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In recent years, deep learning has been widely employed in the field of image compression, the most significant of which is the lossy image compression method on the basis of convolutional neural networks. And we study the application of convolutional neural networks to remote sensing image compression. Consequently, we implement an enhanced residual attention module (ERAM) on the primary and hyper coders. ERAM can apply a spatial attention mechanism to generate importance masks for potential features of the original image. And the importance mask can adaptively adjust the bit distribution and allocate more bits to substantial target regions and fewer bits to unimportant background regions. Additionally, ERAM has the capacity to lessen the channel redundancy of potential features. Furthermore, an accurate probability estimate of a potential feature can affect to a great degree the effectiveness of entropy coding and hence image compression. We propose to utilise the discrete mixed Laplace entropy model to parameterize the probability distribution of latent features, which can improve the compression efficiency of latent features in the entropy encoding process. In the field of remote sensing image compression, the experiments demonstrate that the algorithm described in this paper has good subjective effects as well as good objective effects. [ABSTRACT FROM AUTHOR]

In a one-way design with unknown and unequal error variances, we are interested in testing the null hypothesis H 0 : μ 1 = μ 2 = ⋯ = μ k against the ordered alternative H 1 : μ 1 ≤ μ 2 ≤ ⋯ ≤ μ k (with at least one strict inequality). We propose the likelihood ratio test (LRT) as well as two Min-T tests (Min-T and AMin-T) and study their asymptotic behaviour. For better finite sample properties, a parametric bootstrap procedure is used. Asymptotic accuracy of the parametric bootstrap is established. Simulation results show that all the tests control the nominal level in case of small, moderate, and highly unbalanced sample sizes. This even holds for combinations with large variances. However, the asymptotic likelihood ratio test (ALRT) achieves the nominal size only for large samples and k = 3 . Power comparisons between LRT and Min-T test show that the LRT has more power than Min-T. However, the Min-T test is easier to use as it does not require evaluation of MLEs. Similar observations are made while comparing ALRT and AMin-T test. The robustness of these tests under departure from normality is also investigated by considering five non-normal distributions (t-distribution, Laplace, exponential, Weibull, and lognormal). When high variances are combined with small or highly unbalanced sample sizes, the tests are observed to be robust only for symmetric distributions. If variances of groups are equal and sample sizes of each group are at least 10, the proposed tests perform satisfactorily for symmetric and skewed distributions. R packages are developed for all tests and a practical example is provided to illustrate their application. [ABSTRACT FROM AUTHOR]

The paper deals with the analysis of the empirical distribution of returns of selected market indices of developed and developing markets in relation to applications in the field of financial risks. The probability distribution of returns plays a key role for both the theoretical and practical part of financial theory. The assumption of a normal distribution of returns, which is crucial for several financial theories, is rejected in line with our analysis of the daily returns of 30 markets. From the perspective of financial risk assessment, the choice of an appropriate distribution is key to the accuracy of the achieved results. In this paper, we examine the possibility of applying alternative distributions, in order to better capture the observed leptokurtic behavior of the empirical distribution of daily returns as compared to the assumption of normality. We perform the analysis on the daily returns of stock market indices in order to examine the possible differences between the empirical distribution of developed and emerging markets. We investigate the suitability and relative performance of these alternative distributions: the generalized skewed t distribution (sgt), the generalized lambda distribution (gld), the exponential power distribution (GED), the Hansen's skewed t distribution and the Laplace distribution. The best relative performance of fit for market index returns providing the sgt_2 and gld distributions, with gld appearing to be a more prominent adept than with the perspective of relative stability of quality of fit and also quality of risk estimation. [ABSTRACT FROM AUTHOR]

Estimation of low or high conditional quantiles is called for in many applications, but commonly encountered data sparsity at the tails of distributions makes this a challenging task. We develop a Bayesian joint-quantile regression method to borrow information across tail quantiles through a linear approximation of quantile coefficients. Motivated by a working likelihood linked to the asymmetric Laplace distributions, we propose a new Bayesian estimator for high quantiles by using a delayed rejection and adaptive Metropolis and Gibbs algorithm. We demonstrate through numerical studies that the proposed estimator is generally more stable and efficient than conventional methods for estimating tail quantiles, especially at small and modest sample sizes. [ABSTRACT FROM AUTHOR]

