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The purpose of this note is to point out a problem related to stress-strength models in some published papers. This difficulty has occurred in the asymptotic variance of the maximum likelihood estimator of the stress-strength parameter. The asymptotic variance will be studied in general and then in the mentioned papers. Finally, the correct version of asymptotic variance is computed. [ABSTRACT FROM AUTHOR]

This document is a letter to the editor addressing a typographical error in the formulas for the double Pareto-lognormal distribution and the normal-Laplace distribution. The authors clarify that the formulas themselves are correct, but there was an error in the expression of the Mills ratio in the correction by Amini and Rabbani. The authors provide the correct formulas for both distributions and offer further explanation upon request. The authors are affiliated with Juraj Dobrila University of Pula in Croatia. [Extracted from the article]

In this paper new filters for removing unspecified form of heteroscedasticity are proposed. The filters build on the assumption that the variance of a pre-whitened time series can be viewed as a latent stochastic process by its own. This makes the filters flexible and useful in many situations. A simulation study shows that removing heteroscedasticity before fitting a model leads to efficiency gains and bias reductions when estimating the parameters of ARMA models. A real data study shows that pre-filtering can increase the forecasting precision of quarterly US GDP growth. [ABSTRACT FROM AUTHOR]

The paper of Erich Lehmann (Lehmann 1953) is renowned for its ground-breaking contribution to rank tests within the area of nonparametric statistics. This work, in all likelihood, is known to every statistician. But, what is likely not known to many are some of the novel concepts and models that this paper succinctly introduced to the area of distribution theory. This, unfortunately, has led to some of these being rediscovered in the literature and then being referred to under different names. The purpose of this note is, therefore, two-fold: first to explain the key models that are contained in the mentioned work of Erich Lehmann, and second to point out how some of the known models discussed in the distribution theory and stochastic modeling literature are indeed present either explicitly or implicitly in the paper of Lehmann. [ABSTRACT FROM AUTHOR]

In this paper, a new criterion is constructed for testing hypothesis about covariance function of Gaussian stationary stochastic process with an unknown mean. This criterion is based on the fact that we can estimate the deviation of covariance function from its estimator with a given accuracy and reliability in Lp metric. [ABSTRACT FROM AUTHOR]

This paper presents a flexible family of 2- and 3-parameter distributions whose support is the closed interval [0,1], with explicit density, cumulative density, and quantile functions. These distributions are suited to modeling quantiles, thereby expanding the toolbox of distributions for doubly-bounded random variables. The densities at the boundaries are determined by dispersion and skew parameters, and a third parameter exclusively influences location. The paper also discusses practical issues of parameter estimation and assesses estimation bias, Type I error-rate accuracy, and parameter-estimate collinearity. It also provides three examples of applications to real data using new packages implementing the distributions in R and Stata. [ABSTRACT FROM AUTHOR]

AbstractThis paper investigates a scheduling imperfect maintenance policy for an operating system that works at random times for multiple jobs (n tandem jobs or n parallel jobs). We consider the system suffers from type-I failure which is corrected by a minimal repair, or type-II failure, which is disaster and is eliminated by a corrective maintenance. To control the deterioration process, preventive maintenance is design to go through at a scheduling time T or the completion of multiple jobs, whichever occurs last. Each maintenance is performed imperfectly, the system improves yet its failure characteristic is also changed after maintenance. Lastly, the system is displaced at the N-th maintenance. On the basis minimizes the mean cost rate, this paper derived the optimal scheduling parameters (T*, n*, N*) analytically and numerically, according to its existence and uniqueness. The models we proposed will provide a general structure for maintenance theory of reliability. [ABSTRACT FROM AUTHOR]

