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Seeking the optimal design with a given number of runs is a main problem in fractional factorial designs(FFDs). Resolution of a design is the most widely usage criterion, which is introduced by Box and Hunter(1961), used to be employed to regular FFDs. The resolution criterion is extended to non-regular FFG, called the generalized resolution criterion. This criterion is providing the idea of generalized minimum aberration criterion in non-regular designs. In this paper, we present these criteria and illustrate the advantages of non-regular designs in estimating the factorial effects with a smaller number of runs than that of regular FFDs. Some examples will be given.

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The sample autocorrelation function (acf) of a stationary process has played a central statistical role in traditional time series analysis, where the assumption is made that the marginal distribution has a second moment. Now, the classical methods based on acf are not applicable in heavy tailed modeling. Using the codifference function as dependence measure for such processes be shown it be as a new tool for order identification of stable moving average processes. Based on the empirical characteristic function, we propose a consistent estimator of the codifference function. In addition, we derive the limiting distribution. Finally, simulation study shows the method is good.

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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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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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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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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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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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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 this paper, we discuss generating a random sample from gamma distribution using generalized exponential distribution.

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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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‎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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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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