Abstract Recently, an alternative measure of uncertainty termed by extropy was proposed by Lad et al. Accordingly, a cumulative residual extropy is also introduced by replacing the survival function in place of the density function in the extropy. In this paper, we define negative cumulative extropy (NCEX) measure of information and study several properties of this concept. We then elaborate the NCEX

Abstract We develop a valuation model for mortgage pass-through securities with partial prepayment risk using an intensity-based approach. For the single mortgage contract in a given pool of mortgage loans, the ratio of prepayment amount to outstanding principal at partial prepayment time is described by a stochastic process, and the occurrence time of prepayments is modeled by jump time of a Cox process

Abstract Stochastic precedence order is a natural type of comparison for random variables in numerous engineering applications (e.g., for the stress-strength modeling). In this note, we show that, for a k-out-of-n system, redundancy at the component level is superior to that at the system level with respect to the stochastic precedence order. Cases of active and cold redundancy are considered. Similar

Abstract It often arises in practice that, although the first few moments of a distribution are known, the density of the distribution cannot be determined in closed form. In such cases, Gram-Charlier and Edgeworth series are commonly used to analytically approximate the unknown density in terms of the known moments. Although convenient, these series contain polynomial factors, and can hence lead to

Abstract We consider a general option pricing framework incorporating the double Heston stochastic volatility, stochastic interest rate, jumps and Markov regime switching. Under the proposed framework, we derive the analytical pricing formulae for European options using Fourier transform technique. Numerical examples illustrate that the option prices and the implied volatility curves under different

Abstract In medical research, it is important to compare quantiles of certain measures obtained from treatment and control groups, with the quantile ratio showing the effect of the treatment. In particular, inference of the quantile ratio based on large sample methods can be studied using a normal model. In this paper, we develop noninformative priors such as probability matching priors and reference

Abstract Proportional reversed hazard model and exponentiated distributions have received considerable attention in the statistical literature due to its flexibility. In this paper, we develop the tools for statistical inference of the lifetime distribution of components in a n-component coherent system while the system lifetimes are observed, the system structure is known and the component lifetime

Abstract In this paper, the empirical likelihood-based inference is investigated with varying coefficient panel data models with fixed effect. A naive empirical likelihood ratio is firstly proposed after the fixed effect is corrected. The maximum empirical likelihood estimators for the coefficient functions are derived as well as their asymptotic properties. Wilk’s phenomenon of this naive empirical

Abstract In this paper, the tail properties of the beta-normal distribution and an asymptotic Mills-type ratio are studied. Meanwhile, two applications are presented. The first application obtains the asymptotic behavior of the ratio of probability density functions and the ratio of the tails of the beta-normal and Student’s t distributions. The other one considers the asymptotic distribution of the

Abstract This paper treats the problem of stochastic comparisons of two parallel systems with independent heterogeneous components having lifetimes following exponentiated Kumaraswamy-G model. The cases of same and different parent distribution functions are considered. Majorization type partial orders-based sufficient conditions in comparing the largest order statistics in terms of the usual stochastic

Abstract We propose a frequentist testing procedure that maintains a defined coverage and is optimal in the sense that it gives maximal power to detect deviations from a null hypothesis when the alternative to the null hypothesis is sampled from a pre-specified distribution (the prior distribution). Selecting a prior distribution allows to tune the decision rule. This leads to an increased power, if

Abstract We present some counterexamples of the classical and non-classical bivariate and multivariate normal distributions to widen our knowledge of these distributions. We hope that this paper will provide practitioners and users of bivariate and multivariate normal distributions of better view on the necessary and sufficient conditions leading to bivariate and multivariate normal distributions regarding

Abstract In this article, we propose an ATTRIVAR chart to control the process mean. With the ATTRIVAR chart, the sampling is performed in two stages, collecting attribute and variable sample data from the same sample (attribute plus variable data – ATTRIVAR). That is, if the first m items of the sample fail to pass the go gauge test, or they pass the no-go gauge test, the sampling moves on to stage

Abstract The power law process (PLP) is widely used to analyze the failures of repairable systems, and the PLP parameter estimation is the primary concern for reliability assessment or maintenance decision making. Although the Bayesian estimation of the PLP has been studied in existing research, little attention has been paid to how to obtain its prior distribution, especially when the prior information

Abstract The role of quantile functions in modeling various forms of statistical data is well established. Generally classical procedures like method of moments, L-moments, percentiles etc are employed in estimating the parameters of the model. In the present work an attempt is made to infer parameters in the Bayesian framework with special emphasis to distributions in which the quantile functions