As the most widely-used data form in the field of finance, the open-high-low-close (OHLC) data is being collected by all kinds of financial trading systems all the time. This paper puts forward a pseudo-principal component analysis (PCA) for multi-dimensional OHLC data, which can extract their useful information in a comprehensible way for visualization and easy interpretation. Firstly, a novel feature-based representation for OHLC data is proposed, which contains fruitful and explicit economic implications. Next, we define a full set of numerical characteristics and variance-covariance structures for the feature-based OHLC data. Then, the pseudo-PCA procedure for OHLC data is deduced based on the proposed algebraic operators. Finally, the effectiveness and interpretability of the proposed pseudo-PCA method are verified through finite simulations and three typical empirical experiments. This paper enriches the application scenarios of classical PCA and contributes to the multivariate statistical modeling of symbolic data. The proposed applications can serve as models for related studies. [ABSTRACT FROM AUTHOR]

In this paper, we introduce the notion of strongly generalized convex functions which is called as strongly η-convex stochastic processes. We prove the Hermite-Hadamard, Ostrowski type inequality, and obtain some important inequalities for above processes. Some previous results are special cases of the results obtained in this paper. [ABSTRACT FROM AUTHOR]

In this paper, we propose to consider the dependence structure of the trade/no trade categorical sequence of individual illiquid stocks returns. The framework considered here is wide as constant and time-varying zero returns probability are allowed. The ability of our approach in highlighting illiquid stock's features is underlined for a variety of situations. More specifically, we show that long-run effects for the trade/no trade categorical sequence may be spuriously detected in presence of a non-constant zero returns probability. Monte Carlo experiments, and the analysis of stocks taken from the Chilean financial market, illustrate the usefulness of the tools developed in the paper. [ABSTRACT FROM AUTHOR]

This paper focuses on the likelihood ratio test (LRT) statistics for different hypothesis tests. Assuming that a random sample is from a normal population, we make the sample size n and the dimension p close to infinity and satisfy p < n − c for some 1 ≤ c ≤ 4. Based on this assumption, the moderate deviation principle (MDP) for the LRT will be given under the null hypothesis. The corresponding numerical simulation results are shown at the end of the paper. [ABSTRACT FROM AUTHOR]

In this paper, the seven equivalent conditions of complete moment convergence and complete integral convergence for m -asymptotic negatively associated ( m -ANA, for short) random variables are established. The results obtained in the paper extend and improve some corresponding ones for negatively associated (NA, for short) random variables and negatively orthant dependent (NOD, for short) random variables. As an application of our main results, we present a result on complete consistency for the weighted estimator in a nonparametric regression model based on m-ANA errors. We perform a numerical simulation to verify the validity of the theoretical results. [ABSTRACT FROM AUTHOR]

In several papers, conditional variance and left truncated variance have been studied by several authors. Since one of the most important types of systems structures is the parallel structure, in this paper, we obtain conditional covariance and variance of this system consisting of n identical and independent components under the condition that, at time x, all components are still working. Moreover a lower bound for variance residual life is given and furthermore, we check its behavior. Furthermore, as an aplication, we obtain lower bounds for varextropy. Also we obtain varextropy of a parallel system and the results of the varextropy of order statistics are applied to construct a test for symmetry. A real dataset is examined to illustrate the empirical performance of the proposed test statistics. [ABSTRACT FROM AUTHOR]

The redundancy allocation problem is to find an optimal allocation of redundant components by considering the set of resources and cost constraints. In this research, the satellite attitude determination and control system is studied and its components is introduced, then the reliability of this system is modeled and optimized based on a mathematical approach based on the redundancy allocation. The model studied in this paper is about the structure of a series-parallel system that is in the exact mode of a satellite attitude determination and control system. In this paper, a new approach for modeling and optimization is presented. The mathematical model presented in this paper is into the class of mixed integer non-linear programming (MINLP). Solving these problems is very important for various researchers due to the high mathematical complexity. In this research, a heuristic method is used to the problem exact solution, the results of which have been reported. [ABSTRACT FROM AUTHOR]

In this paper we show how a variant of Stone and Brook's continuum regression criterion may be used to define the least variance ratio estimator of the slope parameters of the simultaneous equations model of econometrics. As a by-product of this approach we identify a family of estimators (distinct from the family of k-class estimators) to which it and two variants of the orthogonal least squares estimator belong. We also take the opportunity to mention several features of linear unbiased scalar residuals omitted from an earlier paper. [ABSTRACT FROM AUTHOR]

