Reliability Properties of Systems with Two Exchangeable Log-Logistic Components

In this article, we study the reliability properties of systems under bivariate log-logistic model which comes out from a particular stress-strength analysis. For this model, we obtain basic reliability characteristics of series and parallel systems and investigate their properties. We also derive distribution and moments of cold standby system under the abovementioned exchangeable model.     

Gamma Kernel Intensity Estimation in Temporal Point Processes

In this article, we propose a nonparametric approach for estimating the intensity function of temporal point processes based on kernel estimators. In particular, we use asymmetric kernel estimators characterized by the gamma distribution, in order to describe features of observed point patterns adequately. Some characteristics of these estimators are analyzed and discussed both through simulated results and applications to real data from different seismic catalogs.     

The generalized exponential family of distributions and its characteristics

In this paper we generalize the exponential family (EF) of distributions into a wider family which includes important distributions such as the normal, log-normal, Student-t, Cauchy, logistic and Birnbaum–Saunders distributions. Furthermore, we derive several characteristics of the proposed family. The importance of such family is also discussed.     

Development of Adaptive Group Sequential Procedure for Changing Sample Size

In this study, we propose a group sequential procedure that allows the change of necessary sample size at intermediary stage in sequential test. In the procedure, we formulate the conditional power to judge the necessity of the change of sample size in decision rules. Furthermore, we present an integral formula of the power of the test and show how to change the necessary sample size by using the power of the test. In simulation studies, we investigate the characteristics of the change of sample size and the pattern of decision across all stages based on generated normal random numbers.     

Bayesian analysis in multivariate regression models with conjugate priors

In this paper, we consider the full rank multivariate regression model with matrix elliptically contoured distributed errors. We formulate a conjugate prior distribution for matrix elliptical models and derive the posterior distributions of mean and scale matrices. In the sequel, some characteristics of regression matrix parameters are also proposed.     

A Class of Distributions with Linear Hazard Quantile Function

In this article, we introduce and study a class of distributions that has linear hazard quantile function. Various distributional properties and reliability characteristics of the class are studied. Some characterizations of the class of distributions are presented. The method of L-moments is employed to estimate parameters of the class of distributions. Finally, we apply the proposed class to a real data set.     

Stochastic ordering of medians in samples from normal distributions

In this paper, we discuss some stochastic comparisons for the sample median in a random sample from a normal distribution. Specifically, we establish that the sample median is stochastically farther than the sample mean to the population mean. To verify the result of comparison, we derive an upper bound for some distributional characteristics of the distance between the sample median and the population mean. The stochastic ordering considered here is the likelihood ratio order.     

A new mixed bivariate geometric-exponential life distribution with applications to series systems

In this paper, a new mixed bivariate geometric-exponential distribution is introduced. We present the properties and numerical characteristics of the distribution. In addition, the applications of this new bivariate distribution are given in a two-unit series system. Through an intensive Monte-Carlo simulation study, we assess the precision of the proposed estimation methods for the parameter inference. A real data is analysed for illustrative purpose.     

On the Choice of Functional Forms: Summary of a Monte Carlo Experiment

The use of flexible functional forms is a standard practice in applied econometrics. Many flexible forms have been proposed. In this study, we investigate the behavior of three of them—the translog, the symmetric McFadden, and the symmetric generalized Barnett. Based on Monte Carlo experiments, we assess the ability of these forms to test theoretical properties and to measure technological characteristics.     

Bayesian Inference for Assessing Effects of Email Marketing Campaigns

Email marketing has been an increasingly important tool for today’s businesses. In this article, we propose a counting-process-based Bayesian method for quantifying the effectiveness of email marketing campaigns in conjunction with customer characteristics. Our model explicitly addresses the seasonality of data, accounts for the impact of customer characteristics on their purchasing behavior, and evaluates effects of email offers as well as their interactions with customer characteristics. Using the proposed method, together with a propensity-score-based unit-matching technique for alleviating potential confounding, we analyze a large email marketing dataset of an online ticket marketplace to evaluate the short- and long-term effectiveness of their email campaigns. It is shown that email offers can increase customer purchase rate both immediately and during a longer term. Customers’ characteristics such as length of shopping history, purchase recency, average ticket price, average ticket count, and number of genres purchased also affect customers’ purchase rate. A strong positive interaction is uncovered between email offer and purchase recency, suggesting that customers who have been inactive recently are more likely to take advantage of promotional offers. Supplementary materials for this article are available online.     

