In this paper, we introduce six Weibull based mixture distributions to model income data. Several statistical properties of these models are derived and their closed forms are presented. The mixture model parameters are estimated using the maximum likelihood method and their performances are assessed with respect to average income per tax unit data for ten countries using information based criteria

This paper concerns the comparison of two sample non parametric regression. An asymptotically correct simultaneous confidence band (SCB) is proposed for the difference of two-sample non parametric regression functions to achieve the goal of comparison. Simulation experiments provide strong evidence that corroborates the asymptotic theory. The proposed SCB is used to analyze different samples of strata

Exponential smoothing is one of the most commonly used prediction methods. When the data has obvious periodicity and seasonality, Holt–Winters usually has a good prediction performance. However, the predicted results often do not meet our expectations when the trend of the original data is not clear. To further reduce the randomness of time series, a new method combining grey generating operator with

Actuaries are often in search of finding an adequate model for actuarial and financial risk management problems. In the present work, we introduce a class of claim distributions useful in a number of lifetime analyses. A special sub-model of the proposed family, called the Weibull claim model, is considered in detail. Some mathematical properties along with certain characterizations are derived and

Recently Pal et al. introduced a mean estimator which generalized most of the known mean estimators. We introduce a class of estimators that performs better than Pal et al. estimator. Expressions for bias and MSE for the proposed estimator are derived up to first order of approximation. We use the six datasets for numerical comparison.

In this paper, we study the multinomial logistic regression with interactive effects. Our approach involves the implementation of the pliable lasso penalty which allows for estimating the main effects of the covariates X and an interaction effects between the covariates and a set modifiers Z. The hierarchical penalty helps to avoid over-fitting by excluding the interaction effects when the corresponding

Partially linear models attract much attention to investigate the association between predictors and the response variable when the dependency on some predictors may be nonlinear. However, the hypothesis test for significance of predictors is still challenging, especially when the number of predictors is larger than sample size. In this paper, we reconsider the test procedure of Zhong and Chen (2011

The volatility is a measure for the uncertainty of an asset’s return and is used to reflect the risk level of a financial asset. In this article, we consider the double kernel nonparametric estimator for the volatility function in a diffusion model over a finite-time span based on high frequency sampling data. Under the minimum conditions, the asymptotic mixed normality for the underlying estimator

Under a heteroscedastic regression superpopulation (HRS) model considered by Rao, Gupt obtained several model-based allocations including two generalized allocations, one of which is generalized auxiliary variable proportional allocation (GAVPA). In this article, we investigate the problem of optimum stratification for GAVPA under the HRS model. Equations giving optimum points of stratification (OPS)

In this paper, we use the probit distribution to model the degree heterogeneity of the directed networks. We refer this model as the Probit Network Model, in which each edge is independently distributed as a Bernoulli random variable with a success probability measured by the probit function with a set of degree parameters. By using the moment equation to estimate the degree parameters, we establish

In rare disease study, the failure rate is low in a large cohort of subjects due to constraint by funding and research time. Case-cohort design is a widely used sampling scheme for cost-effective study. The weighted pseudo-score (PS) estimators are proposed in the additive hazards model with data generated under case-cohort design. In this article, we present two more effective estimators: the generalized

In this paper, we consider a situation when the population variances of the auxiliary variable in the first stage units selected in a sample are known in addition to the known population means of the auxiliary variable. The higher order calibration weights which make use of both the population variances and population means at the estimation stage for both the first stage units and the second stage

The moving block bootstrap can be used to determine critical values for test statistics used to detect a change-point in the marginal distribution of a stationary time series. We examine the impact of incorporating an estimator of the change-point when centering the bootstrap blocks and establish conditions under which the bootstrapped test statistics remain stochastically bounded regardless of whether

We propose two new regressions based on the generalized odd log-logistic log-normal distribution allowing for positive and negative skewness to model bimodal data. The first one is the parametric regression and the second one is an additive partial linear regression. The new regressions aim to estimate the linear and non-linear effects of covariables on the response variable and generalize some existing

We propose two new improved class of difference type estimators for population median under simple random sampling (SRS) and two-phase sampling (TPS). Expressions for bias and MSE are derived up to first order of approximation. We make a comparison of proposed estimators with all other commonly known estimators in literature. Numerical findings show that the proposed class of estimators perform better

