivariate control chart has a better performance compared with T2 control chart.

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In reliability theory, some measures are introduced , called importance measures, to evaluate the relative importance
of individual components or groups of components in a system. Importance measures are quantitive criteria
that ranke the components according to their importance. In the literature, different importance measures are presented
based on different scenarios. These measures can be determined based on the system structure, reliability of
the components and/or component liftime distributions. The purpose of this paper is the study different importance
measures of the components of a system in reliability theory.

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Unimodality is one of the building structures of distributions that like skewness, kurtosis and symmetry is visible in the shape of a function. Comparing two different distributions, can be a very difficult task. But if both the distributions are of the same types, for example both are unimodal, for comparison we may just compare the modes, dispersions and skewness. So, the concept of unimodality of distributions and its characterizations, is important. In this paper, we discuss the concept of unimodality and its generalizations, namely a-unimodality, for discrete and continuous random variables. We shall also review the concept of a-monotonicity of distributions. Finally, we shall reveal certain upper bounds for the variance of a discrete a-unimodal distribution.