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This research delves into the exploration of a statistical testing approach grounded in Laplace transform techniques specifically tailored for the New Better than Used Laplace transform order (NBUL) class of life distributions. The developed test exhibits versatility, accommodating both complete and censored data, and critical values are systematically calculated for its application. Beyond the methodological presentation, our study investigates the test's statistical power and explores Pitman's asymptotic efficiency concerning various alternative distributions. Comparative analyses with other tests within the same class contribute to a comprehensive understanding of the proposed approach. To demonstrate practical applicability, we apply this novel testing technique to authentic engineering and medical datasets. The outcomes of these applications serve as illustrative examples, showcasing the effectiveness and relevance of the proposed methodology in real-world scenarios. [ABSTRACT FROM AUTHOR]

This article completes our studies on the formal construction of asymptotic approximations for statistics based on a random number of observations. Second order Chebyshev–Edgeworth expansions of asymptotically normally or chi-squared distributed statistics from samples with negative binomial or Pareto-like distributed random sample sizes are obtained. The results can have applications for a wide spectrum of asymptotically normally or chi-square distributed statistics. Random, non-random, and mixed scaling factors for each of the studied statistics produce three different limit distributions. In addition to the expected normal or chi-squared distributions, Student's t-, Laplace, Fisher, gamma, and weighted sums of generalized gamma distributions also occur. [ABSTRACT FROM AUTHOR]

The ninth article, "Analysis of Adaptive Progressive Type-II Hybrid Censored Dagum Data with Applications" by Mohammed et al. [[9]], seeks to investigate classical and Bayesian estimations of the Dagum distribution based on the adaptive progressive type II hybrid censoring scheme. In their article entitled "Robust Procedure for Change-Point Estimation Using Quantile Regression Model with Asymmetric Laplace Distribution", Yang [[10]] creates a non-iterative sampling process from a Bayesian perspective and offers a robust change-point estimation method based on a quantile regression model with an asymmetric Laplace error distribution. The second article, "Bayesian Reference Analysis for the Generalized Normal Linear Regression Model", by Tomazella et al. [[2]] suggests using the Bayesian reference analysis to estimate the generalized normal linear regression model's parameters. [Extracted from the article]

When releasing data to the public, a vital concern is the risk of exposing personal information of the individuals who have contributed to the data set. Many mechanisms have been proposed to protect individual privacy, though less attention has been dedicated to practically conducting valid inferences on the altered privacy-protected data sets. For frequency tables, the privacyprotection-oriented perturbations often lead to negative cell counts. Releasing such tables can undermine users' confidence in the usefulness of such data sets. This paper focuses on releasing one-way frequency tables. We recommend an optimal mechanism that satisfies β-differential privacy (DP) without suffering from having negative cell counts. The procedure is optimal in the sense that the expected utility is maximized under a given privacy constraint. Valid inference procedures for testing goodness-of-fit are also developed for the DP privacy-protected data. In particular, we propose a de-biased test statistic for the optimal procedure and derive its asymptotic distribution. In addition, we also introduce testing procedures for the commonly used Laplace and Gaussian mechanisms, which provide a good finite sample approximation for the null distributions. Moreover, the decaying rate requirements for the privacy regime are provided for the inference procedures to be valid. We further consider common users' practices such as merging related or neighboring cells or integrating statistical information obtained across different data sources and derive valid testing procedures when these operations occur. Simulation studies show that our inference results hold well even when the sample size is relatively small. Comparisons with the current field standards, including the Laplace, the Gaussian (both with/without post-processing of replacing negative cell counts with zeros), and the Binomial-Beta McClure-Reiter mechanisms, are carried out. In the end, we apply our method to the National Center for Early Development and Learning's (NCEDL) multi-state studies data to demonstrate its practical applicability. [ABSTRACT FROM AUTHOR]

We propose a new family of linear mixed-effects models based on the generalized Laplace distribution. Special cases include the classical normal mixed-effects model, models with Laplace random effects and errors, and models where Laplace and normal variates interchange their roles as random effects and errors. By using a scale-mixture representation of the generalized Laplace, we develop a maximum likelihood estimation approach based on Gaussian quadrature. For model selection, we propose likelihood ratio testing and we account for the situation in which the null hypothesis is at the boundary of the parameter space. In a simulation study, we investigate the finite sample properties of our proposed estimator and compare its performance to other flexible linear mixed-effects specifications. In two real data examples, we demonstrate the flexibility of our proposed model to solve applied problems commonly encountered in clustered data analysis. The newly proposed methods discussed in this paper are implemented in the R package nlmm. [ABSTRACT FROM AUTHOR]

In practice, we often encounter situations where a sample size is not defined in advance and can be a random value. In the present paper, we derive second-order Chebyshev–Edgeworth and Cornish–Fisher expansions based of Student's t- and Laplace distributions and their quantiles for samples with random size of a special kind. This derivation uses a general transfer theorem, which allows us to construct asymptotic expansions for distributions of randomly normalized statistics from the distributions of the considered nonrandomly normalized statistics and of the random size of the underlying sample. Recently, interest in Cornish–Fisher expansions has increased because of study in risk management. Widespread risk measure Value at Risk (VaR) substantially depends on quantiles of the loss function, which is connected with description of investment portfolio of financial instruments. [ABSTRACT FROM AUTHOR]

