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Robust principal component analysis (RPCA) is a widely used method for recovering low‐rank structure from data matrices corrupted by significant and sparse outliers. These corruptions may arise from occlusions, malicious tampering, or other causes for anomalies, and the joint identification of such corruptions with low‐rank background is critical for process monitoring and diagnosis. However, existing RPCA methods and their extensions largely do not account for the underlying probabilistic distribution for the data matrices, which in many applications are known and can be highly non‐Gaussian. We thus propose a new method called RPCA for exponential family distributions (eRPCA$$ {e}^{\mathrm{RPCA}} $$), which can perform the desired decomposition into low‐rank and sparse matrices when such a distribution falls within the exponential family. We present a novel alternating direction method of multiplier optimization algorithm for efficient eRPCA$$ {e}^{\mathrm{RPCA}} $$ decomposition, under either its natural or canonical parametrization. The effectiveness of eRPCA$$ {e}^{\mathrm{RPCA}} $$ is then demonstrated in two applications: the first for steel sheet defect detection and the second for crime activity monitoring in the Atlanta metropolitan area. [ABSTRACT FROM AUTHOR]

Background: Molecular surveillance of infectious diseases allows the monitoring of pathogens beyond the granularity of traditional epidemiological approaches and is well-established for some of the most relevant infectious diseases such as malaria. The presence of genetically distinct pathogenic variants within an infection, referred to as multiplicity of infection (MOI) or complexity of infection (COI) is common in malaria and similar infectious diseases. It is an important metric that scales with transmission intensities, potentially affects the clinical pathogenesis, and a confounding factor when monitoring the frequency and prevalence of pathogenic variants. Several statistical methods exist to estimate MOI and the frequency distribution of pathogen variants. However, a common problem is the quality of the underlying molecular data. If molecular assays fail not randomly, it is likely to underestimate MOI and the prevalence of pathogen variants. Methods and findings: A statistical model is introduced, which explicitly addresses data quality, by assuming a probability by which a pathogen variant remains undetected in a molecular assay. This is different from the assumption of missing at random, for which a molecular assay either performs perfectly or fails completely. The method is applicable to a single molecular marker and allows to estimate allele-frequency spectra, the distribution of MOI, and the probability of variants to remain undetected (incomplete information). Based on the statistical model, expressions for the prevalence of pathogen variants are derived and differences between frequency and prevalence are discussed. The usual desirable asymptotic properties of the maximum-likelihood estimator (MLE) are established by rewriting the model into an exponential family. The MLE has promising finite sample properties in terms of bias and variance. The covariance matrix of the estimator is close to the Cramér-Rao lower bound (inverse Fisher information). Importantly, the estimator's variance is larger than that of a similar method which disregards incomplete information, but its bias is smaller. Conclusions: Although the model introduced here has convenient properties, in terms of the mean squared error it does not outperform a simple standard method that neglects missing information. Thus, the new method is recommendable only for data sets in which the molecular assays produced poor-quality results. This will be particularly true if the model is extended to accommodate information from multiple molecular markers at the same time, and incomplete information at one or more markers leads to a strong depletion of sample size. [ABSTRACT FROM AUTHOR]

Generalized Linear Models (GLMs) are a popular class of regression models when the responses follow a distribution in the exponential family. In real data the variability often deviates from the relation imposed by the exponential family distribution, which results in over- or underdispersion. Dispersion effects may even vary in the data. Such datasets do not follow the traditional GLM distributional assumptions, leading to unreliable inference. Therefore, the family of double exponential distributions has been proposed, which models both the mean and the dispersion as a function of covariates in the GLM framework. Since standard maximum likelihood inference is highly susceptible to the possible presence of outliers, we propose the robust double exponential (RDE) estimator. Asymptotic properties and robustness of the RDE estimator are discussed. A generalized robust quasi-deviance measure is introduced which constitutes the basis for a stable robust test. Simulations for binomial and Poisson models show the excellent performance of the RDE estimator and corresponding robust tests. Penalized versions of the RDE estimator are developed for sparse estimation with high-dimensional data and for flexible estimation via generalized additive models (GAMs). Real data applications illustrate the relevance of robust inference for dispersion effects in GLMs and GAMs. for this article are available online. [ABSTRACT FROM AUTHOR]