In this paper, a three components repairable system with K-mixed redundancy strategy is proposed, in which the lifetimes of components, the repair time of failure components and the vacation time are distributed with different phase-type (PH) distributions. The different phases can represent different operational levels, repair levels and vacation levels. The multiple vacation policy is also adopted so that the human resources can be fully utilized. The repairable system is studied in both transient and stationary regimes with the matrix-analytic method, and not only some traditional reliability indexes are obtained, but also several new reliability indexes are obtained by employing Kronecker operator theory and aggregated stochastic theory. Finally, a numerical example is implemented to illustrate the results obtained in the paper. [ABSTRACT FROM AUTHOR]

This paper investigates the power performance of five tests, including improved versions of two existing tests, for jointly testing the equality of origin and scale parameters of two samples from a shifted (two-parameter) exponential distribution. The power of the test varies with a shift in either or both of the two parameters. Therefore, a power surface is observed for various tests. Different tests are optimal for different shift sizes. This paper also compares the volume under the five tests' power surfaces to determine an overall best when the shift size is unknown. The generalized likelihood ratio (GLR) test, the Bayoud and Kittaneh test based on Weitzman's overlapping coefficient, recently designed Max and Distance tests, and an improved likelihood-based procedure are compared. The shifted exponential distribution is often an appropriate probability model for the lifetime of a product with a warranty, high voltage current in specific semiconductor transistors, and military personnel vehicles' mileages that failed in operation. The number of survival days for patients with irreversible lung cancer often follows the same distribution. This distribution plays a vital role in the engineering and biomedical sciences. We observe that the newly designed tests and the exact GLR test are almost always preferable to the other tests. We illustrate the proposed exact test procedures with two practical examples. [ABSTRACT FROM AUTHOR]

Record linkage is the process of matching together records from different data sources that belong to the same entity. Record linkage is increasingly being used by many organizations including statistical, health, government etc. to link administrative, survey, and other files to create a robust file for more comprehensive analysis. Therefore, it becomes necessary to assess the ability of a linking method to achieve high accuracy or compare between methods with respect to accuracy. In this paper, we evaluate the accuracy of individual link using varying block sizes and different cutoff values by utilizing a Markov Chain based Monte Carlo simulation approach (MaCSim). MaCSim utilizes two linked files to create an agreement matrix. The agreement matrix is simulated to generate re-sampled versions of the agreement matrix. A defined linking method is used in each simulation to link the files and the accuracy of the linking method is assessed. The aim of this paper is to facilitate optimal choice of block size and cutoff value to achieve high accuracy in terms of minimizing average False Discovery Rate and False Negative Rate. The analyses have been performed using a synthetic dataset provided by the Australian Bureau of Statistics (ABS) and indicated promising results. [ABSTRACT FROM AUTHOR]

In a recent paper, Yu (2021) define a k = (k 1 , k 2 , ... , k d) -th order derivative of self-intersection local times with respect to d-dimensional fractional Brownian motion. By the existence and Hölder continuity proved in Yu (2021), we study the smoothness of derivative of self-intersection local times with respect to fractional Brownian motion in this paper. We also consider the cases of intersection local times and collision local times, respectively. [ABSTRACT FROM AUTHOR]

First-order rotatable designs for the lifetime response with distributions such as lognormal, Weibull, gamma, and exponential, assuming autocorrelated errors have been studied. A first-order model in practice is an adequate approximation to the true unknown surface in a small region of the explanatory variables x's. For an unknown experimental region or a system with any curvature, then the second-order model is always appropriate. It is aimed herein to extend the above ideas in the current paper for second-order models. Second-order lifetime correlated models along with rotatability conditions have been derived in the paper. Invariant (independent of the above considered four distributions) robust (independent of the correlation parameter values) second-order rotatable designs have been derived for the autocorrelated error structure. The derived designs in the paper are robust second-order rotatable for all values of the autocorrelation coefficient, and for all the above considered four lifetime distributions. The present derived designs in the paper satisfy four lifetime distributions with autocorrelated errors, while the usual uncorrelated second-order designs are unable to satisfy the similar conditions. In this sense, the current designs are most appropriate for lifetime improvement experiments. [ABSTRACT FROM AUTHOR]