Abstract In this paper, we present some new ordering properties between two parallel systems comprising general independent heterogeneous components. More precisely, let X 1 , ⋯ , X n and Y 1 , ⋯ , Y n be independent non-negative random variables with X i ∼ F ( x ; α i , β i ) and Y i ∼ F ( x ; θ i , λ i ) , i = 1 , ⋯ , n , where F ( . ) is an absolutely continuous distribution function with reversed

Abstract A non-monotonic ageing class based on failure rate average has been introduced and its relationships with existing classes are explored. Closure properties under the basic reliability operations have been discussed and survival probability bounds as well as moment bounds have been derived. We also propose a nonparametric test to detect trend change in failure rate average assuming that proportion

Abstract In this paper, we discuss distributional and asymptotic properties of lower exponential spacings obtained from order statistics taken from progressive type-II censoring samples. We find conditions under which the sequence of logarithmic lower exponential spacings converges in probability and with probability one.

Abstract Measurement errors and missing data are often arise in practice. Under this circumstance, we focus on using jackknife empirical likelihood (JEL) and adjust jackknife empirical likelihood (AJEL) methods to construct confidence intervals for the error variance in linear models. Based on residuals of the models, the biased-corrected inverse probability weighted estimator of the error variance

Abstract In the presented paper, we introduce a partial functional linear model, where a scalar response variable is explained by a multivariate random variable and a functional random variable, and the relationship between the scalar response and both of the predictors is linear. Besides, the model has autoregressive errors. To estimate the model, we first expand the functional predictor and functional

We obain an almost sure limit theorem for the joint version of maxima and minima of a non-stationary random field defined over discrete subsets of R 2 , under some dependence conditions.

It is important to understand the behavior within a social network, particularly excessive communications between nodes. Such excessive activities in a network provide an insight into the pattern of communication between nodes, which, in some cases, could lead to a fraudulent behavior. Scan statistics have been applied before to detect the excessive communications in email networks. However, they alone

Post-selection inference has been an active research topic recently. A lot of work provided different ways to solve practical problems in many fields such as medicine, finance, and so on. In particular, post-selection inference under the linear model is widely discussed. We extend it to generalized linear model and present new approaches for post-selection inference for penalized least squares method

In this article, we develop the estimation of the sensitive attribute proportion of the population which is composed of several clusters by applying unequal probability sampling to the Su et al.’s model which is an adjusted Kuk’s model. We estimate the sensitive parameter, its variance and variance estimator for each unequal probability sampling and two-stage equal probability sampling. We extend our

Aljarrah et al. (2015) [A New Weibull-Pareto Distribution. Communications in Statistics - Theory and Methods, 44:19, 4077-4095] introduced and studied a new Weibull-Pareto distribution based on the quantile of log-logistic distribution.They used the method of maximum likelihood to estimate the parameters of the Weibull-Pareto distribution. But they made some mistakes in presenting the log-likelihood

Sliced orthogonal arrays are useful combinatorial tools that can be used to construct sliced space-filling designs for planning computer experiments with both quantitative and qualitative input variables. A new class of sliced orthogonal arrays called the sliced orthogonal arrays of parallel-flats type is proposed in this paper to address this practical issue. Specifically, a set of sufficient and

In the spectrally negative Lévy risk model, we investigate the absolutely continuous dividend problem with a general discount function, which results in a time-inconsistent control problem. Under the assumptions of a time value of ruin and an exponential time horizon, we study the equilibrium dividend strategies within a game theoretic framework for the return function composed by the discount expected

In this article, we first study the likelihood ratio ordering of generalized order statistics (GOS) in both one-sample and two-sample problems. Then, we establish the transmission of the increasing hazard rate and decreasing reversed hazard rate aging properties of GOS. To do this, we extend Karlin’s basic composition theorem for the functions of three variables. Then, we settle certain open problems

The outliers cause wrong prediction and estimation results in regression models. Therefore, it is important to identify the outliers correctly in the context of regression analysis. Information criteria can be used to perform this task with corrections but these corrected versions of criteria require some subjective parameters. In this article, an objective correction approach is proposed within the

Some new resolvable group divisible designs not found in Clatworthy (1973 Clatworthy, W. H. 1973. Tables of two-associate-class partially balanced designs, Gaithersburg, MD: Natl. Bur, Stand. (U.S.), Appl. Math. Ser: 63. [Google Scholar]), Sinha (1991 Sinha, K. 1991. A list of new Group divisible designs. Journal of Research of the National Institute of Standards and Technology 96:1–3.[Crossref], [Web