Full-waveform inversion (FWI) is a powerful methodology employed in estimating subsurface physical parameters. FWI is classically formulated as a data-fitting problem based on minimizing the squared l 2 -norm of the difference between the observed data and modeled data (i.e., the data residuals or errors). The FWI based on l 2 -norm (hereafter classical FWI) stems from the assumption that the errors follow a Gaussian probability distribution. However, since, in most cases the error is non-Gaussian for non-linear problems and therefore, the classical FWI tends to fail. In this work, we consider the Tsallis q-deformation of the exponential function, which is widely used in the field of statistical physics, to derive an alternative misfit function to mitigate the FWI sensitivity to spurious measurements (outliers). In this regard, we formulated the FWI from a q-generalization of the Laplace probability distribution (or q-Laplace distribution). Application on a typical Brazilian pre-salt velocity model with an acoustic synthetic noisy-data is presented, in which we compare the performance of our proposal against the classical FWI. In addition, we compare also our methodology with the robust misfit function based on l 1 -norm, which is based on the Laplace distribution. The results show that our proposal outperforms classical FWI, and also the robust FWI based on l 1 -norm. The results also reveal that our proposal accelerates the data inversion process when the data is polluted by outliers. [ABSTRACT FROM AUTHOR]

We propose a method for studying the reliability of series systems with redundancy and recovery strategies, which provide for a change in the repair intensity depending on the number of failed units. The case of the exponential distribution of the time to failure of units, the non-exponential distribution of the recovery time, and one repair channel are considered. Formulas for determining Laplace transforms of the distribution of the number of failed units during the busy period of the repair channel and of the distribution functions of the busy period and to calculate the stationary indices are obtained. [ABSTRACT FROM AUTHOR]

In this paper, the shape mixtures of the skew Laplace normal (SMSLN) distribution is introduced as a flexible extension of the skew Laplace normal distribution which is also a heavy-tailed distribution. The SMSLN distribution includes an extra shape parameter, which controls skewness and kurtosis. Some distributional properties of this distribution are derived. Besides, we propose finite mixtures of SMSLN distributions to model both skewness and heavy-tailedness in heterogeneous data sets. The maximum likelihood estimators for parameters of interests are obtained via the expectation–maximization algorithm. We also give a simulation study and examine a real data example for the numerical illustration of proposed estimators. [ABSTRACT FROM AUTHOR]

Quantile regression is a powerful tool for modeling non-Gaussian data, and also for modeling different quantiles of the probability distributions of the responses. We propose a Bayesian approach of estimating the quantiles of multivariate longitudinal data where the responses contain excess zeros. We consider a Tobit regression approach, where the latent responses are estimated using a linear mixed model. The longitudinal dependence and the correlations among different (latent) responses are modeled by the subject-specific vector of random effects. We consider a mixture representation of the Asymmetric Laplace Distribution (ALD), and develop an efficient MCMC algorithm for estimating the model parameters. The proposed approach is used for analyzing data from the health and retirement study (HRS) conducted by the University of Michigan, USA; where we jointly model (i) out-of-pocket medical expenditures, (ii) total financial assets, and (iii) total financial debt for the aged subjects, and estimate the effects of different covariates on these responses across different quantiles. Simulation studies are performed for assessing the operating characteristics of the proposed approach. [ABSTRACT FROM AUTHOR]

We present a single-species metapopulation model structured by population size that is discrete in time. The novel formulation of our model allows for explicit incorporation of both the local, in space, dynamics and new details of the dispersal process. To study the impact of between-patch dynamics in the model, we construct various functions to describe density-dependent dispersal, recolonization, and between-patch stochasticity. Due to the complexity of the model, numerical simulations are used to obtain the distribution of the metapopulation. Moreover, we can use our model to predict the proportion of patches occupied, expected patch density, and variance in patch density. Our results provide insight into the influence that each of these processes play in the distribution of the metapopulation. In particular, our findings emphasize the benefit of explicitly modelling these processes. We consider two density-dependent dispersal strategies based upon individuals wanting to form average-sized patches and illustrate the differences in the metapopulation distributions. For recolonization of empty suitable patches, we look at two simplistic redistribution strategies modeled as either a continuous uniform or Laplace distribution. The between-patch stochasticity is modelled using redistribution kernels where we consider both thin-tailed and fat-tailed kernels. We find that the form of density-dependent dispersal has a major influence on the distribution of the metapopulation while recolonization is a key process for metapopulation persistence. In addition, fatter tails for the between-patch stochasticity can decrease the proportion of occupied patches and increase the expected patch density and variance in patch density. [ABSTRACT FROM AUTHOR]

