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Inferences on the location parameter λ in location-scale families can be carried out using Studentized statistics, i.e., considering estimators λ ˜ of λ and δ ˜ of the nuisance scale parameter δ , in a statistic T = g (λ ˜ , δ ˜) with a sampling distribution that does not depend on (λ , δ) . If both estimators are independent, then T is an externally Studentized statistic; otherwise, it is an internally Studentized statistic. For the Gaussian and for the exponential location-scale families, there are externally Studentized statistics with sampling distributions that are easy to obtain: in the Gaussian case, Student's classic t statistic, since the sample mean λ ˜ = X ¯ and the sample standard deviation δ ˜ = S are independent; in the exponential case, the sample minimum λ ˜ = X 1 : n and the sample range δ ˜ = X n : n − X 1 : n , where the latter is a dispersion estimator, which are independent due to the independence of spacings. However, obtaining the exact distribution of Student's statistic in non-Gaussian populations is hard, but the consequences of assuming symmetry for the parent distribution to obtain approximations allow us to determine if Student's statistic is conservative or liberal. Moreover, examples of external and internal Studentizations in the asymmetric exponential population are given, and an ANalysis Of Spacings (ANOSp) similar to an ANOVA in Gaussian populations is also presented. [ABSTRACT FROM AUTHOR]

In the field of quality control, statistical process control (SPC) has its significance. The control charts are important tools of the SPC to observe the outputs of the production process. The cumulative sum (CUSUM) charting structure is one such technique that is designed to identify the medium and slight changes in the process parameters. In the literature, the assumption of normality is considered ideal for the control chart but in practice, many quality characteristics do not follow the assumption of normality. The current study proposes a class of CUSUM control charts for the location parameter of the process and investigates the performance of said location charts based on ranked set sampling (RSS) for quality characteristics having different environments. Different point estimators of location are considered in this study to develop the location control charts under normal, and a variety of non‐normal environments. The numerical results show that the newly designed schemes perform uniformly well than their competitors. A real‐life example linked with the manufacturing process is also provided for the practical implementation of the proposed scheme. [ABSTRACT FROM AUTHOR]

Abstract–The Weibull distribution is the most applied model in reliability field for lifetime analysis. The Weibull location parameter, characterizing the minimum possible life, plays a significant role in engineering applications. In this paper, we consider the interval estimation on the location parameter when the product's lifetime follows the three-parameter Weibull distribution with a known shape parameter. A novel approach based on the relationship between the minimum order statistics, the location parameter, and the sample size is developed to construct confidence intervals for the Weibull location parameter. Thereafter, we compare it with other two interval estimation approaches by the performances of the coverage probability and the average length via simulations and a real application. The results show that the proposed method outperforms the pivot quantity (PQ) method and the bias-corrected and accelerated (Bca) bootstrap method in small and medium samples in terms of coverage probability. [ABSTRACT FROM AUTHOR]

Control charts are prominent tools in monitoring various variables of manufacturing processes. In this paper, the control chart based on sample median is proposed for process location parameter using Shewhart's approach. The proposed control chart is developed under some distributions including normal distribution. Its performance is studied in terms of power, average run length (ARL) and standard deviation of run length (SDRL). Also, the effect of non normality on this control chart is discussed. [ABSTRACT FROM AUTHOR]

The nonparametric (distribution-free) Shewhart-type control chart based on the Pettitt test has recently been introduced in the literature for joint monitoring of the location and the scale parameters of a continuous process. The chart is based on a simple random sampling (SRS) technique (denoted as SP-SRS chart). In the literature, the ranked set sampling (RSS) technique is preferred over the SRS technique as it reduces the variability and improves the performance of the control chart. The aim of this paper is to develop a distribution-free control chart based on the Pettitt test using the RSS technique (denoted as SP-RSS Chart) further to enhance the joint monitoring of location and scale. The run length performance of the proposed SP-RSS chart is compared with the SP-SRS chart. The comparison revealed that the proposed SP-RSS chart outperforms the SP-RSS chart for joint monitoring of the location and scale of a continuous process. [ABSTRACT FROM AUTHOR]