This paper is presenting a new flexible probability distribution which named as Khalil new generalized exponential (KNGEx) distribution. We introduce its mathematical properties. The hazard function of the KNGEx distribution can be increasing, decreasing, and inverted bathtub. The parameters of the distribution are estimated using eight classical methods. Simulation studies based on complete sample are done. Finally, two applications to medicine and engineering data sets are presented. The analyzed data revealed that the proposed distribution could potentially be very useful in describing and modeling both data sets as compared to many other competing distributions. [ABSTRACT FROM AUTHOR]

In this article, a new family of bivariate discrete distributions is proposed based on the copula concept, in the so-called bivariate discrete odd generalized exponential-G family. Some distributional properties, including the joint probability mass function, joint survival function, joint failure rate function, median correlation coefficient, and conditional expectation, are derived. After proposing the general class, one special model of the new bivariate family is discussed in detail. The maximum likelihood approach is utilized to estimate the family parameters. A detailed simulation study is carried out to examine the bias and mean square error of maximum likelihood estimators. Finally, the importance of the new bivariate family is explained by means of two distinctive real data sets in various fields. [ABSTRACT FROM AUTHOR]

The stochastic literature contains several extensions of the exponential distribution which increase its applicability and flexibility. In the present article, some properties of a new power modified exponential family with an original Kies correction are discussed. This family is defined as a Kies distribution which domain is transformed by another Kies distribution. Its probabilistic properties are investigated and some limitations for the saturation in the Hausdorff sense are derived. Moreover, a formula of a semiclosed form is obtained for this saturation. Also the tail behavior of these distributions is examined considering three different criteria inspired by the financial markets, namely, the VaR, AVaR, and expectile based VaR. Some numerical experiments are provided, too. [ABSTRACT FROM AUTHOR]

In this paper, we present a modified one-stage multiple comparison procedure for exponential location parameters with the control under heteroscedasticity including one-sided and two-sided confidence intervals to improve the coverage probability and average confidence length than the old one. These intervals can be used to identify a subset which includes all no-worse-than-the-control treatments in an experimental design and to identify better-than-the-control, worse-than-the- control and not-much-different-from-the-control products in agriculture, stock market, pharmaceutical industries in terms of the minimum guarantee lifetimes. A simulation comparison is done for this modified procedure with the old one in terms of the confidence length and coverage probability. One example is given to demonstrate the proposed modified procedure. [ABSTRACT FROM AUTHOR]

The process of discretization of continuous distributions creates and provides a large set of discrete probabilistic models used in various statistical applications. The most common way of doing so is by considering the probability distribution of the integral part of a continuous random variable. In this note we explore the following problem related to the latter discretization process and pose the following question: If the family of distributions that is discretized is an exponential family on the real line, when the (integral) resulting discrete probability model also generates an exponential family? We give a complete answer to this question and provide necessary and sufficient conditions under which the discretized version of an exponential family is also an exponential family. [ABSTRACT FROM AUTHOR]

Uniformly most powerful confidence distributions are obtained for parameters in selected models of the exponential family. A conditioning on the selection event as well as on the sufficient statistics of nuisance parameters guarantees valid post-selection inference. Optimal confidence intervals are obtained directly from the confidence distribution without requiring an inversion of pivotal quantities. Simulations showcase that the method works also when all models are misspecified. • Valid inference after model selection for parameters in exponential family models. • Confidence curves conditional on the selected model. • Confidence distributions yield correct p-values and best confidence intervals. • Finite sample uniformly most powerful confidence curves for continuous distributions. • Good approximations for discrete distributions. [ABSTRACT FROM AUTHOR]

In this article, we have considered the estimation of the probability density function and cumulative distribution function of the one-parameter polynomial exponential family of distributions. A number of probability distributions like the exponential, Lindley, length-biased Lindley and Sujatha are particular cases. Two estimators—maximum likelihood and uniformly minimum variance unbiased estimators of the probability density function and cumulative distribution function of the family have been discussed. The estimation issues of the length-biased Lindley and Sujatha distribution have been considered in detail. The estimators have been compared in mean squared error sense. Monte Carlo simulations and real data analysis are performed to compare the performances of the proposed estimators. [ABSTRACT FROM AUTHOR]