We study a modified Markovian bulk-arrival and bulk-service queue incorporating general state-dependent control. The stopped bulk-arrival and bulk-service queue is first investigated, and the relationship between this stopped queue and the full queueing model is examined and exploited. Using this relationship, the equilibrium behaviour for the full queueing process is studied and the probability generating function of the equilibrium distribution is obtained. Queue length behaviour is also examined, and the Laplace transform of the queue length distribution is presented. The important questions regarding hitting times and busy period distributions are answered in detail, and the Laplace transforms of these distributions are presented. Further properties regarding the busy period distributions including expectation and conditional expectation of busy periods are also explored. [ABSTRACT FROM AUTHOR]

The probabilistic neural network (PNN) is an efficient approach that can compute nonlinear decision boundaries, widely used for classification. In this paper, the often used Gaussian distribution function is replaced by a new probability density function which provides a new variant of the PNN method. Most of the higher-dimensional data are statistically found to be not from the normal distribution, and hence, we have replaced it by the symmetric Laplace distribution. Further, the estimation of the smoothing parameter in the proposed PNN model is carried out with three different evolutionary algorithms, namely bat algorithm (BA), grey wolf optimizer (GWO), and whale optimization algorithm (WOA) with a novel fitness function. These different proposed PNN models with variable smoothing parameter estimation methods are tested on five different benchmark data sets. The performance of proposed three Laplace distribution-based variants of PNN incorporated with BA, GWO, and WOA are reported and compared with Gaussian-based variants of PNN and also other commonly used classifiers: the conventional PNN, extreme learning machine, and K-nearest neighbor in terms of measurement accuracy. The results demonstrate that the proposed approaches using evolutionary algorithms can provide as much as a ten percent increase in accuracy over the conventional PNN method. [ABSTRACT FROM AUTHOR]

Scale mixtures of normal distributions, i.e., mixtures of normal distributions on the variance parameters, have wide applications. The testing of homogeneity is one of the fundamental challenges in the application of scale mixtures of normal distributions. Recently, Chen and Li (Ann Stat 37:2523-2542, ) proposed a class of EM-tests for testing homogeneity in mixtures of normal distributions on the mean parameters and both the mean and variance parameters. In this paper, we retool the EM-test proposed in Chen and Li () for testing homogeneity in scale mixtures of normal distributions. We show that the EM-test has the simple null limiting distribution $$\frac{1}{2} \chi ^2_0 + \frac{1}{2}\chi ^2_1$$ , an equal mixture of a distribution with point mass at zero and a $$\chi ^2_1$$ distribution. We also use a computational method to provide an empirical value for the tuning parameter selection. Simulation studies show that the EM-test has an accurate size and is more powerful than existing methods such as the likelihood ratio test and the method in Chen and Li () when the data are generated from scale mixtures of normal distributions or mixtures of normal distributions on both the mean and variance parameters with two component means being slightly different. To demonstrate the application of the proposed method, we analyze a real-data example. [ABSTRACT FROM AUTHOR]

In some quarters, especially beginners learning statistics and probability, one generally accepts a claim such as a ${\chi _{1}^{2}}$ random variable (rv) must be the square of a standard normal rv or a F rv must be the square of a Student's t rv. This feeds into more misconceptions later. Hence, we begin with a brief but general construct and then illustrate a number of rvs explicitly which are drastically different from a standard normal or Student's t rv whose squares are distributed as $\chi _{1}^{2}$ or F respectively. This simply presented note reinforces basic understanding of lessons in such core topics covered in classrooms for both undergraduate and graduate students. [ABSTRACT FROM AUTHOR]