Inferences on the location parameter λ in location-scale families can be carried out using Studentized statistics, i.e., considering estimators λ˜ of λ and δ˜ of the nuisance scale parameter δ, in a statistic T=g(λ˜,δ˜) with a sampling distribution that does not depend on (λ,δ). If both estimators are independent, then T is an externally Studentized statistic; otherwise, it is an internally Studentized statistic. For the Gaussian and for the exponential location-scale families, there are externally Studentized statistics with sampling distributions that are easy to obtain: in the Gaussian case, Student’s classic t statistic, since the sample mean λ˜=X¯ and the sample standard deviation δ˜=S are independent; in the exponential case, the sample minimum λ˜=X1:n and the sample range δ˜=Xn:n−X1:n, where the latter is a dispersion estimator, which are independent due to the independence of spacings. However, obtaining the exact distribution of Student’s statistic in non-Gaussian populations is hard, but the consequences of assuming symmetry for the parent distribution to obtain approximations allow us to determine if Student’s statistic is conservative or liberal. Moreover, examples of external and internal Studentizations in the asymmetric exponential population are given, and an ANalysis Of Spacings (ANOSp) similar to an ANOVA in Gaussian populations is also presented.

The outcomes of many real-life experiments are sequences of record-breaking data sets, where only observations that exceed (or only those that fall below) the current extreme value are recorded. Records are needed when it is difficult to obtain observations or when observations are being destroyed when subjected to an experimental test. Records are applied in many real-life applications, such as hydrology, industrial stress testing, demise of glaciers, crop production, meteorological analysis, sporting and athletic events, and oil and mining surveys. For instance, in the threshold modeling the observations are those that cross a certain threshold value. Effectively estimating the location parameters for equally likely (uniformly distributed) records is needed in many real-life experiments. The practice demonstrated that the widely used estimators, such as the best linear unbiased estimator (BLUE) and maximum likelihood estimator (MLE), have some defects. This manuscript improves the MLE and BLUE of the location parameters for uniformly distributed records by investigating the corresponding shrinkage estimator using prior information about the BLUE and MLE. To measure the accuracy and precision of the proposed shrinkage estimator, the bias and mean square error (MSE) of the proposed estimators are investigated that provide sufficient conditions to get unbiased estimator with minimum MSE. The numerical results demonstrated that the proposed estimator are dominating over the existing estimators. [ABSTRACT FROM AUTHOR]

This research introduces a shifted Kumaraswamy distribution (SKD). The SKD is capable of modelling real-world phenomena with asymmetrical and bathtub-shaped characteristics with exceptional proficiency. The mathematical and reliability characteristics are thoroughly examined. To better comprehend its behaviour, density and hazard rate functions are plotted. The parameters of the model are estimated through the use of the maximum likelihood estimation method. The effectiveness of the SKD is demonstrated through its application to four real-world lifetime datasets, resulting in significantly improved outcomes compared to other well-known models and providing the closest fit to the data. This superiority confirms the SKD as a preferable choice over the baseline model. [ABSTRACT FROM AUTHOR]

In this article, the inference on location parameter for the skew-normal population under dependent samples is considered. First, the Bootstrap test statistics and Bootstrap confidence intervals for the Behrens–Fisher-type problem are constructed, respectively, when the scale parameter or skewness parameter is known. Second, the Monte-Carlo simulation results indicate that the Bootstrap approach is better than the approximate approach in most cases. Finally, the above approaches are illustrated by using the real data examples of gross domestic product and stock closing price. [ABSTRACT FROM AUTHOR]

Traditional control charts are based on the assumption that the process observations are normally distributed. However, in many applications, there is insufficient information to justify this assumption. Thus, nonparametric control charts have been designed in literature to monitor location parameter and scale parameter of a process. In this paper, a single nonparametric control chart based on modified Lepage test is proposed for simultaneously monitoring of location and scale parameters of any continuous process distribution. The charting statistic combines two nonparametric test statistics namely Baumgartner test for location and Ansari-Bradely test for scale. The performance of the proposed chart is examined through simulation studies in terms of the mean, the standard deviation, the median and some percentiles of the run length distribution. The average run length (ARL) performance of the proposed chart is compared with that of the existing nonparametric Shewhart-Cucconi (SC) and Shewhart-Lepage (SL) charts for joint monitoring of location and scale. [ABSTRACT FROM AUTHOR]