In this work, we present a new class of continuous distributions called the exponentiated reduced-Kies-G family. The basic mathematical properties of the new family are addressed. A special sub-model of the proposed family, called the exponentiated reduced-Kies exponential (ERKiEx), is studied in detail concerning the aspect of estimation and inference, we described eight estimation methods. A comprehensive set of simulation studies are performed to compare and rank the proposed methods based on partial and overall ranks. Two real-life reliability engineering data applications are employed to explore the applicability and flexibility of the new ERKiEx distribution as compared to well-known other exponential extensions such as the Marshall{Olkin exponential, Kumaraswamy exponential and exponentiated exponential distributions. [ABSTRACT FROM AUTHOR]

In this paper, we propose two multimodal circular distributions which are suitable for modeling circular data sets with two or more modes. Both distributions belong to the regular exponential family of distributions and are considered as extensions of the von Mises distribution. Hence, they possess the highly desirable properties, such as the existence of non-trivial sufficient statistics and optimal inferences for their parameters. Fine particulates (PM2.5) are generally emitted from activities such as industrial and residential combustion and from vehicle exhaust. We illustrate the utility of our proposed models using a real data set consisting of fine particulates (PM2.5) pollutant levels in Houston region during Fall season in 2019. Our results provide a strong evidence that its diurnal pattern exhibits four modes; two peaks during morning and evening rush hours and two peaks in between. [ABSTRACT FROM AUTHOR]

Every random variable (rv) X (or random vector) with finite moments generates a set of orthogonal polynomials, which can be used to obtain properties related to the distribution of X. This technique has been used in statistical inference, mainly connected to the exponential family of distributions. In this paper a review of some of its more relevant uses is provided. The first one deals with properties of expansions in terms of orthogonal polynomials for the Uniformly Minimum Variance Unbiased Estimator of a given parametric function, when sampling from a distribution in the Natural Exponential Family of distributions with Quadratic Variance Function. The second one compares two relevant methods, based on expansions in Laguerre polynomials, existing in the literature to approximate the distribution of linear combinations of independent chi‐square variables. [ABSTRACT FROM AUTHOR]

We propose tractable symmetric exponential families of distributions for multivariate vectors of 0's and 1's in p dimensions, or what are referred to in this paper as binary vectors, that allow for nontrivial amounts of variation around some central value μ∈{0,1}p. We note that more or less standard asymptotics provides likelihood‐based inference in the one‐sample problem. We then consider mixture models where component distributions are of this form. Bayes analysis based on Dirichlet processes and Jeffreys priors for the exponential family parameters prove tractable and informative in problems where relevant distributions for a vector of binary variables are clearly not symmetric. We also extend our proposed Bayesian mixture model analysis to datasets with missing entries. Performance is illustrated through simulation studies and application to real datasets. [ABSTRACT FROM AUTHOR]

Exponential family random graph models (ERGMs) are widely used to model networks by parameterizing graph probability in terms of a set of user-selected sufficient statistics. Equivalently, ERGMs can be viewed as expressing a probability distribution on graphs arising from the action of competing social forces that make ties more or less likely, depending on the state of the rest of the graph. Such forces often lead to a complex pattern of dependence among edges, with nontrivial large-scale structures emerging from relatively simple local mechanisms. While this provides a powerful tool for probing macro-micro connections, much remains to be understood about how local forces shape global outcomes. One very simple question of this type is that of the conditions needed for social forces to stabilize a particular structure: that is, given a specific structure and a set of alternatives (e.g., arising from small perturbations), under what conditions will said structure remain more probable than the alternatives? We refer to this property as local stability and seek a general means of identifying the set of parameters under which a target graph is locally stable with respect to a set of alternatives. Here, we provide a complete characterization of the region of the parameter space inducing local stability, showing it to be the interior of a convex cone whose faces can be derived from the change scores of the sufficient statistics vis-\à-vis the alternative structures. As we show, local stability is a necessary but not sufficient condition for more general notions of stability, the latter of which can be explored more efficiently by using the "stable cone" within the parameter space as a starting point. In addition to facilitating the understanding of model behavior, we show how local stability can be used to determine whether a fitted model implies that an observed structure would be expected to arise primarily from the action of social forces, versus by merit of the model permitting a large number of high probability structures, of which the observed structure is one (i.e., entropic effects). We also use our approach to identify the dyads within a given structure that are the least stable, and hence predicted to have the highest probability of changing under the current social forces. The utility of the "stable cone" for ERGM parameter optimization is then demonstrated on a physical model of amyloid fibril formation. This demonstration features a visualization of the stable region, whereby it is shown that the majority of the region of the model's parameter space where ERGM simulations produce the highest fibril yield lies within the "stable cone. [ABSTRACT FROM AUTHOR]