We consider the nonparametric analysis of length-biased and right-censored data (LBRC) by quantile difference. With its desirable properties such as superior robustness and easy interpretation, quantile difference has been widely used in practice, in particular, for missing and survival data. Existing approaches for nonparametric estimation of quantile difference in length-biased survival data, however

It is critical to incorporate additional information of parameters into the simultaneous estimation process. In this paper, we propose a new confidence method that utilizes the information on parameter priority and keeps the elegance and simplicity of Holm’s weighted testing procedure. The new method is grounded on the method of random partitions, in conjunction with probability inequalities, to ensure

In the literature, the variable sample size and sampling interval (VSSI) coefficient of variation (CV) chart was shown to have a better statistical performance than the Shewhart (SH) CV chart which uses fixed sample size and sampling interval. The VSSI CV chart adopts more frequent sampling and larger sample size when the process quality deteriorates for quicker detection of a process shift as there

We note that log transformations can be problematic when the variance of the underlying distribution is other than very small. We illustrate these problems in terms of lognormal sampling issues, interval estimation of the mean, and comparison of lognormal and logbinomial distributions with similar means and variances.

Atmospheric dispersion is a process that involves many uncertainties in model parameters, inputs and source parameters. In this article, we present an uncertainty management procedure for the height release at source which is a key parameter in modeling the subsequent dispersal of contamination after a nuclear accident. When setting the initial parameters of a dispersal model, it is difficult to estimate

In this paper, we consider estimation and inference procedures in spatial linear models when some of the covariates are measured with errors. It is assumed that the additive error distributed according to the law belonging to the class of elliptically contoured distributions. The development of the corrected score function with the family of elliptical distributions is the basis for derivation of the

In the paper, we consider the pricing problem of exchange option where the two underlying stocks are correlated and imperfectly liquid. Firstly, we obtain an explicit pricing formula for the exchange option in the incomplete market by Esscher measure transformation. Then, a Bayesian statistical method is proposed to estimate the unknown parameters, since the parameter calibration of exchange option

This article considers the two-sample testing problem of the survival function of the non terminal event time under semi-competing risks data. The empirical likelihood function is constructed for the survival function estimation of the non terminal event time, then maximize it by the PSO (Particle swarm optimization) algorithm to obtain the MLE. For the testing problem, the article develops the empirical

This paper is a study on comparison between coherent systems with independent and heterogeneous components. Specifically, we consider 3-component coherent systems composed of two different types of components where we assume that component lifetimes follow the well-known proportional hazards model. We stochastically compare such systems under different situations and based on some assumptions on the

Under the condition that the Choquet integral exists, we study the complete convergence theorem for negatively dependent random variables under sub-linear expectation space. Two general complete convergence theorems under sub-linear expectation space are obtained, where the coefficient of weighted sum is the general function. This paper not only extends the complete convergence theorem in the traditional

We present analytic expressions (in terms of roots of the underlying characteristic equation) for the steady-state distributions of the number of customers for the finite-state queueing model G e o X / G / 1 / N + 1 with partial-batch rejection policy. We obtain the system-length distributions at a service-completion epoch by applying the imbedded Markov chain technique. Using the roots of the related

In the Inverse Gaussian Regression (IGR), there is a significant increase in the variance of the commonly used Maximum Likelihood (ML) estimator in the presence of multicollinearity. Alternatively, we suggested the Liu Estimator (LE) for the IGR that is the generalization of Liu. In addition, some estimation methods are proposed to estimate the optimal value of the Liu shrinkage parameter, d. We investigate

While empirical Bayes methods thrive in the presence of the thousands of simultaneous hypothesis tests in genomics and other large-scale applications, significance tests and confidence intervals are considered more appropriate for small numbers of tested hypotheses. Indeed, for fewer hypotheses, there is more uncertainty in empirical Bayes estimates of the prior distribution. Confidence intervals have

The classical finite mixture model is an effective tool to describe the lifetimes of the items existing in a random sample which are selected from some heterogeneous populations. This paper carries out stochastic comparisons between two classical finite mixture models in the sense of the usual stochastic order, when the subpopulations follow a wide class of distributions including the scale model,

It is of great importance in both theory and application to test the equality of two covariance matrices Σ1 and Σ2. This article proposes a new robust test based on spatial sign statistic regarding H0:Σ1=Σ2 in high-dimensional setting, and shows that the test statistic is asymptotically normal under elliptical distribution. Besides theoretical properties, simulation results also show that the new test

In this article, we first prove Borel–Cantelli lemma and some strong laws of large numbers for APND random variables. Then, we introduce a new class of dependent random elements, called briefly WAPND, taking values in a separable Banach space. For this new class, we extend some strong laws of large numbers.