The three-parameter Weibull distribution is popular in reliability analysis. However, in the context of a small sample size, the issue of parameter estimation of the three-parameter Weibull distribution is difficult to address. If only a small sample size is available, a reasonable method is to empirically determine the shape parameter, and the emphasis is placed on location parameter estimation. This paper presents a theoretical model to establish the relationship between the location parameter, the minimal sample value, and the sample size. Moreover, an iterative method is proposed to estimate the Weibull location parameter and scale parameter with an empirical value for the shape parameter. Compared with the maximum likelihood method (MLE), the Weibull plot with the sample correlation coefficient and TL-moment, the proposed method can more effectively estimate the parameters of the three-parameter Weibull distribution. [ABSTRACT FROM AUTHOR]

In this paper, the statistical inference on the location parameter vector is studied in the multivariate skew-normal model with unknown scale parameter and known shape parameter. Based on the distribution of the generalized Hotelling's T2 statistic, confidence regions and hypothesis tests on the location parameter, μ , are obtained. The power function of the test is studied numerically as well. For illustration the effectiveness and applicability of our purposed methods, the traffic accident data from the National Highway Traffic Safety Administration (NHTSA) in U.S. Department of Transportation are analyzed. [ABSTRACT FROM AUTHOR]

We consider the problem of robust mean and location estimation with respect to any pseudo-norm of the form x ∈ R d ↦ x S = sup v ∈ S 〈 v , x 〉 where S is any symmetric subset of R d . We show that the deviation-optimal minimax sub-Gaussian rate for confidence 1 - δ is max ℓ ∗ (Σ 1 / 2 S) N , sup v ∈ S Σ 1 / 2 v 2 log (1 / δ) N where ℓ ∗ (Σ 1 / 2 S) is the Gaussian mean width of Σ 1 / 2 S and Σ the covariance of the data. This improves the entropic minimax lower bound from Lugosi and Mendelson (Probab Theory Relat Fields 175(3–4):957–973, 2019) and closes the gap characterized by Sudakov's inequality between the entropy and the Gaussian mean width for this problem. This shows that the right statistical complexity measure for the mean estimation problem is the Gaussian mean width. We also show that this rate can be achieved by a solution to a convex optimization problem in the adversarial and L 2 heavy-tailed setup by considering minimum of some Fenchel–Legendre transforms constructed using the median-of-means principle. We finally show that this rate may also be achieved in situations where there is not even a first moment but a location parameter exists. [ABSTRACT FROM AUTHOR]

The paper aims to capitalize on the new features that are offered by the Microsoft Excel calculation program for reliability modeling, using the Median Ranks estimator that is calculated directly with the BETA.INV function, not estimated by various algebraic estimators, as is generally the case. Starting from this first step, a method of modeling reliability is elaborated through the three-parametric Weibull model that is based exclusively on this software, which is accessible to anyone and can be used even in the case of online learning, which is widespread in recent years due to the pandemic situation. The probability plotting method is applied, using the Median Ranks estimator that is calculated directly with the BETA.INV function for a probability equal to 0.5. A flowchart is made for the proposed method, which could be easily translated into a calculation program. By representing in logarithmic coordinates, we determined the Weibull models for different values that were initially adopted for the location parameter: using as a criterion the coefficient of determination that was obtained using the trendline function for the linear model, it was possible to identify, by successive tests, the optimal value of the location parameter—for which the three-parametric model has a good likelihood. By the proposed method, this value can be found following this iterative process. So, based on the current facilities of the Microsoft Excel program, a precise and easy-to-apply method has been achieved, through which an appropriate three-parametric Weibull model can be identified. [ABSTRACT FROM AUTHOR]