This paper provides an empirical analysis of the distributional properties and statistical regularities of virtual, intra-virtual and traditional currency exchange rates. To perform the analysis, the most relevant virtual, intra-virtual and foreign currency exchange rates between October 2015 and December 2018 are examined. The analysis shows that, in spite of their differing mode of formation, daily log-returns of all currency types share tent-shaped empirical densities, one of the characteristics of a Laplace distribution at semi-log scale. This peculiar property has also been examined thoroughly in other fields of economic literature. Moreover, the empirical results show that virtual and traditional currencies hold the same functional form, even after the 2018 hype. However, in spite of these similarities virtual and intra-virtual currencies display fatter tails and steeper towering peaks than regular foreign currencies which underscores the rather speculative nature of this asset class. [ABSTRACT FROM AUTHOR]

We consider exact procedures for testing the equality of means (location parameters) of two Laplace populations with equal scale parameters based on corresponding independent random samples. The test statistics are based on either the maximum likelihood estimators or the best linear unbiased estimators of the Laplace parameters. By conditioning on certain quantities we manage to express their exact distributions as mixtures of ratios of linear combinations of standard exponential random variables. This allows us to find their exact quantiles and tabulate them for several sample sizes. The powers of the tests are compared either numerically or by simulation. Exact confidence intervals for the difference of the means corresponding to those tests are also constructed. The exact procedures are illustrated via a real data example. [ABSTRACT FROM AUTHOR]

This work focuses on extending some classical spatio-temporal models in disease mapping. The objective is to present a family of flexible models to analyze real data naturally organized in two different levels of spatial aggregation like municipalities within health areas or provinces, or counties within states. Model fitting and inference will be carried out using integrated nested Laplace approximations. The performance of the new models compared to models including a single spatial random effect is assessed by simulation. Results show good behavior of the proposed two-level spatially structured models in terms of several criteria. Brain cancer mortality data in the municipalities of two regions in Spain will be analyzed using the new model proposals. It will be shown that a model with two-level spatial random effects overcomes the usual single-level models. [ABSTRACT FROM AUTHOR]

In this paper, a new model for retinal Optical Coherence Tomography (OCT) images is proposed. This statistical model is based on introducing a nonlinear Gaussianization transform to convert the probability distribution function (pdf) of each OCT intra-retinal layer to a Gaussian distribution. The retina is a layered structure and in OCT each of these layers has a specific pdf which is corrupted by speckle noise, therefore a mixture model for statistical modeling of OCT images is proposed. A Normal-Laplace distribution, which is a convolution of a Laplace pdf and Gaussian noise, is proposed as the distribution of each component of this model. The reason for choosing Laplace pdf is the monotonically decaying behavior of OCT intensities in each layer for healthy cases. After fitting a mixture model to the data, each component is gaussianized and all of them are combined by Averaged Maximum A Posterior (AMAP) method. To demonstrate the ability of this method, a new contrast enhancement method based on this statistical model is proposed and tested on thirteen healthy 3D OCTs taken by the Topcon 3D OCT and five 3D OCTs from Age-related Macular Degeneration (AMD) patients, taken by Zeiss Cirrus HD-OCT. Comparing the results with two contending techniques, the prominence of the proposed method is demonstrated both visually and numerically. Furthermore, to prove the efficacy of the proposed method for a more direct and specific purpose, an improvement in the segmentation of intra-retinal layers using the proposed contrast enhancement method as a preprocessing step, is demonstrated. [ABSTRACT FROM AUTHOR]

Accurate lesion metabolic response estimation is imperative for efficient tumor staging and follow-up studies. Positron emission tomography (PET) successfully images the lesion metabolic activity. Nonetheless, on course of accurate delineation, chances are high to end up with activity underestimation as, due to the limited resolution, the PET images suffer from partial volume effects. Recently, PET images were modeled as a fuzzy mixture to delineate lesions accurately. We extend this work by proposing a statistical lesion activity computation (SLAC) approach to robustly estimate the total lesion activity (TLA) directly from the modeled partial volume mixtures, without an explicit delineation. To evaluate the proposed method, PET scans of phantoms containing spherical and non-spherical lesions with increased activity uptake were simulated. The PET images were reconstructed with the standard clinically used maximum likelihood expectation maximization and an edge preserving maximum a posteriori (MAP) algorithm, both with resolution recovery. From these images, the TLA was estimated in each lesion using the proposed method and compared to the TLA estimation in the tumor delineations obtained with three state-of-the-art PET delineation schemes. SLAC outperformed TLA estimation via tumor delineation and showed robust against variation in reconstruction parameters. With reference to the ground truth knowledge, SLAC gives median $$\delta $$TLA $$~\approx $$ 5 % for spherical lesions. For more realistic non-spherical lesions, median $$\delta $$TLA $$~\approx $$ 15 %. [ABSTRACT FROM AUTHOR]