The problem of multihypothesis testing with controlled sensing of observations is considered. The distribution of observations collected under each control is assumed to follow a single-parameter exponential family distribution. The goal is to design a policy to find the true hypothesis with minimum expected delay while ensuring that the probability of error is below a given constraint. The decision-maker can reduce the delay by intelligently choosing the control for observation collection in each time slot. A policy for this problem is derived that satisfies given constraints on the error probability, and it is shown that this policy is asymptotically optimal in the sense that it asymptotically achieves an information-theoretic lower bound on the expected delay. Numerical results are provided that illustrate an application of the policy to medical diagnostic inference. [ABSTRACT FROM AUTHOR]

For the generalized positive exponential family of distributions, the problems of confidence interval estimation, bounded risk point estimation, and minimum risk point estimation of the rth power of unknown parameter θ are handled. Two-stage and purely sequential methodologies are developed for the estimation purpose. Sequential procedures are developed based on the maximum likelihood estimator (MLE) of the parameter. The exact operating characteristics of these procedures are given. [ABSTRACT FROM AUTHOR]

We introduce a Bayesian approach for analyzing (possibly) high-dimensional dependent data that are distributed according to a member from the natural exponential family of distributions. This problem requires extensive methodological advancements, as jointly modeling high-dimensional dependent data leads to the so-called "big n problem." The computational complexity of the "big n problem" is further exacerbated when allowing for non-Gaussian data models, as is the case here. Thus, we develop new computationally efficient distribution theory for this setting. In particular, we introduce the "conjugate multivariate distribution," which is motivated by the Diaconis and Ylvisaker distribution. Furthermore, we provide substantial theoretical and methodological development including: results regarding conditional distributions, an asymptotic relationship with the multivariate normal distribution, conjugate prior distributions, and full-conditional distributions for a Gibbs sampler. To demonstrate the wide-applicability of the proposed methodology, we provide two simulation studies and three applications based on an epidemiology dataset, a federal statistics dataset, and an environmental dataset, respectively. for this article are available online. [ABSTRACT FROM AUTHOR]

In this paper, the reconcilability between the P-value and the posterior probability in testing a point null hypothesis against the one-sided hypothesis is considered. Two essential families, non regular and exponential family of distributions, are studied. It was shown in a non regular family of distributions; in some cases, it is possible to find a prior distribution function under which P-value and posterior probability are achieved. However, in the exponential family of distributions, this agreement is based on the complete monotonicity of a function of hazard rate. [ABSTRACT FROM AUTHOR]

This research studied and explored the Burr X and Exponential families of distributions. However, we introduced a new family of distribution called Burr X Exponential-G family of distribution. We obtained a new distribution called Burr X Exponential – Exponential; by showing its respective density and distribution functions from the proposed family of distributions. The validity of the new family of distribution is proved. Also, the survival and hazard functions of the family are presented. However, this new family of distributions will serve as an additional generator to the existing ones in the literature; for developing a new model for modeling positive real data sets. [ABSTRACT FROM AUTHOR]

Let G be the graph corresponding to the graphical model of nearest neighbor interaction in a Gaussian character. We study Natural Exponential Families (NEF) of Wishart distributions on convex cones QG and PG, where PG is the cone of tridiagonal positive definite real symmetric matrices, and QG is the dual cone of PG. The Wishart NEF that we construct include Wishart distributions considered earlier for models based on decomposable(chordal) graphs. Our approach is, however, different and allows us to study the basic objects of Wishart NEF on the cones QG and PG. We determine Riesz measures generating Wishart exponential families on QG and PG, and we give the quadratic construction of these Riesz measures and exponential families. The mean, inverse-mean, covariance and variance functions, as well as moments of higher order, are studied and their explicit formulas are given. [ABSTRACT FROM AUTHOR]