A procedure is outlined for point and interval estimation of location parameters associated with polytomous items, or raters assessing studied subjects or cases, which follow the rating scale model. The method is developed within the framework of latent variable modeling, and is readily applied in empirical research using popular software. The approach permits testing the goodness of fit of this widely used model, which represents a rather parsimonious item response theory model as a means of description and explanation of an analyzed data set. The procedure allows examination of important aspects of the functioning of measuring instruments with polytomous ordinal items, which may also constitute person assessments furnished by teachers, counselors, judges, raters, or clinicians. The described method is illustrated using an empirical example. [ABSTRACT FROM AUTHOR]

We propose two tests to distinguish between separable classes of distribution tails, the first of which is invariant with respect to the scale parameter and the second is invariant with respect to both location and scale parameters. The asymptotic properties of the proposed tests are established. The distributions are not assumed to belong to any maximum domain of attraction. [ABSTRACT FROM AUTHOR]

This paper surveys the location Y ¯ chart based on concomitants of ranked set sampling (RSS), a triangular modification of RSS, which is known as maximum ranked set sampling with unequal sample (MRSSU) and the extreme ranked set sampling (ERSS) from the Farlie–Gumbel–Morgenstern bivariate family. We also remarked both heavy-tailed symmetric and skewed distributions throughout the paper. For the performance evaluation of the charts, extensive utilization of the Monte Carlo simulations is carried out using average run length (ARL), extra quadratic loss (EQL), relative ARL (RARL), and performance comparison index (PCI) measures, and finally, conclusion ends this research. [ABSTRACT FROM AUTHOR]

In this paper, the inference on location parameter for the skew-normal population is considered when the scale parameter and skewness parameter are unknown. Firstly, the Bootstrap test statistics and Bootstrap confidence intervals for location parameter of single population are constructed based on the methods of moment estimation and maximum likelihood estimation, respectively. Secondly, the Behrens-Fisher type and interval estimation problems of two skew-normal populations are discussed. Thirdly, by the Monte Carlo simulation, the proposed Bootstrap approaches provide the satisfactory performances under the senses of Type I error probability and power in most cases regardless of the moment estimator or ML estimator. Further, the Bootstrap test based on the moment estimator is better than that based on the ML estimator in most situations. Finally, the above approaches are applied to the real data examples of leaf area index, carbon fibers' strength and red blood cell count in athletes to verify the reasonableness and effectiveness of the proposed approaches. [ABSTRACT FROM AUTHOR]

In several applications, the assumption of normality is often violated in data with some level of skewness, so skewness affects the mean's estimation. The class of skew–normal distributions is considered, given their flexibility for modeling data with asymmetry parameter. In this paper, we considered two location parameter (μ) estimation methods in the skew–normal setting, where the coefficient of variation and the skewness parameter are known. Specifically, the least square estimator (LSE) and the best unbiased estimator (BUE) for μ are considered. The properties for BUE (which dominates LSE) using classic theorems of information theory are explored, which provides a way to measure the uncertainty of location parameter estimations. Specifically, inequalities based on convexity property enable obtaining lower and upper bounds for differential entropy and Fisher information. Some simulations illustrate the behavior of differential entropy and Fisher information bounds. [ABSTRACT FROM AUTHOR]

Researchers typically assume that they are working from a normal distribution and with independent sampling. Both assumptions are often violated. Our goal was to explore the intersection of the violations: Is the net effect good or bad? Using the family of skew-normal distributions, which is a superset of the family of normal distributions, we tested whether the mean squared error (MSE) is less under dependence or under independence. We found that the MSE is less under dependence, under the assumption that elements in both samples are identically distributed related to the population distribution. In addition, increasing skewness and increasing sample size also decrease the MSE. Finally, the largest differences in MSE between dependence and independence occur under moderate skewness. [ABSTRACT FROM AUTHOR]