The logrank test is a well-known nonparametric test which is often used to compare the survival distributions of two samples including right-censored observations, it is also known as the Mantel-Haenszel test. The G ρ family of tests, generalizes the logrank test by using weights assigned to observations. In this paper, we present a switch monotonicity property for the G ρ family of tests, which was motivated by the need to derive bounds for the test statistic in case of imprecise data observations. This property states that, when all observations from two independent groups are ranked together, the value of the z-test statistic is monotonically increasing after switching a pair of adjacent values from the two groups. Two examples are provided to motivate and illustrate the result presented in this paper. [ABSTRACT FROM AUTHOR]

Various objective priors have been defined for the common correlation coefficient concerning several bivariate normal populations. In this paper, the proposed approach relies on the asymptotic matching of coverage probabilities corresponding to Bayesian credible intervals considering the corresponding frequentist ones. In the present paper, we focus on several matching criteria including quantile matching, distribution function matching, highest posterior density matching, and matching via inversion of test statistics. In addition, we consider reference priors for different groups of ordering. The proposed methods are investigated and compared between each other in terms of a frequentist coverage probability and then, they are illustrated through a simulation study and two real data examples. [ABSTRACT FROM AUTHOR]

Recently, multi-regional trials have attracted much attention from sponsors as well as regulatory authorities. For researchers, it is always concerned about how to design a multi-regional trial. The fixed effect model is usually used to design a multi-regional trial. These methods were based on the assumption that true effect size is uniform across regions. However, this assumption is based on no ethnic or environmental factor among regions. In practice, it is necessary to consider the existence of ethnic or environmental factor among regions for a multi-regional trial. The random effect model is employed to deal with the heterogeneous effect size among regions. However, Most papers focus on multi-regional trials for three regions. In this paper, the multi-regional trials by a fixed effect model and a random effect model for four or five regions are designed and evaluated. The design of the multi-regional trials is evaluated by the proposed criteria considering the number of the regions. The assurance probability of proposed criteria considering the number of the regions is employed to determine if the clinical design is suitable for a multi-regional trial. More regions in a multi-regional trial can detect the variation among the regions more easily. [ABSTRACT FROM AUTHOR]

In this paper, the complete convergence for maximum of weighted sums of widely negative orthant dependent (WNOD) random variables are investigated. Some sufficient conditions for the convergence are provided and a relationship between the weight and the boundary function is revealed. Additionally, a Marcinkiewicz-Zygmund type strong law of large number for weighted sums of WNOD random variables is obtained. The results obtained in this paper generalize some corresponding ones for independent and some dependent random variables. As an application, the strong consistency for the weighted estimator in a non-parametric regression model is established. MR(2010) Subject Classification: 60F15; 62G05. [ABSTRACT FROM AUTHOR]

In this paper, we consider the kernel method to estimate sliced average variance estimation (SAVE). SAVE is a tool as SIR (sliced inverse regression), recommended to identify and to estimate the central dimension reduction (CDR) subspace. CDR subspace is the intersection of all dimension reduction subspaces which are at the base to describe the conditional distribution of the response Y given a d − dimensional predictor vector X. SAVE and even SIR are used to estimate CDR subspace. Two versions are very popular: slice version and kernel version. In this paper, we are looking at the kernel version. For Kernel SAVE version, two asymptotic properties have been demonstrated in particular: asymptotic normality and convergence in probability. And we know that these two properties, although important, are weak in front of almost sure convergence. However, until now, the strong consistency has not yet been obtained. In this paper, we obtain, under weaker assumptions, this asymptotic property. [ABSTRACT FROM AUTHOR]

