In the present paper, the asymmetric type II compound Laplace distribution is introduced and various properties are studied. The maximum likelihood estimation procedure is employed to estimate the ...parameters of the proposed distribution and an algorithm in R package is developed to carry out the estimation. Simulation studies for various choices of parameter values are performed to validate the algorithm. Finally, we fit the asymmetric type II compound Laplace, asymmetric Laplace, and log-normal distributions to five microarray gene expression datasets and compare them.
Light-fidelity (LiFi) is a networked optical wireless communication (OWC) solution for high-speed indoor connectivity for fixed and mobile optical communications. Unlike conventional radio frequency ...wireless systems, the OWC channel is not isotropic, meaning that the device orientation affects the channel gain significantly, particularly for mobile users. However, due to the lack of a proper model for device orientation, many studies have assumed that the receiver is vertically upward and fixed. In this paper, a novel model for device orientation based on experimental measurements of 40 participants has been proposed. It is shown that the probability density function (PDF) of the polar angle can be modeled either based on a Laplace (for static users) or a Gaussian (for mobile users) distribution. In addition, a closed-form expression is obtained for the PDF of the cosine of the incidence angle based on which the line-of-sight (LOS) channel gain is described in OWC channels. An approximation of this PDF based on the truncated Laplace is proposed and the accuracy of this approximation is confirmed by the Kolmogorov-Smirnov distance. Moreover, the statistics of the LOS channel gain are calculated and the random orientation of a user equipment (UE) is modeled as a random process. The influence of the random orientation on signal-to-noise-ratio performance of OWC systems has been evaluated. Finally, an orientation-based random waypoint (ORWP) mobility model is proposed by considering the random orientation of the UE during the user's movement. The performance of ORWP is assessed on the handover rate and it is shown that it is important to take the random orientation into account.
Inference in quantile analysis has received considerable attention in the recent years. Linear quantile mixed models (Geraci and Bottai 2014) represent a ?exible statistical tool to analyze data from ...sampling designs such as multilevel, spatial, panel or longitudinal, which induce some form of clustering. In this paper, I will show how to estimate conditional quantile functions with random e?ects using the R package lqmm. Modeling, estimation and inference are discussed in detail using a real data example. A thorough description of the optimization algorithms is also provided.
After its introduction by Koenker and Basset (1978), quantile regression has become an important and popular tool to investigate the conditional response distribution in regression. The R package ...bayesQR contains a number of routines to estimate quantile regression parameters using a Bayesian approach based on the asymmetric Laplace distribution. The package contains functions for the typical quantile regression with continuous dependent variable, but also supports quantile regression for binary dependent variables. For both types of dependent variables, an approach to variable selection using the adaptive lasso approach is provided. For the binary quantile regression model, the package also contains a routine that calculates the fitted probabilities for each vector of predictors. In addition, functions for summarizing the results, creating traceplots, posterior histograms and drawing quantile plots are included. This paper starts with a brief overview of the theoretical background of the models used in the bayesQR package. The main part of this paper discusses the computational problems that arise in the implementation of the procedure and illustrates the usefulness of the package through selected examples.
Let X and Y be independent variance-gamma random variables with zero location parameter; then the exact probability density function of the product XY is derived. Some basic distributional properties ...are also derived, including formulas for the cumulative distribution function and the characteristic function, as well as asymptotic approximations for the density, tail probabilities and the quantile function. As special cases, we deduce some key distributional properties for the product of two independent asymmetric Laplace random variables as well as the product of four jointly correlated zero mean normal random variables with a particular block diagonal covariance matrix. As a by-product of our analysis, we deduce some new reduction formulas for the Meijer G-function.
The filter bank multi-carrier with offset quadrature amplitude modulation (FBMC/OQAM) is extensively utilized in communication scenarios characterized by severe Doppler interference, owing its ...remarkable ability for precise time–frequency positioning concentration. However, the distinctive staggered superposition structure leads to an additional increase in peak-to-average power ratio (PAPR). In this letter, we discover that the unique superposition structure results in a high likelihood of abnormal minima in FBMC/OQAM, consequently diminishing the efficacy of the general companding transform scheme relying on Gaussian distribution for PAPR reduction. Thus, we introduce a general companding transform scheme based on the Laplace distribution. The simulation results demonstrate that the proposed scheme offers a 3 dB advantage in PAPR reduction compared to the traditional general companding scheme, while also maintaining a nearly 1 dB advantage in BER.
The robust identification problem of the linear parameter varying (LPV) systems with output data corrupted by outliers is considered in this paper. The local identification approach is used, and the ...LPV model is obtained by interpolating the local models with an exponential weighting function. In order to handle outliers that could occur in industrial processes, the corresponding probabilistic model is established with the process noise assumed to be mixture Laplace distributed, then the formulas to iteratively update the unknown model parameters and noise-free output are derived under the Variational Bayesian (VB) framework, which approximates the required posteriors and could avoid high dimensional integrals. One numerical example and a practical chemical process are employed to verify the efficacy of the developed algorithm.
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