A new three-parameter distribution with decreasing, increasing, and bathtub-shaped hazard rates obtained by compounding geometric, power series, and exponential distributions is introduced. It includes some well-known distributions as particular cases. Various mathematical properties of the new distribution as well as details of the maximum likelihood estimation and a sensitivity analysis for its parameters are presented. Finally, two real data applications are presented. [ABSTRACT FROM AUTHOR]

We propose a way to construct fiducial distributions for a multidimensional parameter using a step-by-step conditional procedure related to the inferential importance of the components of the parameter. For discrete models, in which the non-uniqueness of the fiducial distribution is well known, we propose to use the geometric mean of the “extreme cases” and show its good behavior with respect to the more traditional arithmetic mean. Connections with the generalized fiducial inference approach developed by Hannig and with confidence distributions are also analyzed. The suggested procedure strongly simplifies when the statistical model belongs to a subclass of the natural exponential family, called conditionally reducible, which includes the multinomial and the negative-multinomial models. Furthermore, because fiducial inference and objective Bayesian analysis are both attempts to derive distributions for an unknown parameter without any prior information, it is natural to discuss their relationships. In particular, the reference posteriors, which also depend on the importance ordering of the parameters, are the natural terms of comparison. We show that fiducial and reference posterior distributions coincide in the location-scale models, and we characterize the conditionally reducible natural exponential families for which the same coincidence holds. The discussion of some classical examples closes the paper. [ABSTRACT FROM AUTHOR]

The coefficient of determination, a.k.a. R2, iswell-defined in linear regression models, and measures the proportion of variation in the dependent variable explained by the predictors included in themodel. To extend it for generalized linearmodels, we use the variance function to define the total variation of the dependent variable, as well as the remaining variation of the dependent variable after modeling the predictive effects of the independent variables. Unlike other definitions that demand complete specification of the likelihood function, our definition of R2 only needs to know the mean and variance functions, so applicable to more general quasi-models. It is consistent with the classicalmeasure of uncertainty using variance, and reduces to the classical definition of the coefficient of determination when linear regression models are considered. [ABSTRACT FROM AUTHOR]

Second-generation sequencing technologies have replaced array-based technologies and become the default method for genomics and epigenomics analysis. Second-generation sequencing technologies sequence tens of millions of DNA/cDNA fragments in parallel. After the resulting sequences (short reads) are mapped to the genome, one gets a sequence of short read counts along the genome. Effective extraction of signals in these short read counts is the key to the success of sequencing technologies. Nonparametric methods, in particular smoothing splines, have been used extensively for modeling and processing single sequencing samples. However, nonparametric joint modeling of multiple second-generation sequencing samples is still lacking due to computational cost. In this article, we develop an adaptive basis selection method for efficient computation of exponential family smoothing splines for modeling multiple second-generation sequencing samples. Our adaptive basis selection gives a sparse approximation of smoothing splines, yielding a lower-dimensional effective model space for a more scalable computation. The asymptotic analysis shows that the effective model space is rich enough to retain essential features of the data. Moreover, exponential family smoothing spline models computed via adaptive basis selection are shown to have good statistical properties, e.g., convergence at the same rate as that of full basis exponential family smoothing splines. The empirical performance is demonstrated through simulation studies and two second-generation sequencing data examples. [ABSTRACT FROM AUTHOR]

In this article, we consider the problem of estimation of the stress–strength parameterδ = P(Y < X) based on progressively first-failure-censored samples, whenXandYboth follow two-parameter generalized inverted exponential distribution with different and unknown shape and scale parameters. The maximum likelihood estimator ofδand its asymptotic confidence interval based on observed Fisher information are constructed. Two parametric bootstrap boot-pand boot-tconfidence intervals are proposed. We also apply Markov Chain Monte Carlo techniques to carry out Bayes estimation procedures. Bayes estimate under squared error loss function and the HPD credible interval ofδare obtained using informative and non-informative priors. A Monte Carlo simulation study is carried out for comparing the proposed methods of estimation. Finally, the methods developed are illustrated with a couple of real data examples. [ABSTRACT FROM AUTHOR]