The derivation of the sample covariance is difficult compared to that of the distribution of the sample correlation coefficient. This paper deals with the distributions of covariance structures appearing in real scalar/vector/matrix variables. Covariance structure is a bilinear structure. Consider a bilinear form u = X ′ A Y where X and Y are p × 1 and q × 1 real vectors and A is a constant p × q matrix. The basic aim in this paper is to derive the distribution of such a structure when the components are scalar/vector/matrix Gaussian variables. The procedure used is to examine the Laplace transform or the moment generating function (mgf) coming from such a bilinear form in real scalar/vector/matrix variables. Covariance structures in several situations are shown to produce a mgf of the type (1 − λ 2 t 2) − α , λ > 0 , α > 0 , − 1 λ < R (t) < 1 λ where t is the mgf parameter, R (·) means the real part of (·) , and λ and α are real scalar parameters. Explicit evaluation of the density of u is considered when α is a positive integer as well as for a general α. It is shown that the exact densities can be written as linear functions of double gamma densities and double exponential or Laplace densities when α is a positive integer. For the general value of α, it is shown that the exact density can be written in terms of double Mittag-Leffler or a double confluent hypergeometric function. [ABSTRACT FROM AUTHOR]

Sensitivity analysis of random systems may convey important information on the dynamical properties of the system. In this paper, we determine the effects of parameters' perturbation on two dynamic poverty indexes: the headcount ratio and the income gap ratio. This is achieved by perturbing the generator of the Markov process governing the evolution in time of the economic agents among three classes of income, the initial distribution of individuals and the vector of mean income for poverty class. The paper presents two bounds on the aforementioned poverty indexes which show how the perturbations on the model parameters propagate on the poverty indexes. The paper contributes to the literature presenting for the first time effective bounds for dynamic poverty indicators and exploring the applicability of the perturbation approach to real data. [ABSTRACT FROM AUTHOR]

This paper examines the problem of stochastic comparisons of series and parallel systems with independent heterogeneous new extended Weibull distributed components. For series systems, we obtain the usual stochastic order via the concepts of weak weighted and unordered majorization orders. Also, we strengthen this result to the hazard rate order under a restriction. For parallel systems, with the help of weak supermajorization and weak submajorization orders, we establish the usual stochastic order. The results of this paper can be used to find some bounds for the important aging characteristics of series and parallel systems consisting of independent heterogeneous new extended Weibull distributed components. [ABSTRACT FROM AUTHOR]

Kageyama (1972) presented a survey of resolvable solutions of balanced incomplete block designs. Clatworthy (1973) produced tables of two associate classes partially balanced designs in the practical range of r, k ≤ 10 and presented resolvable solutions whenever possible. Here, the minimum α (≤1) – resolvable solutions of partially balanced designs not found in Clatworthy (1973) and Saurabh and Sinha (2020) are presented. This paper is in sequel to the paper by Saurabh and Sinha (2020). [ABSTRACT FROM AUTHOR]

The beta generator technique entails constructing a univariate distribution function as a composite function of two distribution functions. The success of this technique in the univariate setting has prompted research into the possibility of generalization to the bivariate case. Such a generalization, using copulas, has already been proposed in the literature. In this paper, we construct bivariate distribution functions by passing a bivariate distribution function as an argument to the univariate beta distribution function. The class of distributions obtained is identical to an existing class of distributions; however, the elementary elements of the two classes differ (i.e., some distributions are simple to construct using one of the techniques considered and difficult to construct using the other). This paper provides a rigorous derivation of the parameter space of the beta-generated distributions, as well as a result relating to the dependence structure of the marginals. Finally, a practical example is included demonstrating the use of a beta-generated distribution in the modeling of observed losses in the energy market. [ABSTRACT FROM AUTHOR]

This paper studies the problems of optimally allocating one/two active redundancies to series systems in the sense of stochastic orders. For the case of allocating one redundancy to a series system, we show that allocating the redundancy to the weaker component can lead a longer system's lifetime in the sense of the hazard rate and reversed hazard rate orders. For two redundancies case, we also demonstrate that allocating the relatively stronger redundancy to the weaker component can lead a longer system's lifetime in the sense of the hazard rate and reversed hazard rate orders. These results generalize and strengthen the results of several papers. Finally, two applications are also presented to illustrate our results. [ABSTRACT FROM AUTHOR]