In this paper, the inference on location parameter for the skew-normal population is considered when the scale parameter and skewness parameter are unknown. Firstly, the Bootstrap test statistics and Bootstrap confidence intervals for location parameter of single population are constructed based on the methods of moment estimation and maximum likelihood estimation, respectively. Secondly, the Behrens-Fisher type and interval estimation problems of two skew-normal populations are discussed. Thirdly, by the Monte Carlo simulation, the proposed Bootstrap approaches provide the satisfactory performances under the senses of Type I error probability and power in most cases regardless of the moment estimator or ML estimator. Further, the Bootstrap test based on the moment estimator is better than that based on the ML estimator in most situations. Finally, the above approaches are applied to the real data examples of leaf area index, carbon fibers’ strength and red blood cell count in athletes to verify the reasonableness and effectiveness of the proposed approaches.

In several applications, the assumption of normality is often violated in data with some level of skewness, so skewness affects the mean’s estimation. The class of skew–normal distributions is considered, given their flexibility for modeling data with asymmetry parameter. In this paper, we considered two location parameter (μ) estimation methods in the skew–normal setting, where the coefficient of variation and the skewness parameter are known. Specifically, the least square estimator (LSE) and the best unbiased estimator (BUE) for μ are considered. The properties for BUE (which dominates LSE) using classic theorems of information theory are explored, which provides a way to measure the uncertainty of location parameter estimations. Specifically, inequalities based on convexity property enable obtaining lower and upper bounds for differential entropy and Fisher information. Some simulations illustrate the behavior of differential entropy and Fisher information bounds.

The exponentially weighted moving average (EWMA) control chart is a memory chart that is widely used in process monitoring to spot small and persistent disturbances in the process parameter(s). This chart requires normality of the quality characteristic(s) of interest and a smaller choice of smoothing parameter. Any deviations from these conditions affect its performance in terms of efficiency and robustness. For the said two concerns, this study develops a new mixed EWMA chart under progressive setup (mixed EWMA–progressive mean [MEP] chart). The proposed MEP chart combines the advantages of robustness (under nonnormal scenarios) and high sensitivity to small and persistent shifts in the process mean. The performance of the proposed MEP control chart is evaluated in terms of average run length and some other characteristics of run length distribution. The assessment of the proposed chart is made under standard normal, student's t, gamma, Laplace, logistic, exponential, contaminated normal and lognormal distributions. The performance of the proposed MEP chart is also compared with some existing competitors including the classical EWMA, the classical cumulative sum (CUSUM), the homogenously weighted moving average, the mixed EWMA–CUSUM, the mixed CUSUM–EWMA and the double EWMA charts. The analysis reveals that the proposal of this study offers a superior design structure relative to its competing counterparts. An application from substrates manufacturing process (in which flow width of the resist is the key quality characteristic) is also provided in the study. [ABSTRACT FROM AUTHOR]

Control charts are popular monitoring tools in statistical process control toolkit. These are used to identify assignable causes in the process parameters (location and/or dispersion). These assignable causes result in a shift in the process parameter(s). The shift can be categorized into three sizes (small, moderate, and large). Memory control charts such as the exponentially weighted moving average (EWMA) and cumulative sum (CUSUM) charts are effective for identifying small‐to‐moderate shift(s) in the process. Likewise, mixed memory control charts are useful for efficient process monitoring. In this study, we have proposed two new mixed memory control charts based on auxiliary information named MxMEC and MxMCE control charts to improve the efficiency of these mixed charts. The MxMEC chart is a merger of the auxiliary information based MxEWMA chart and the classical CUSUM chart. Likewise, the MxMCE chart integrates the auxiliary information based MxCUSUM with the classical EWMA chart. The proposed MxMEC and MxMCE charts are evaluated through famous performance measures including average run length, extra quadratic loss, relative average run length, and performance comparison index. The performance of the study proposals is compared with the existing counterparts such as the classical CUSUM and EWMA, MxCUSUM, MxEWMA, MEC, MCE, and runs rules‐based CUSUM charts. The comparisons revealed the superiority of the proposed charts against other competing charts particularly for small‐to‐moderate shifts in the process location. Finally, a real‐life data is used to show the implementation procedure of the proposed charts in practical situations. [ABSTRACT FROM AUTHOR]