High order stop-loss transforms provide a risk measure that enables some flexibility on the weight given to high or low values of the risk. We interpret stop-loss transforms as iterated distributions and prove a recursive representation for risks expressed as convolutions. We apply this to the case of gamma distributions with integer shape parameter, the Erlang distributions, proving that high order

Length-biased sampling data are commonly observed in cross-sectional surveys and epidemiological cohort studies. Due to study design or accident, some components of the covariate vector are often missing. This article considers the statistical inference for the transformation models with length-biased sampling data and missing covariates. The reweighting estimating procedures are proposed for the unknown

Robust high dimensional estimation is one of the most important problems in statistics. In a high dimensional structure with a small number of non-zero observations, the dimension of the parameters is larger than the sample size. For modeling the sparsity of outlier response vector, we randomly selected a small number of observations and corrupted them arbitrarily. There are two distinct ways to overcome

This article proposes a two-sided run sum ratio chart for monitoring the ratio of two normal variables. A Markov chain procedure is applied to evaluate the statistical performance of the chart by using both average run length (ARL) and expected average run length (EARL) criteria. A numerical comparison with the Shewhart ratio and synthetic ratio charts for the zero state analysis reveals that the run

Anisotropic functional deconvolution model is investigated in the bivariate case when the design points ti , i = 1 , 2 , ⋯ , N , and xl , l = 1 , 2 , ⋯ , M , are irregular and follow known densities h 1, h 2, respectively. In particular, we focus on the case when the densities h 1 and h 2 have singularities, but 1 / h 1 and 1 / h 2 are still integrable on [0, 1]. We construct an adaptive wavelet estimator

A control chart for monitoring the multivariate coefficient of variation (MCV) is used when the focus is on monitoring the ratio of relative multivariate variability to the mean of a multivariate process. The MCV chart is useful in process monitoring when practitioners are not interested in the consistency of the mean vector or covariance matrix. This study proposes a one-sided upward variable sampling

In this article, we introduce generalized Mittag-Leffler Lévy (GMLL) process. GMLL distribution is represented as a general Lévy subordinator delayed by a gamma process. We show various properties of this new process like it’s corresponding Lévy density function and the so-called long-range dependence property. We provide also an explicit representation for the cumulative density function (CDF) for

In this study, we consider a new aspect of belief function or Dempster-Shafer theory to define a belief set and cosine similarity measure between two belief sets under uncertainty. For this purpose, firstly, the concept of belief sets will be represented as a triple vector space that is characterized by truth-belief degree, uncertainty-belief degree; and falsity-belief degree. Then, the cosine similarity

In the real world, there are point patterns where the offspring points are asymmetrically scattered around the parent points and have skewness in their locations. However, the existing distributions for the offspring locations in Neyman-Scott processes are usually assumed to be without any skewness in the clusters. This paper introduces a generalization of the Thomas process where the offspring points

The present investigation deals with the estimation of population variance in successive sampling in presence and absence of measurement error. We have suggested a chain type estimator of population variance and compared its performances with natural sample variance estimator in presence and absence of measurement errors. The dominance of the proposed strategies over conventional ones has been demonstrated

The aim of this article is to introduce a hybrid method, based on the combination of Monte Carlo simulation and neural networks, which ensures for a general model an optimal compromise between accuracy and computing time. The major contribution of this work is that the aforesaid improvements are made whatever the hypotheses adopted to simplify the reality of the studied problem. In this article, this

A control chart is an important tool to monitor an industrial process and the use of prior knowledge by Bayesian theory can be helpful in-control charting. In this paper, we have used the Bayesian approach with two different loss function (LF) symmetric and asymmetric loss function namely Linex LF and squared error LF under informative (conjugate) prior and non informative prior (uniform and Jeffery

In this paper, an expression for computing the Pearson’s correlation coefficient between the random upper record value, X and the random number of observations, Y is obtained. Also derived are theoretical results for the joint bivariate probability function (pf) of X and Y , their marginal pf, and an alternate expression (to the correlation coefficient) measuring their dependence, where the support

In logistic regression models, the maximum likelihood method is commonly used to estimate the model parameters. However, unstable parameter estimates are obtained as a result of multicollinearity. In this article, a new biased estimator is proposed to combat multicollinearity in the binary logistic regression models. The proposed estimator is a general estimator which includes other biased estimators

Queueing systems with batch Markovian arrival process (BMAP) have paramount applications in the domain of wireless communication. The BMAP has been used to model the superposition of video sources and to approximate the super-position of data, voice and video traffic. This article analyzes an infinite-buffer generally distributed batch-service queue with BMAP, general bulk service (a, b) rule and