The Tsallis entropy has high performance in handling uncertain information, which is the extension of information entropy. The extropy is a complementary dual of entropy, which is a research hot spot. This paper proposed the Tsallis eXtropy and maximum Tsallis eXtropy, which are the complementary of Tsallis entropy and maximum Tsallis entropy respectively. When the non-extensive parameter is equal to 1, then the Tsallis eXtropy and the maximum Tsallis eXtropy will degenerate into information extropy and maximum information extropy respectively. Some meaningful theorems and proofs of the Tsallis eXtropy and the maximum Tsallis eXtropy has been proposed. Numerical examples have been designed to prove the effectiveness of the proposed models in evaluating uncertainties. Comparison application has been applied to prove the superiority of the proposed models than other models. The experimental results have shown that the proposed models are very high effective in measuring unknown issues. [ABSTRACT FROM AUTHOR]

The Exchange Market Pressure Index (EMPI) is an indicator of pressure on a currency. Because of the presence of serial correlation, financial time series may not be normally distributed even for large sample sizes. They may have undefined parameters and hence parametric tests of normality may give misleading results. In this paper, we look at the time series of EMPI of eleven countries of the world, put the data to normality check using tests suggested by various scholars. We also apply a test used exclusively for serially correlated data. No one has used this test earlier. In this context, we also compare the power of these statistical tests, which is another novel contribution of this paper. On the basis of these tests the EMPI time series is found to be non-normal. Two tests are found to be the most powerful. The test which is designed exclusively for time series data is found to be powerful only for China and South Korea, the countries which had the lowest EMPI- standard- deviation in the group of all the eleven countries studied in this paper. [ABSTRACT FROM AUTHOR]

In this paper, we propose a least-squares estimator based on Logistic transformation of order statistics (LLSE) and grouped LLSE for the generalized Logistic distribution. Some asymptotic results are provided. Two simulations are undertaken to assess the performance of the proposed method and to compare them with other methods suggested in this paper. The simulation results indicate that LLSE performs better than some other methods and grouped LLSE performs fairly well in small sample size. Finally, LLSE is applied to a real dataset. [ABSTRACT FROM AUTHOR]

Linear Hawkes processes are widely used in many fields and means are the basic and critical information of them. However, there is little research on linear Hawkes processes' means. In this paper, we present a numerical method based on the Laplace transform and inverse Laplace transform for means of linear Hawkes processes. The advantage of this method is that whatever the kernel function is, we can always obtain the numerical solutions of means for a linear Hawkes process. In addition, this numerical method provides the basic information of linear Hawkes processes by means. As an application, the numerical method is applied in a WeChat network model. [ABSTRACT FROM AUTHOR]

In the real world, monitoring the number of transactions between nodes in many networks such as transportation, sales, financial communications, etc. is very important, from which network stakeholders can enjoy significant benefits, as well. The present paper attempts to show a significant reduction in the performance of the statistical methods in detecting network anomalies resulting from losing information due to disregarding the weights of edges in the case of modeling and monitoring weighted networks through using binary models. This paper focuses on and applies normal distribution in a real non social network because the statistical distribution of edges in most weighted networks is normal. The performance of the statistical model in the form of a case study, monitoring electronic components exchange network in a repair company, is described. Using simulation, the ability of the model in detecting network anomalies is compared with the binary model. [ABSTRACT FROM AUTHOR]