In this article, we investigate the potential usefulness of the three-parameter transmuted generalized exponential distribution for analyzing lifetime data. We compare it with various generalizations of the two-parameter exponential distribution using maximum likelihood estimation. Some mathematical properties of the new extended model including expressions for the quantile and moments are investigated. We propose a location-scale regression model, based on the log-transmuted generalized exponential distribution. Two applications with real data are given to illustrate the proposed family of lifetime distributions. [ABSTRACT FROM AUTHOR]

The horizontal distribution of the vertical gradient of atmospheric refractivity is important for the assessment of the propagation of electromagnetic waves on nearly horizontal paths. A 5-year set of meteorological data, obtained from the ERA-Interim numerical weather product, has been used to analyze this distribution statistically. Vertical gradient maps of the Central European region have been processed to derive empirical probability distributions of the difference between local point gradient values at two locations. The difference of the effective (path-averaged) gradient along the path and the local gradient is shown to be statistically distributed so that the quantiles increase linearly with distance in the interval from 100 to 1000 km. Finally, a spatial correlation function is obtained and described by an exponential model with correlation distances determined in the range of 400-700 km. [ABSTRACT FROM AUTHOR]

The Levenberg-Marquardt algorithm is a flexible iterative procedure used to solve non-linear least-squares problems. In this work, we study how a class of possible adaptations of this procedure can be used to solve maximum-likelihood problems when the underlying distributions are in the exponential family. We formally demonstrate a local convergence property and discuss a possible implementation of the penalization involved in this class of algorithms. Applications to real and simulated compositional data show the stability and efficiency of this approach. [ABSTRACT FROM AUTHOR]

In the context of heteroscedastic time-varying autoregressive (AR)-process we study the estimation of the error/innovation distributions. Our study reveals that the non-parametric estimation of the AR parameter functions has a negligible asymptotic effect on the estimation of the empirical distribution of the residuals even though the AR parameter functions are estimated non-parametrically. The derivation of these results involves the study of both function-indexed sequential residual empirical processes and weighted sum processes. Exponential inequalities and weak convergence results are derived. As an application of our results we discuss testing for the constancy of the variance function, which in special cases corresponds to testing for stationarity. [ABSTRACT FROM AUTHOR]

Cordeiro and de Castro proposed a new family of generalized distributions based on the Kumaraswamy distribution (denoted as Kw-G). Nadarajah et al. showed that the density function of the new family of distributions can be expressed as a linear combination of the density of exponentiated family of distributions. They derived some properties of Kw-G distributions and discussed estimation of parameters using the maximum likelihood (ML) method. Cheng and Amin and Ranneby introduced a new method of estimating parameters based on Kullback-Leibler divergence (the maximum spacing (MSP) method). In this article, the estimates of parameters of Kw-G distributions are obtained using the MSP method. For some special Kw-G distributions, the new estimators are compared with ML estimators. It is shown by simulations and a real data application that MSP estimators have better properties than ML estimators. [ABSTRACT FROM AUTHOR]

In this paper, a new class of goodness of fit tests for exponential distribution is proposed. The tests use the equidistribution characterizations of exponential distribution. Based on the U-empirical Laplace transforms of equidistributed statistics, test statistics of the integral type are formed. They are U-statistics with estimated parameters. Their asymptotic properties are derived. Two families of exponentiality tests from this class, based on two selected characterizations, are presented. The approximate Bahadur efficiency is used to assess their quality. Finally, their simulated powers are calculated and the tests are compared with different exponentiality tests. [ABSTRACT FROM AUTHOR]

For a one-sided truncated exponential family of distributions with a natural parameter θ and a truncation parameter γ as a nuisance parameter, it is shown by Akahira (2013) that the second-order asymptotic loss of a bias-adjusted maximum likelihood estimator (MLE) θML* of θ for unknown γ relative to the MLE θMLγ of θ for known γ is given and θML* and the maximum conditional likelihood estimator (MCLE) θMCL are second-order asymptotically equivalent. In this paper, in a similar way to Akahira (2013), for a two-sided truncated exponential family of distributions with a natural parameter θ and two truncation parameters γ and ν as nuisance ones, the stochastic expansions of the MLE θMLγ,ν of θ for known γ and ν and the MLE θML and the MCLE θMCL of θ for unknown γ and ν are derived, their second-order asymptotic means and variances are given, a bias-adjusted MLE θML* and θMCL are shown to be second-order asymptotically equivalent, and the second-order asymptotic losses of θML* and θMCL relative to θMLγ,ν are also obtained. Further, some examples including an upper-truncated Pareto case are given. [ABSTRACT FROM AUTHOR]