It is shown that in general, with arbitrary levels of quantitative treatment factor, the constant block-sum balanced incomplete block designs do not exist. I then provide, assuming it exists, a general approach to construct a constant block-sum equireplicated block design, possibly with unequally spaced treatments, from the incidence matrix of a block design with same parameters but without constant

For multi-sample covariance testing, the classical likelihood ratio test is often efficient and powerful in low-dimensional normal cases. However, when the dimension is larger than the sample size, it fails to work in practice and theory. This paper proposes a permutation based test to handle high-dimensional covariance testing problem with more than two samples. Numerical studies show that the test

This paper deals with the problem of the nonparametric analysis by the relative-error regression when the explanatory of a variable is of infinite dimension. Based on k-Nearest Neighbors procedure (kNN), we construct an estimator and establish its asymptotic properties. Precisely, we show its Uniform consistency in Number of Neighbors (UNN) with the precision of the convergence rate. Some empirical

This paper presents an innovative Bayesian method for assessing the status and progression of HIV infection using biomarkers such as the CD4 count and viral load variables. A distribution of viral loads in subjects starting antiretroviral treatment and followed over time may show a mixture of two subgroups: one subgroup representing “non-progressor” subjects and another subgroup of “progressor” subjects

The problem of testing the scale parameter (γ) of the power-law process for a single system is taken into account when dealing with incomplete failure data. In this study, the modified signed log-likelihood ratio test is introduced as a method for testing parameter γ. The accuracy of the proposed method is evaluated in the literature. For incomplete failure data, the modified signed log-likelihood

The correlational structure of a set of variables is often conveniently described by the pairwise partial correlations as they contain the same information as the Pearson correlations with the advantage of straightforward identifications of conditional linear independence. For mathematical convenience, multiple matrix representations of the pairwise partial correlations exist in the literature but

In this paper, we investigate the Fisher–Rao geometry of the two-parameter family of Pareto distribution. We prove that its geometrical structure is isometric to the Poincaré upper half-plane model, and then study the corresponding geometrical features by presenting explicit expressions for connection, curvature and geodesics. It is then applied to Bayesian inference by considering the Jeffreys prior

In this paper, we propose the designing methodology of multiple deferred (dependent) state repetitive group sampling plan for lot sentencing when the quality characteristic of the product follows normal distribution. This sampling plan incorporates the features of two existing sampling plans such as multiple deferred (dependent) state sampling plan and repetitive group sampling plan. Under the proposed

In classical linear regression analysis problems, the ordinary least-squares (OLS) estimation is the popular method to obtain the regression weights, given the essential assumptions are satisfied. However, often, in real-life studies, the response data and its associated explanatory variables do not meet the required conditions, in particular under multicollinearity, and hence results can be misleading

The entropy power inequality (EPI) for convolution of two independent random variables was first proposed by Shannon, C. E., 1948. However, in practice, there are many situations in which the involved random variables are not independent. In this article, considering additive noise channels, it is shown that, under some conditions, EPI holds for the case when the involved random variables are dependent

In this paper, a new class of marginally regular multivariate counting processes is developed and its stochastic properties are studied. The dependence of the proposed multivariate counting process is generated from two sources: by means of mixing and by sharing a common counting process. Even under a rather complex dependence structure, the stochastic properties of the multivariate process and its

In this paper, we study the asymptotic behavior of the kernel bivariate distribution function estimator for negatively superadditive dependent. The exponential convergence rates for the kernel estimator are investigated. Under certain regularity conditions, the optimal bandwidth rate is determined with respect to mean squared error criteria. A simulation study is used to justify the behavior of the

In progressive Type-II censoring, it is often claimed that the withdrawn items are further tested under different conditions but a model incorporating this information has not been discussed so far. Introducing the model of Type-II stage life testing, we propose an approach to include information from progressively censored units subject to additional life testing by assuming a cumulative exposure

Localization of quantum Bernoulli noises (LQBNs) are the family of local annihilation and local creation operators acting on Bernoulli functionals. In this paper, we construct a density operator ρk represented by LQBNs, and define a new quantum entropy S ( ρ k ) based on LQBNs. Furthermore, we demonstrate that this quantum entropy S ( ρ k ) also has the basic properties of von Neumann entropy, such

In reliability and life testing, when the exponentially distributed components are put in series, it is generally assumed that the lifetimes of the components are independently distributed, which leads to some errors when in fact they are not independent. In this paper, we study the relative errors incurred in different reliability measures due to such assumptions when actually they follow some bivariate