A new class of statistics obtained by ordering the absolute values of the observations arising from absolutely continuous distributions which are symmetrically distributed about zero is introduced in this paper. The statistics generated by the above method are named as absolved order statistics (AOS) of the given sample. The association of the distribution of these statistics with the distribution of order statistics arising from the folded form of the parental density about zero is outlined. The vector of AOS is proved to be a minimal sufficient statistic for the class F θ (1) of all absolutely continuous distributions which are symmetrically distributed about zero. A method of estimation of the scale parameter of any distribution belonging to F θ (1) using AOS is described. Illustration on the advantage of the above method of estimation is described for the distributions such as (i) logistic, (ii) normal, and (iii) double Weibull. A more realistic censoring scheme involving AOS as well is discussed in this paper. We have derived the U-statistic estimator based on AOS for the scale parameter σ of any distribution f (x , σ) ∈ F θ (1) using the best linear unbiased estimate (BLUE) based on AOS of a preliminary sample as kernel. We have illustrated the performance of this estimator with an U-statistic generated from BLUE based on order statistics for each of (i) logistic (ii) normal and (iii) double Weibull distributions. [ABSTRACT FROM AUTHOR]

The change point estimation concept is usually useful in time series models. This concept helps to decrease the decision making or production costs by monitoring the stock market and production lines. It is also applied in several fields such as Financing and Quality Control. In this paper, it is assumed that the ARMA (1) model exists between the sample statistics of x ¯ control chart. A maximum likelihood technique is developed to estimate the change point at which the stationary ARMA (1) model changes into a non-stationary process. For the estimation of unknown parameters after the change point, the Smoothing of Dynamic Linear Model has been used based on singular value decomposition. It is assumed that there exists a correlation between sample statistics. Simulation results show the effectiveness of the estimators proposed in this paper to estimate the change point of the stationary state in ARMA (1) model. An example is provided to illustrate the application. [ABSTRACT FROM AUTHOR]

In this paper, we consider the equilibrium excess-of-loss reinsurance and investment problem for both an insurer and a reinsurer. The risk process of the insurer is described by a classical Cramér-Lundberg (C-L) risk model and the insurer can purchase excess-of-loss reinsurance from the reinsurer. Both the insurer and the reinsurer are allowed to invest in a financial market consisting of a risk-free asset and two risky assets. The market price of risk depends on a Markovian, affine-form and square-root stochastic factor process. Dynamic mean-variance criterion is considered in this paper. We aim to maximize the weighted sum of the insurer's and the reinsurer's objectives with different risk averse coefficients. By solving the corresponding extended Hamilton-Jacobi-Bellman (HJB) equations, we derive the equilibrium reinsurance and investment strategies and the corresponding equilibrium value function. Finally, the economic implications of our findings are illustrated. [ABSTRACT FROM AUTHOR]

Pólya urn models are of the well-known probabilistic concepts and stochastic processes. The proportion of the colors is the question of the most interest in these models. Always, the structure (The number of all the balls in the urn and the proportion of the colors) of the urn at the beginning is given. Also, in the studies where the outcome of certain withdrawals is known, these withdrawals are connected to the first structure, and there is no gap between the known structure and the additional information about the color of the withdrawn balls. The existing gap between the first structure and any relevant information motivates this paper. In the present article, we consider the Pólya-Eggenberger urn model. We prove that an urn with an initial known structure after some unknown withdrawals – conditioned to meet an assumption – behaves like an urn with a known structure. By the results of the present paper, we overcome the complexity and ambiguity caused by the unknown withdrawals, and in spite of the lack of information concerning some withdrawals, we deal with the urn as a process that behaves like a completely determined structure. To illustrate the truth of the obtained results, we simulate several urns and survey the variation in the probabilities of the colors. [ABSTRACT FROM AUTHOR]

This paper explores possibilities of applying multiple comparison tests (MCTs) that are commonly used in statistics to group the means once the analysis of variance (ANOVA) procedure rejects the hypothesis that all the means are equal. It is proposed here to apply MCT procedure to perform clustering when the data are repetitive and multidimensional. Since MCT procedure may result in overlapping clusters, we further develop an approach to first form initial clusters and then apply K -means procedure to construct non overlapping clusters. It may be noted that the choice of initial clusters for K -means procedure is still ambiguous. Accordingly, the paper is presented in a sequence covering (i) an algorithm for step-by-step implementation of K -means procedure for clustering, (ii) an algorithm for step-by-step implementation of MCT procedure for clustering and (iii) an algorithm for step-by-step implementation of a combined procedure to resolve the overlapping clusters. Numerical examples including an open data set are considered to demonstrate the algorithms and also to study their performance in terms of total mean square errors. [ABSTRACT FROM AUTHOR]

