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In this manuscript first a brief introduction to the Skew-t and Weighted exponential distributions is considered and some of their important properties will be studied. Then we will show that the Skew-t distribution is prefered to the Weighted exponential distribution in fitting by using the real data. Finally we will prove our claim by using the simulation method.

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In recent years, multilevel regression models were intensely developed in many fields like medicine, psychology economic and the others. Such models are applicable for hierarchical data that micro levels are nested in macros. For modeling these data, when response is not normality distributed, we use generalized multilevel regression models. In this paper, at first, multilevel ordinal logistic regression models and some estimation methods are explained. So their applications are investigated in the effect of patient’s environment on economic burden of diabetes type 2.

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For almost two centuries, Poisson process with memoryless property of corresponding exponential distribution served as the simplest, and yet one of the most important stochastic models. On the other hand, there are many processes that exhibit long memory (e.g., network traffic and other complex systems). It would be useful if one could generalize the standard Poisson process to include these processes. This generalization adds a parameter $alin (0, 1]$, and is called the fractional exponent of the process. In this thesis, we clearly derive the transition from standard Poisson process to its fractional generalization (fractional Poisson process (fPp)). The link fPp and $alpha$-stable density is established by solving an integral equation. The link then leads to an algorithm for generating fPp that discovering more interesting properties. Method-of-moments estimators for the intensity rate $mu$ and fractional order $alpha$ derived and showing asymptotic normality of the estimators and construction of the corresponding confidence interval. Then the properties of the estimators are then tested using simulated data.

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In this paper, a new family of distributions with many applications in financial engineering have been introduced. This distribution contains important statistical distributions such as the triangular, exponential and uniform distribution. Initially considered a special case of this distribution And then survey The important features of it. How to calculate maximum likelihood estimates are presented along with a numerical example. Finally, using real data We have presented an application example.

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In the study of reliability of the technical systems, records model play an important role. Assume that the lower limit value of the first record is known, then we propose a definiton of the mean residual life of the future record. We predict mean residual of the future records under condition that the lower limit value of the mth record is known. Furthermore, we present generalization of the mean residual life of record based on the sequance of k-recordsand study its various properties. Finally some simulation results are provided.

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Abstract: Depending on the type of distribution, estimation of parameters are not sometimes simple in practice. In particular, this is the case for Birnbaum-Saunders distribution (BS). In this article, we present four different methods for estimating the parameters of a BS distribution. First, a simple graphical technique, analogous to probability plotting, is used to estimate the parameters and check for goodness-of-fit of failure times following a Birnbaum-Saunders distribution. Then, the maximum likelihood estimators and a modification of the moment estimators of a two-parameter Birnbaum–Saunders distribution are discussed. Finally, The jackknife technique is considered as another method which is appropriate for the small sample size case. Monte Carlo simulation is also used to compare the performance of all these estimators.

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The search designs first introduced in Srivastava (1975) is reviewed. In a ceritan problem, there may be some search designs with same runs. Some criteria for evaluation of search designs are the other topic in the paper. Criteria based on searching probability and expected Kullback- Leibler are reviewd. Some examples are given in each case.

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Nowadays there has been an increasing interest in more flexible distributions like skew distributions that can represent observed behavior more closely. These distributions are often used in the medical and behavioral sciences for real-valued random variables whose distributions are not symmetric. Because high Application of skew distributions, in this paper after a brief review of famous skew distributions, normal, t, skew normal and skew t distributions were fitted on a real data set taken from Mobarakeh Steel Company medical data and then best fit was selected using AIC.

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In this paper, four approaches are presented to the problem of fitting a linear regression model in the presence of spatially misaligned data. These approaches are plug-in method‎, ‎simulation‎, ‎regression calibration and maximum likelihood‎. In the first two approaches‎, ‎with modeling the correlation between the explanatory variable, prediction of explanatory variable is determined at sites corresponding to response variable. Then the model is fitted using the predictions as a covariate in regression model. It is shown that this creates Berkson error and this error leads to bias in estimation of the slope of regression model. To adjust the bias, regression calibration approach is provided. In the maximum likelihood approach, misaligned data is used directly, and the regression model parameters are estimated. In fact, it is not required to predict explanatory variable at sites corresponding to response. Unfortunately, the maximum likelihood estimator properties can not be accurately assessed due to lack of analytical form. In a simulation study, the performance of all these approaches is assessed under several spatial models for explanatory variable. It is observed that regression calibration can significantly reduce the bias of slope of regression line compared to other methods. Moreover, Nominal coverage of confidence interval of slope of regression line is notable by this method.

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In this paper, we study the properties of power weighted means, arithmetic, geometry and harmonic for two copulas.

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

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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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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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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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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.