Abstract: Modeling of loads on a vehicle through Laplace moving averages is extended to the multivariate setting and efficient methods of computing the damage indexes are discussed. Multivariate Laplace moving averages are used as statistical models of multi-axial loads represented by forces and moments measured at some locations of a cultivator. As opposed to models based on the Gaussian distribution, these models account explicitly for transients that have a common origin—vibrations that can be caused by large obstacles encountered by a cultivator or a vehicle driving into potholes. The model is characterized by a low number of parameters accounting for fundamental characteristics of multivariate signals: the covariance matrix representing size of loads and their mutual dependence, the excess kurtosis that in the model is related to relative size of transients, and the time scale that accounts for the vehicle speed. These parameters can be used to capture diversity of environmental conditions in which the vehicle operates. Distributions of parameter values that are specific to a given market or encountered by specific customers can be then used to describe the long term loading. The model is validated by analysis of the resulting damage index. It is shown that the parameters enter this index in a multiplicative and explicit manner and, for a given damage exponent, only the factor representing dependence on the kurtosis has to be obtained through regression approximation based on Monte Carlo simulations. An example of actual cultivator data is used to illustrate the accuracy of damage and fatigue life prediction. [Copyright &y& Elsevier]

We introduce a family of leptokurtic symmetric distributions represented by the difference of two gamma variates. Properties of this family are discussed. The Laplace, sums of Laplace and normal distributions all arise as special cases of this family. We propose a two-step method for fitting data to this family. First, we perform a test of symmetry, and second, we estimate the parameters by minimizing the quadratic distance between the real parts of the empirical and theoretical characteristic functions. The quadratic distance estimator obtained is consistent, robust and asymptotically normally distributed. We develop a statistical test for goodness of fit and introduce a test of normality of the data. A simulation study is provided to illustrate the theory. [ABSTRACT FROM PUBLISHER]

In one-parameter (θ) families, we were not aware of explicit hypothesis testing scenarios where maximal invariant statistics failed to distinguish the models. We start with a concrete example (Sec. 2.2) to highlight such a hypothesis testing problem involving markedly different models. In this problem, because of the absence of a nontrivial uniformly most powerful invariant (UMPl) test, we briefly suggest two approaches to test the hypothesis. The first resolution (Sec. 3.1) is frequentist in nature. It utilizes a weight function on the parameter space and compares "average" distributions obtained under the null and alternative models in the sense of Wald (1947, 1950). In contrast a fully Bayesian resolution (Sec. 3.2) is also included. The note ends with a series of other interesting examples involving one parameter families where maximal invariant statistics fail to distinguish the hypothesized models. The examples include easy-to-construct families of probability models involving only a single location or scale parameter θ. [ABSTRACT FROM AUTHOR]

In this paper a class of goodness-of-fit tests for the Laplace distribution is proposed. The tests are based on a weighted integral involving the empirical characteristic function. The consistency of the tests as well as their asymptotic distribution under the null hypothesis are investigated. As the decay of the weight function tends to infinity the test statistics approach limit values. In a particular case the resulting limit statistic is related to the first nonzero component of Neyman's smooth test for this distribution. The new tests are compared with other omnibus tests for the Laplace distribution. [ABSTRACT FROM AUTHOR]

A new stochastic process was developed by considering the internal performance of macro-states in which the sojourn time in each one is phase-type distributed depending on time. The stationary distribution was calculated through matrix-algorithmic methods and multiple interesting measures were worked out. The number of visits distribution to a determine macro-state were analyzed from the respective differential equations and the Laplace transform. The mean number of visits to a macro-state between any two times was given. The results were implemented computationally and were successfully applied to study random telegraph noise (RTN) in resistive memories. RTN is an important concern in resistive random access memory (RRAM) operation. On one hand, it could limit some of the technological applications of these devices; on the other hand, RTN can be used for the physical characterization. Therefore, an in-depth statistical analysis to model the behavior of these devices is of essential importance. [ABSTRACT FROM AUTHOR]

We consider a random walk of n steps starting at x0  =  0 with a double exponential (Laplace) jump distribution. We compute exactly the distribution of the gap dk,n between the kth and th maxima in the limit of large n and large k, with fixed. We show that the typical fluctuations of the gaps, which are of order O(n−1/2), are described by a universal -dependent distribution, which we compute explicitly. Interestingly, this distribution has an inverse cubic tail, which implies a non-trivial n-dependence of the moments of the gaps. We also argue, based on numerical simulations, that this distribution is universal, i.e. it holds for more general jump distributions (not only the Laplace distribution), which are continuous, symmetric with a well-defined second moment. Finally, we also compute the large deviation form of the gap distribution for , which turns out to be non-universal. [ABSTRACT FROM AUTHOR]

Highlights from the article: Regression is used to quantify the relationship between response variables and some covariates of interest. The second paper presents a new link function for distribution-specific quantile regression based on vector generalized linear and additive models to directly model specified quantile levels. The fourth paper introduces the regularized quantile regression method using pairwise absolute clustering and sparsity penalty, extending from mean regression to quantile regression setting.