This article aims to present the steady-state analysis in finite-buffer M/G/1 queues with starting failures under a randomized control of N-policy. When the system empties, the server is turned off. If the system size reaches the threshold N, the server is turned on with probability p or turned off with probability 1−p. The server needs a startup time before providing service. If the server is started

Evolutionary algorithms (EAs) is a family of population-based nature optimization methods. In contrast to classical optimization techniques, EAs provide a set of approximated solutions for different test suites of optimization and real-world problems in single simulation. In the last few years, hybrid EAs have received much attention by utilizing the valuable aspects of different nature of search strategies

(2020). Preface. Communications in Statistics - Theory and Methods: Vol. 49, Third International Symposium on Stochastic Models in Reliability Engineering, Life Sciences and Operations Management, pp. 3585-3588.

This paper considers the optimization problems for a consecutive-2-out-of-n:G system where n is considered to be fixed or random. When the number of components is constant, the optimal number of components and the optimal replacement time are discussed by minimizing the expected cost rates. Furthermore, we focus on the above discussions again when n is a random variable. We give an approximate value

In this paper, we improve upon the negative binomial randomized response model by implementing a two-stage randomization process. Using the modified estimator of the proportion of members of a population possessing a sensitive attribute, we claim to achieve both better efficiency and better protection. The findings are verified based on extensive simulation study. Then we improvise the technique of

This paper investigates the reliability and sensitivity analysis for a repairable k-out-of-n:G system with retrial of failed components. Such a model has important practical applications in fully automatic systems, and the most typical one is fully automatic manufacturing system. Markov models for availability and reliability of the system whose components are all subject to two failure modes are presented

Although LASSO has been criticized for selecting too many covariates, it is illustrated in this paper that the bigger model chosen by LASSO method is suitable for exploratory research aiming at identifying all potential causes for further scientific investigation. Up to now, all criticisms assume that the covariates are observed without measurement errors, which is not likely to be true in many practical

In analysis of variance (ANOVA) models, it is generally assumed that the distribution of the error terms is normal with mean zero and constant variance σ2. Traditionally, a least square (LS) method is used for estimating the unknown parameters and testing the null hypothesis. It is known that, when the normality assumption is not satisfied, LS estimators of the parameters and the test statistics based

A periodically time varying long memory parameter version of the fixed long memory parameter case local asymptotic normality (LAN) results are implemented here. The process is assumed to be invertible and causal for simplicity. We prove that the general condition of LAN is verified by our model. The simulation experiment is carried out for studying the distribution of the central sequence in LAN property

This paper considers a step-stress accelerated dependent competing risks model under progressively Type-I censoring schemes. The dependence structure between competing risks is modeled by a general bivariate function, the cumulative exposure model is assumed and the accelerated model is described by the power rule model. The point and interval estimation of the model parameters and the reliability

For a multicomponent system, a maintenance strategy based on system structure updating and group importance measure is proposed. First, a system structure is determined by redefining its component grades, furthermore, the system structure updating is realized by introducing its survival signature. And based on the current system structure, a corrective maintenance that combines sequentially minimal

In this article, complete and complete integral convergence theorems are obtained for arrays of row wise widely negative dependent random variables under the sub-linear expectations. We improve the results by (Lin and Feng 2019 Lin, Y. W., and X. W. Feng. 2019. Complete convergence and strong law of large numbers for arrays of random variables under sublinear expectations. Communications in Statistics:

Let X(t) be a time-homogeneous jump-diffusion process. We assume that the jump size depends on the value of X(t). We obtain analytical results for the moments of T(x) and of X(T(x)), where T(x) is the first time that the process leaves the interval (a, b). We also compute P[X(T(x))≤a]. These results have applications in financial mathematics.