Monitoring of any manufacturing, production, or industrial process can be controlled and improved by removing these special cause of variations using control charts. Shewhart‐type control charts are effective to control a large amount of special variations, whereas, cumulative sum (CUSUM) and exponentially weighted moving average (EWMA) charts detect small and moderate variations efficiently in the process parameters. Monitoring of location parameter can be done with mean control charts under the assumption that the parameters are known or correctly estimated from in‐control samples and data are free from outliers (but in practice data occasionally have outliers). In this study, we have proposed generalized mixed EWMA‐CUSUM median control charts structures for known and unknown parameters based on auxiliary variables for detecting shifts in process location parameter. The proposed charts are compared with the corresponding charts for the mean, based on contaminated and uncontaminated data. Different performance measures are used to evaluate the performance of proposed control charts and revealed through results that the median‐based charts are more sensitive to detect a shift in process location parameter in the presence of outliers. An illustrative example using real data is also shown for practical consideration. [ABSTRACT FROM AUTHOR]

We consider method-of-quantiles estimators of unknown one-dimensional parameters, namely the analogue of method-of-moments estimators obtained by matching empirical and theoretical quantiles at some probability level λ ∈ (0 , 1) . The aim is to present large deviation results for these estimators as the sample size tends to infinity. We study in detail several examples; for specific models we discuss the choice of the optimal value of λ and we compare the convergence of the method-of-quantiles and method-of-moments estimators. [ABSTRACT FROM AUTHOR]

Summary: In this paper, we provide a detailed study of a general family of asymmetric densities. In the general framework, we establish expressions for important characteristics of the distributions and discuss estimation of the parameters via method‐of‐moments as well as maximum likelihood estimation. Asymptotic normality results for the estimators are provided. The results under the general framework are then applied to some specific examples of asymmetric densities. The use of the asymmetric densities is illustrated in a real‐data analysis. [ABSTRACT FROM AUTHOR]

Strategies for comparison of alternative tests do not receive much attention in econometrics. The purpose of this paper is to introduce the concept of stringency and illustrate it in the context of a very simple hypothesis testing problem. Systematic use of this concept can be very helpful in evaluating relative performance of tests.

Control charts, based on ranked set sampling schemes, had been proposed recently for efficient monitoring of process location. All the proposals in the literature are based on the ideal assumption of normally distributed quality characteristics. No study as of yet investigated the performance of location charts based on ranked set sampling for non‐normal processes. In this study, we investigated the location Y‾ chart based on simple random sampling (SRS) and three well‐known rank‐based schemes ie, ranked set sampling (RSS), median ranked set sampling (MRSS), and extreme ranked set sampling (ERSS), considering normal and a variety of non‐normal parent distributions. Both heavy‐tailed symmetric and skewed cases have been considered in this study. The performance of the charts is evaluated using average run length (ARL), extra quadratic loss (EQL), and relative ARL (RARL) measures. A real life example is also presented that details the monitoring of pH levels in water for an experiment conducted to study the reproduction of Mysids. The study will help quality practitioners to choose the Y‾ chart based on an efficient sampling scheme for normal and non‐normal processes. [ABSTRACT FROM AUTHOR]

In this paper, some remarks for more efficient analysis of two-dimensional elastostatic problems using the method of fundamental solutions are made. First, the effects of the distance between pseudo and main boundaries on the solution are investigated and by a numerical study a lower bound for the distance of each source point to the main boundary is suggested. In some cases, the resulting system of equations becomes ill-conditioned for which, the truncated singular value decomposition with a criterion based on the accuracy of the imposition of boundary conditions is used. Moreover, a procedure for normalizing the shear modulus is presented that significantly reduces the condition number of the system of equations. By solving two example problems with stress concentration, the effectiveness of the proposed methods is demonstrated. [ABSTRACT FROM AUTHOR]