This paper is concerned with the consistency of nonparametric regression model. For the weighted estimator of unknown regression function, the strong consistency, the complete consistency and the convergence rate of the complete consistency are investigated under some mild conditions. These results extend or improve the corresponding ones of Yang et al. (2018) for extended negatively dependent (END, for short) random variables to asymptotically almost negatively associated random variables. Also, the simulation study of the finite samples provided in this paper shows the validity of our results. [ABSTRACT FROM AUTHOR]

In this paper, we study the asymptotic distribution of the plug-in kernel density estimator of the Matusita's overlapping measure. By utilizing the convergence of functional of stochastic processes, we show, under certain conditions, that the asymptotic distribution of the plug-in kernel density estimator (KDE) of Matusita's overlapping measure is normal distribution. Also, a small simulation study is conducted to support the theoretical finding of this paper. Furthermore, we apply our finding to a breast cancer data. [ABSTRACT FROM AUTHOR]

In this paper, we introduce a new concept of preinvex functions which is called general h-harmonic preinvex for real-valued stochastic processes. Further, we define the multidimensional general h-harmonic preinvex stochastic processes. We prove the Hermite-Hadamard inequality and obtain some important results for these processes. Some previous results are special cases of the results obtained in this paper. [ABSTRACT FROM AUTHOR]

Non-negative limited normal or gamma distributed random variables are commonly used to model physical phenomenon such as the concentration of compounds within gaseous clouds. This paper demonstrates that when a collection of random variables with limited normal or gamma distributions represents a stationary process for which the underlying variables have exponentially decreasing correlations, then a central limit theorem applies to the correlated random variables. [ABSTRACT FROM AUTHOR]

This paper focuses on nonparametric regression modeling of time-series and incomplete observations. In this sense, the observations are subject to both left truncation and right censoring (LTRC) and satisfy an association dependency. Using the well-known kernel estimation method, we establish the strong uniform consistency with a rate of the kernel estimator proposed in this paper. Simulation studies are conducted to assess the impact of both incompleteness and association dependency on the estimation. [ABSTRACT FROM AUTHOR]

Let F be a continuous distribution function and let Q be its associated quantile function. Let Fh be the kernel estimator of F and Qh that of Q. In this article the L2 right inversion distance between Qh and Q is introduced. It is shown that this distance can be represented in terms of Fh and F, more precisely it is established that the right inversion distance is equal to the conventional integrated squared error between Fh and F. This representation shows that any good bandwidth for Fh is a reasonable bandwidth for Qh and, this fact enables us to suggest methods to choose the smoothing parameter of Q h. Let Q h ̂ c v be the kernel estimator of Q equipped with the global crossvalidation bandwidth h ̂ c v designed for F h. Let Q h ̂ p i be the linear kernel estimator of Q, h ̂ p i being the plug-in bandwidth function. A small scale simulation study presented in this paper contains some examples of distributions for which Q h ̂ c v appears to be superior to Q h ̂ p i . This paper also contains some properties of the classical L2 distance between Qh and Q. [ABSTRACT FROM AUTHOR]

Abstract In this paper, we investigate a GI X /M/1 queue with the two-stage vacation policy. The system will first enter a working vacation once the system becomes empty in the normal busy period, during which the service rate will be switched to a lower rate. After this working vacation, if the system is nonempty, the service rate will be switched to the normal rate immediately; otherwise, the system will enter multiple vacations during which the service rate reduces to zero until the system is nonempty after one vacation and a new normal busy period starts. The distinguishing feature of this paper is the use of a general algorithm for solving the difference equation based on the right shift operator method to obtain the queue length distribution at pre-arrival time and arbitrary time. Moreover, the sojourn time of arbitrary customer is analyzed. Finally, several typical numerical examples are provided to validate our computational algorithm. [ABSTRACT FROM AUTHOR]