Medical costs are often skewed to the right, heteroscedastic, and having a sophisticated relation with covariates. Moreover, medical cost datasets are always massive, such as in the New York Statewide Planning and Research Cooperative System Expenditure Study. Different observations can depend on each other as the spatial distribution of diseases induces complex correlation among patients coming from

We propose a new symmetric extension of the bivariate Farlie-Gumbel-Morgenstern (FGM) copula with given marginals. The main feature of this new extension is the higher dependence level it permits between random variables. It is shown that the range of Spearman’s Rho is [−.33, 1]. We use this new extension to estimate reliability in a dependent stress-strength model with an application to the Egyptian

Exponential type charts are useful tools to monitor the time between events in high-quality processes with a low defect rate. Most studies on exponential charts are designed with the average run length (ARL) metric. The only use of ARL in the design of control charts is sometimes criticized because the shape of the run length (RL) distribution of control charts changes with the shift size. In fact

Partially linear models attract much attention to investigate the association between predictors and the response variable when the dependency on some predictors may be nonlinear. However, the hypothesis test for significance of predictors is still challenging, especially when the number of predictors is larger than sample size. In this paper, we reconsider the test procedure of Zhong and Chen (2011

Abstract Many economic theories suggest that the relation between two variables y and x follow a function forming a convex or concave curve. In the classical linear model (CLM) framework, this function is usually modeled using a quadratic regression model, with the interest being to find the extremum value or turning point of this function. In the CLM framework, this point is estimated from the ratio

Hazard models with cubic spline functions have a number of advantages to the existing regression models. For analysis of right-censored data, we introduce a penalized Cox regression method using five M-spline basis functions. The proposed spline model is more flexible than the existing parametric models as it produces the increasing, decreasing, convex, concave, and constant hazard functions. To illustrate

This paper is concerned with high-dimensional asymptotic results for W- and Z- rules when the sample size N and the dimension are large. Firstly, we give a unified location and scale mixture expression of the standard normal distribution for W and Z statistics. Then, the EPMCs (Expected Probability of Misclassifications) of W- and Z- rules are obtained in expanded forms with errors of O(N−2). It is

In a generalized random graph with random vertex weights, we investigate the asymptotic behaviors for two crucial empirical measures: The empirical pair measure, which represents the number of edges connecting each pair of weights, and the empirical neighborhood measure, which interprets the number of vertices of a given weight connected to a given number of vertices of each weight. By some mixing

For panel data models with spatial errors, the empirical likelihood ratio statistics are constructed for the parameters of the models. It is shown that the limiting distributions of the empirical likelihood ratio statistics are chi-squared distributions, which are used to construct confidence regions for the parameters of the models. A simulation study is conducted to show the performance of the proposed

Survival data with ultrahigh-dimensional covariates have been frequently encountered in medical studies and other fields. In this article, we propose a non-marginal feature screening procedure for the additive hazard model with ultrahigh-dimensional covariates. The proposed method utilizes the joint effects between covariates, which can effectively identify active covariates that are jointly dependent

Frequentist and Bayesian approaches for interval estimation usually produce conflicting results if applied to analyze the same data set. Paradoxically, there is no unanimity in the literature on whether frequentist and Bayesian approaches are indeed concurrent theories. Thus, a fundamental question arises: frequentist and Bayesian approaches for interval estimation could be somehow reconciled? This

This paper explores how localized mixture models can be used for prediction using time series data. The estimation method presented in this study is a kernel-weighted version of an EM-algorithm, where exponential kernels with different bandwidths are used as weight functions. Nadaraya–Watson and local linear estimators are used to carry out localized estimations. Furthermore, in order to demonstrate

In this paper, a semiparametric mixture of regression models is proposed, where the regression functions are partially linear additive while the mixing proportions and variances are unknown constant. The asymptotic normality of the SBK estimators and the model selection consistency of the proposed BIC based on B-spline estimators are established. Simulations and applications are presented to illustrate

The aim of this article is to extend the inactivity probability order, defined by Abouelmagd et al. (Communications in Statistics-Theory and Methods 47, 3293–3304, 2018), to the case of non independent random variables. It is done by defining a new stochastic order based on the inactivity times of two non negative dependent random variables and the stochastic precedence order. Some characterizations

The present article proposes three series of partially balanced incomplete constant block sum designs constructed using regular graphs. Two series develop a three-associate class PBIB designs and one develops a five-associate class PBIB design. Moreover, we were able to show the existence of constant block sum PBIB designs with their parameters for a specified association scheme. Towards the end, we

A supersaturated design (SSD) is a factorial design whose run size is not enough for estimating all the main effects. Such designs have received much recent interest because of their potential in factor screening experiments. This paper first shows that the design obtained by the Kronecker sum of a balanced design and a generalized Hadamard matrix (i.e., a matrix with both itself and its transpose