In this study, a New Lindley Exponential distribution was studied using the Lindley generalized family of distributions. Expressions for its densities, survival function, hazard function, quantile function and distribution of order statistics were derived. Its sub-models were identified and the New Lindley Exponential distribution was applied to two real life datasets to assess its flexibility over the Lindley distribution and the Exponential distribution. The results indicate that the New Lindley Exponential distribution performed better than both the Lindley distribution and the Exponential distribution based on their log-likelihood and Akaike Information Criteria values. [ABSTRACT FROM AUTHOR]

A new class of distributions called the hyperbolic cosine - F (HCF) distribution is introduced and its properties are explored. This new class of distributions is obtained by compounding a baseline F distribution with the hyperbolic cosine function. This technique resulted in adding an extra parameter to a family of distributions for more flexibility. A special case with two parameters has been considered in details namely; hyperbolic cosine exponential (HCE) distribution. Various properties of the proposed distribution including explicit expressions for the moments, quantiles, moment generating function, failure rate function, mean residual lifetime, order statistics, stress-strength parameter and expression of the Shannon entropy are derived. Estimations of parameters in HCE distribution for two data sets obtained by eight estimation procedures: maximum likelihood, Bayesian, maximum product of spacings, parametric bootstrap, non-parametric bootstrap, percentile, least-squares and weighted least-squares. Finally, these data sets have been analyzed for illustrative purposes and it is observed that in both cases the proposed model fits better than Weibull, gamma and generalized exponential distributions. [ABSTRACT FROM AUTHOR]

Control charts are effective tools for signal detection in both manufacturing processes and service processes. Much service data come from a process with variables having non-normal or unknown distributions. The commonly used Shewhart variable control charts, which depend heavily on the normality assumption, should not be properly used in such circumstances. In this paper, we propose a new variance chart based on a simple statistic to monitor process variance shifts. We explore the sampling properties of the new monitoring statistic and calculate the average run lengths (ARLs) of the proposed variance chart. Furthermore, an arcsine transformed exponentially weighted moving average (EWMA) chart is proposed because the ARLs of this modified chart are more intuitive and reasonable than those of the variance chart. We compare the out-of-control variance detection performance of the proposed variance chart with that of the non-parametric Mood variance (NP-M) chart with runs rules, developed by Zombade and Ghute [Nonparametric control chart for variability using runs rules. Experiment. 2014;24(4):1683–1691], and the nonparametric likelihood ratio-based distribution-free exponential weighted moving average (NLE) chart and the combination of traditional exponential weighted moving average (EWMA) mean and EWMA variance (CEW) control chart proposed by Zou and Tsung [Likelihood ratio-based distribution-free EWMA control charts. J Qual Technol. 2010;42(2):174–196] by considering cases in which the critical quality characteristic has a normal, a double exponential or a uniform distribution. Comparison results showed that the proposed chart performs better than the NP-M with runs rules, and the NLE and CEW control charts. A numerical example of service times with a right-skewed distribution from a service system of a bank branch in Taiwan is used to illustrate the application of the proposed variance chart and of the arcsine transformed EWMA chart and to compare them with three existing variance (or standard deviation) charts. The proposed charts show better detection performance than those three existing variance charts in monitoring and detecting shifts in the process variance. [ABSTRACT FROM PUBLISHER]

In this paper we discuss estimation and diagnostic procedures for partially linear models with first-order autoregressive [AR(1)] symmetric errors. The symmetric class includes all symmetric continuous distributions, particularly distributions with heavier and lighter tails than the normal ones, such as Student-t, power exponential and logistic, among others. Estimation is performed by maximum penalized likelihood and by using natural cubic splines. We derive the penalized score functions and the penalized Fisher information matrices for the parameters in the model. A reweighted iterative process based on the back-fitting algorithm is derived for the parameter estimation and the inference is based on the penalized Fisher information matrix. We discuss the effective degrees of freedom estimation and procedures for selecting the smoothing parameter. A small simulation study is performed for assessing the empirical distribution of the parameter estimates obtained from partially linear models with AR(1) errors. Residual analysis and derivation of conformal normal curvatures of local influence for some perturbation schemes are also given. Finally, a real data set is analyzed under partially linear models with AR(1) symmetric errors. [ABSTRACT FROM AUTHOR]