This paper proposes estimators of the first-order autocorrelation that are based on suitably transformed ratios of successive observations. The new estimators are given by simple functions of the observations. Numerical optimization is not required. Simulations show that they are highly robust against extreme values and clusters of high volatility and are therefore particularly useful for the estimation of serial correlation in return series. Besides, the results of the simulation study also call into question the common practice of correcting the small-sample bias of conventional estimators. [ABSTRACT FROM AUTHOR]

Control charts are commonly used tools in statistical process control for the detection of shifts in process parameters. Shewhart-type charts are efficient for large shift values, whereas cumulative sum (CUSUM) charts are effective in detecting medium and small shifts. Control chart use commonly assumes that data are free of outliers and parameters are known or correctly estimated based on an in-control process. In practice, these assumptions are not often true because some processes occasionally have outliers. Monitoring the location parameter is usually based on mean charts, which are seriously affected by violations of these assumptions. In this paper we propose several CUSUM median control charts based on auxiliary variables, and offer comparisons with their corresponding mean control charts. To monitor the location parameter, we examined the performance of mean and median control charts in the presence and absence of outliers. Both symmetric and non-symmetric processes were studied to examine the properties of the proposed control charts to monitor the location parameter using CUSUM control charts. We used different run length measures to study in-control and out-of-control performances of CUSUM charts. Results revealed that our proposed control charts perform much better than the traditional charts in the presence of outliers. A real application of our study was provided using data on concrete compressive strength as it relates to the quality of cement manufacturing. [ABSTRACT FROM AUTHOR]

Multivariate autoregressive (MAR) models are an attractive choice for applications in the processes related to finance, medical, and industry. For the monitoring of such processes, control chart is the most important and widely used tool of statistical process control tool kit. Moreover, the presence of auxiliary information helps in better estimation of different process parameters. The literature on use of auxiliary variables in control charts assumes independence of observations. In practice, we may come across processes dealing with autocorrelated outcomes. In such situations, a control chart usually produces high false alarms and exhibits slow detection of shifts when the process is out-of-control. This study intends to suggest some auxiliary information-based Shewhart charts for autocorrelated univariate and bivariate AR(1) processes. The proposed structures take into account the autocorrelation structure and offer more effective designs of control charts for efficient process monitoring. The performance measures used in this study are based on run length measures such as average run length, extra quadratic loss, relative average run length and performance comparison index. A detailed performance analysis is carried out to sort out the best performing charts. In addition, we have considered an application from a manufacturing process to demonstrate the implementation of the proposed charting structures in real scenario. [ABSTRACT FROM AUTHOR]

In this paper, we devote to constructing the one-sided empirical Bayes (EB) test for the location parameter in the Gamma distribution by nonparametric method. Under some mild conditions, we prove that the EB test is asymptotically optimal with the rate of the order O(n−δs2s+1), where 1/2 ≤ δ < 1 and s > 1 is a given natural number. An example is also given to illustrate that the conditions of the main theorems are easily satisfied. [ABSTRACT FROM AUTHOR]

In the Bayesian Statistics, the use of conjugate prior distributions allows to obtain exact posterior quantities, avoiding the use of approximate methods. However, there are only a few conjugate structures available, which limits the use in practical problems. In this work we propose a general procedure to obtain the posterior distribution in an exact form in non-conjugate location parameter models with known (possibly, heteroskedastic) variance. The theory is based on special functions, specifically the H-function, which embraces most of the probability distributions. We express explicitly in a computable form all the Bayesian tools for posterior inferences, that is the posterior and the posterior predictive distributions and their moments, as well as the cumulative posterior distribution. As an illustration we consider a problem in astronomy of estimating the distance to the Large Magellanic Cloud, the largest galaxy now orbiting the Milky Way Galaxy. [ABSTRACT FROM AUTHOR]

Mukhopadhyay and Padmanabhan (Metrika 40:121-128, 1993) considered the construction of fixed-width confidence intervals for the difference of location parameters of two negative exponential distributions via triple sampling when the scale parameters are unknown and unequal. Under the same setting, this paper deals with the problem of fixed-width confidence interval estimation for a linear combination of location parameters, using the above mentioned three-stage procedure. [ABSTRACT FROM AUTHOR]