A Monte Carlo-based pseudo-coefficient of determination for generalized linear models with binary outcome

In this article, we focus on a pseudo-coefficient of determination for generalized linear models with binary outcome. Although there are numerous coefficients of determination proposed in the literature, none of them is identified as the best in terms of estimation accuracy, or incorporates all desired characteristics of a precise coefficient of determination. Considering this, we propose a new coefficient of determination by using a computational Monte Carlo approach, and exhibit main characteristics of the proposed coefficient of determination both analytically and numerically. We evaluate and compare performances of the proposed and nine existing coefficients of determination by a comprehensive Monte Carlo simulation study. The proposed measure is found superior to the existent measures when dependent variable is balanced or moderately unbalanced for probit, logit, and complementary log–log link functions and a wide range of sample sizes. Due to the extensive design space of our simulation study, we identify new conditions in which previously recommended coefficients of determination should be used carefully.     

函数数据聚类分析方法探析

函数数据是目前数据分析中新出现的一种数据类型,它同时具有时间序列和横截面数据的特征,通常可以描述为关于某一变量的函数图像,在实际应用中具有很强的实用性。首先简要分析函数数据的一些基本特征和目前提出的一些函数数据聚类方法,如均匀修正的函数数据K均值聚类方法、函数数据层次聚类方法等,并在此基础上,从函数特征分析的角度探讨了函数数据聚类方法,提出了一种基于导数分析的函数数据区间聚类分析方法,并利用中国中部六省的就业人口数据对该方法进行实证分析,取得了聚类结果。     

A New Quantile Function with Applications to Reliability Analysis

In this article, we propose a new class of distributions defined by a quantile function, which nests several distributions as its members. The quantile function proposed here is the sum of the quantile functions of the generalized Pareto and Weibull distributions. Various distributional properties and reliability characteristics of the class are discussed. The estimation of the parameters of the model using L-moments is studied. Finally, we apply the model to a real life dataset.     

Modeling wind energy flux by a Birnbaum–Saunders distribution with an unknown shift parameter

In this paper, we discuss a Birnbaum–Saunders distribution with an unknown shift parameter and apply it to wind energy modeling. We describe structural aspects of this distribution including properties, moments, mode and hazard and shape analyses. We also discuss estimation, goodness of fit and diagnostic methods for this distribution. A computational implementation in R language of the obtained results is provided. Finally, we apply such results to two unpublished real wind speed data from Chile, which allows us to show the characteristics of this statistical distribution and to model wind energy flux.     

Quantile based reliability aspects of partial moments

Partial moments are extensively used in literature for modeling and analysis of lifetime data. In this paper, we study properties of partial moments using quantile functions. The quantile based measure determines the underlying distribution uniquely. We then characterize certain lifetime quantile function models. The proposed measure provides alternate definitions for ageing criteria. Finally, we explore the utility of the measure to compare the characteristics of two lifetime distributions.     

An improved estimator to analyse missing data

Missing data due to nonresponse, though undesirable, is a reality of any survey. In this paper we consider a situation in which, at a given time, observations are missing for one of the several auxiliary characteristics; thus the ‘missing’ phenomenon occurs for the characteristics separately but not simultaneously. A new method, making use of all the available observations, is proposed. A simulation study based on three real populations was performed to test the proposed technique.     

Fitting three-dimensional Laguerre tessellations to foam structures

Foam models, especially random tessellations, are powerful tools to study the relations between the geometric structure of foams and their physical properties. In this paper, we propose the use of random Laguerre tessellations, weighted versions of the well-known Voronoi tessellations, as models for the microstructure of foams. Based on geometric characteristics estimated from a tomographic image of a closed-cell polymer foam, we fit a Laguerre tessellation model to the material. It is shown that this model allows for a better fit of the geometric structure of the foam than some classical Voronoi tessellation models.     

A class of distributions with the linear mean residual quantile function and it’s generalizations

In the present paper, we introduce and study a class of distributions that has the linear mean residual quantile function. Various distributional properties and reliability characteristics of the class are studied. Some characterizations of the class of distributions are presented. We then present generalizations of this class of distributions using the relationship between various quantile based reliability measures. The method of L-moments is employed to estimate parameters of the class of distributions. Finally, we apply the proposed class of distributions to a real data set.     

The First Exit Time Theory Applied to Life Table Data: The Health State Function of a Population and Other Characteristics

In this article, we summarize the main parts of the first exit time theory developed in connection to the life table data and the resulting theoretical and applied issues. New tools arise from the development of this theory and especially the Health State Function and some important characteristics of this function.

We provide both simple and complex models and propose a methodology for reconstructing the health state function from the provided first exit time density distribution (for the appropriate computer program, see http://www.cmsim.net). In the simpler case, this theory is applied for the reconstruction of the so-called Inverse-Gaussian function.     

Monitoring two-stage processes with a profile at the second stage

In the multistage processes, quality of a process or a product at each stage is related to the previous stage(s). This property is referred to as a cascade property. Sometimes, quality of a process is characterized by a profile. In this paper, we consider a two-stage process with a normal quality characteristic in the first stage and a simple linear regression profile in the second stage. Then we propose two methods to monitor quality characteristics in both stages. The performance of the proposed two methods is evaluated through a numerical example in terms of average run length criterion.