The exponentiated exponential distribution is one of the most seminal distributions of the 20th century. Here, we propose a discrete exponentiated exponential distribution. We derive its mathematical properties and procedures for estimation by common methods. The estimation procedures are assessed by simulation. Finally, the proposed distribution is compared with one of the most recent discrete distributions using two real data sets on insurance. [ABSTRACT FROM AUTHOR]

A broad class of local divergences between two probability measures or between the respective probability distributions is proposed in this paper. The introduced local divergences are based on the classic Csiszár $$\phi $$ -divergence and they provide with a pseudo-distance between two distributions on a specific area of their common domain. The range of values of the introduced class of local divergences is derived and explicit expressions of the proposed local divergences are also derived when the underlined distributions are members of the exponential family of distributions or they are described by multivariate normal models. An application is presented to illustrate the behavior of local divergences. [ABSTRACT FROM AUTHOR]

We show, for a class of discrete Fleming–Viot (or Moran) type particle systems, that the convergence to the equilibrium is exponential for a suitable Wasserstein coupling distance. The approach provides an explicit quantitative estimate on the rate of convergence. As a consequence, we show that the conditioned process converges exponentially fast to a unique quasi-stationary distribution. Moreover, by estimating the two-particle correlations, we prove that the Fleming–Viot process converges, uniformly in time, to the conditioned process with an explicit rate of convergence. We illustrate our results on the examples of the complete graph and of N particles jumping on two points. [ABSTRACT FROM AUTHOR]

A generalized k-out-of-n system which is denoted by ((n1,\ldots,nN),f,k) consists of N modules ordered in a line or a circle, and the ith module is composed of ni components in parallel (ni\geq 1,i=1,\ldots,N). The system fails iff there exist at least f failed components or at least k consecutive failed modules. In this paper, we compute the signature of this system when n1=\ldots=nN=n, and present illustrative examples to demonstrate its application. Simulation based computation of the signature is provided when the modules have different numbers of components. [ABSTRACT FROM AUTHOR]

Empirical analysis on human mobility has caught extensive attentions due to the accumulated human dynamical data and the advance of data mining technique. But the results of related research still have to further investigate on some issues such as spatial scale. In this paper, we explore human mobility in greater Kaohsiung area by using long-term taxicabs' GPS data. The trip distance in our dataset exhibits exponential decay for short trips and power-law scaling for long trips. We propose an approach to investigate the possible mechanism of the power-law tail. Moreover, we utilize the method of simulation and random relinking trip path to explain the empirical observation. Our results show that the origin of power-law movement distribution may be largely due to the power-law population distribution. [ABSTRACT FROM AUTHOR]

Since their introduction in the 1920s, control charts have played a key role in process monitoring and control in a variety of areas, from manufacturing to healthcare. Many of these charts are designed to monitor a single process parameter, such as the mean or the variance, of a normally distributed process, although recently, a number of charts have been developed for jointly monitoring the mean and variance. In practice, however, there are processes that follow multi-parameter nonnormal distributions, but the joint monitoring of parameters of nonnormal distributions remains largely unaddressed in the literature. This paper proposes several control charts and monitoring schemes for the origin and the scale parameters of a process that follows the two-parameter (or the shifted) exponential distribution. This distribution arises in various applications in practice, particularly with time to an event data, such as in reliability studies, and has been studied extensively in the statistical testing and estimation literature. Exact derivations and computer simulations are used to study performance properties of the proposed charts. An illustrative example is provided along with a summary and some conclusions. [ABSTRACT FROM AUTHOR]

In this article, we introduce the notion of trace variance function which is the trace of the variance-covariance matrix. Under some conditions, we prove that this trace variance function characterizes the Natural Exponential Family (NEF). We apply this characterization in order to estimate the distribution which belongs to some NEFs. Therefore, we introduce the estimator of this trace variance function. We give the asymptotic properties of this estimator. Finally, we illustrate our results using a simulation study. [ABSTRACT FROM AUTHOR]