We consider a class of two-queue polling systems with exhaustive service, where the order in which the server visits the queues is governed by a discrete-time Markov chain. For this model, we derive an expression for the probability generating function of the joint queue length distribution at polling epochs. Based on these results, we obtain explicit expressions for the Laplace-Stieltjes transforms of the waiting-time distributions and the probability generating function of the joint queue length distribution at an arbitrary point in time. We also study the heavy-traffic behaviour of properly scaled versions of these distributions, which results in compact and closed-form expressions for the distribution functions themselves. The heavy-traffic behaviour turns out to be similar to that of cyclic polling models, provides insights into the main effects of the model parameters when the system is heavily loaded, and can be used to derive closed-form approximations for the waiting-time distribution or the queue length distribution. [ABSTRACT FROM AUTHOR]

We consider in this note a class of two-dimensional determinantal Coulomb gases confined by a radial external field. As the number of particles tends to infinity, their empirical distribution tends to a probability measure supported in a centered ring of the complex plane. A quadratic confinement corresponds to the complex Ginibre Ensemble. In this case, it is also already known that the asymptotic fluctuation of the radial edge follows a Gumbel law. We establish in this note the universality of this edge behavior, beyond the quadratic case. The approach, inspired by earlier works of Kostlan and Rider, boils down to identities in law and to an instance of the Laplace method. [ABSTRACT FROM AUTHOR]

In this paper asymptotic formulas are obtained for determining the principal terms in global theorems for the distribution function of a geometric random sum. The obtained result implies that among all symmetric distributions the Bernoulli distribution has an asymptotically extreme nature under geometric summation. [ABSTRACT FROM AUTHOR]

A stochastic prediction model for the sunspot cycle is proposed. The prediction model is based on a modified binary mixture of Laplace distribution functions and a moving-average model over the estimated model parameters. A six-parameter modified binary mixture of Laplace distribution functions is used for the modeling of the shape of a generic sunspot cycle. The model parameters are estimated for 23 sunspot cycles independently, and the primary prediction-model parameters are derived from these estimated model parameters using a moving-average stochastic model. A correction factor (hump factor) is introduced to make an initial prediction. The hump factor is computed for a given sunspot cycle as the ratio of the model estimated after the completion of a sunspot cycle ( post-facto model) and the prediction of the moving-average model. The hump factors can be applied one at a time over the moving-average prediction model to get a final prediction of a sunspot cycle. The present model is used to predict the characteristics of Sunspot Cycle 24. The methodology is validated using the previous Sunspot Cycles 21, 22, and 23, which shows the adequacy and the applicability of the prediction model. The statistics of the variations of sunspot numbers at high solar activity are used to provide the lower and upper bound for the predictions using the present model. [ABSTRACT FROM AUTHOR]

Non-Gaussian stochastic fields are introduced by means of integrals with respect to independently scattered stochastic measures distributed according to generalized Laplace laws. In particular, we discuss stationary second order random fields that, as opposed to their Gaussian counterpart, have a possibility of accounting for asymmetry and heavier tails. Additionally to this greater flexibility the models discussed continue to share most spectral properties with Gaussian processes. Their statistical distributions at crossing levels are computed numerically via the generalized Rice formula. The potential for stochastic modeling of real life phenomena that deviate from the Gaussian paradigm is exemplified by a stochastic field model with Matérn covariances. [ABSTRACT FROM AUTHOR]

In this paper we generalize the quality and cost trade-off problem of Chang and Hung (Qual Quant 41: 291–301, 2007) under the LINEX loss function. We consider the general input characteristic given by the random variable X with moment generating function m X( t) and output characteristic given by the deterministic transformation Y = g( X). The two cases we consider are when g( X) is an affine function of X and X follows (1) the gamma distribution, and (2) the double exponential distribution. [ABSTRACT FROM AUTHOR]

The Fisher information matrix for a mixture of two Laplace distributions is derived. Numerical tabulations of the matrix and a computer program are provided for practical purposes. The work is motivated by two real-life examples discussed in Hsu (Appl Stat 28:62-72, 1979) and Bhowmick et al. (Biostatistics 7:630-41, 2006). [ABSTRACT FROM AUTHOR]