A discrete Ramos-Louzada distribution for asymmetric and over-dispersed data with leptokurtic-shaped: Properties and various estimation techniques with inference

<abstract> <p>In this paper, a flexible probability mass function is proposed for modeling count data, especially, asymmetric, and over-dispersed observations. Some of its distributional properties are investigated. It is found that all its statistical and reliability properties can be expressed in explicit forms which makes the proposed model useful in time series and regression analysis. Different estimation approaches including maximum likelihood, moments, least squares, Andersonӳ-Darling, Cramer von-Mises, and maximum product of spacing estimator, are derived to get the best estimator for the real data. The estimation performance of these estimation techniques is assessed via a comprehensive simulation study. The flexibility of the new discrete distribution is assessed using four distinctive real data sets ԣoronavirus-flood peaks-forest fire-Leukemia? Finally, the new probabilistic model can serve as an alternative distribution to other competitive distributions available in the literature for modeling count data.</p> </abstract>

Estimation and Analysis of Wave Spectrum Parameter using HeMOSU-2 Observation Data

In this study, wave spectrum data were calculated using the water surface elevation data observed at 5Hz intervals from the HeMOSU-2 meteorological tower installed on the west coast of Korea, and wave parameters were estimated using wave spectrum data. For all significant wave height ranges, the peak enhancement parameter (γ opt ) of the JONSWAP spectrum and the scale parameter (α) and shape parameter (β) of the modify BM spectrum were estimated based on the observed spectrum, and the distribution of each parameter was confirmed. As a result of the analysis, the peak enhancement parameter (γ opt ) of the JONSWAP spectrum was calculated to be 1.27, which is very low compared to the previously proposed 3.3. And in the range of all significant wave heights, the distribution of the peak enhancement parameter (γ opt ) was shown as a combined distribution of probability mass function (PMF) and probability density function (PDF). In addition, the scale parameter (α) and shape parameter (β) of the modify BM spectrum were estimated to be [0.245, β1.278], which are lower than the existing [0.300, -1.098], and the result of the linear correlation analysis between the two parameters was β = =3.86α.

Neurophysiological Characterization of Posteromedial Hypothalamus in Anaesthetized Patients

Deep brain stimulation (DBS) requires a precise localization, which is especially difficult at the hypothalamus, because it is usually performed in anesthetized patients. We aimed to characterize the neurophysiological properties posteromedial hypothalamus (PMH), identified by the best neurophysiological response to electrical stimulation. We obtained microelectrode recordings from four patients with intractable aggressivity operated under general anesthesia. We pooled data from 1.5 mm at PMH, 1.5 mm upper (uPMH) and 1.5 mm lower (lPMH). We analyzed 178 units, characterized by the mean action potential (mAP). Only 11% were negative. We identified the next types of units: P1N1 (30.9%), N1P1N2 (29.8%), P1P2N1 (16.3%), N1P1 and N1N2P1 (6.2%) and P1N1P2 (5.0%). Besides, atypical action potentials (amAP) were recorded in 11.8%. PMH was highly different in cell composition from uPMH and lPMH, exhibiting also a higher percentage of amAP. Different kinds of cells shared similar features for the three hypothalamic regions. Although features for discharge pattern did not show region specificity, the probability mass function of inter-spike interval were different for all the three regions. Comparison of the same kind of mAP with thalamic neurons previously published demonstrate that most of cells are different for derivatives, amplitude and/or duration of repolarization and depolarization phases and also for the first phase, demonstrating a highly specificity for both brain centers. Therefore, the different properties described for PMH can be used to positively refine targeting, even under general anesthesia. Besides, we describe by first time the presence of atypical extracellular action potentials.

The Novel Bivariate Distribution: Statistical Properties and Real Data Applications

This article proposes a novel class of bivariate distributions that are completely defined by stating their conditionals as Poisson exponential distributions. Numerous statistical properties of this distribution are also examined here, including the conditional probability mass function (PMF) and moments of the new class. The techniques of maximum likelihood and pseudolikelihood are used to estimate the model parameters. Additionally, the effectiveness of the bivariate Poisson exponential conditional (BPEC) distribution is compared to that of the bivariate Poisson conditional (BPC), the bivariate Poisson (BP), the bivariate Poisson–Lindley (BPL), and the bivariate negative binomial (BNB) distributions using a real-world dataset. The findings of Akaike information criterion (AIC) and Bayesian information criterion (BIC) reveal that the BPEC distribution performs better than the other distributions considered in this study. As a result, the authors claim that this distribution may be used to fit dependent and overspread count data.

A New Skewed Discrete Model: Properties, Inference, and Applications

In this paper, a new probability discrete distribution for analyzing over-dispersed count data encountered in biological sciences was proposed. The new discrete distribution, with one parameter, has a log-concave probability mass function and an increasing hazard rate function, for all choices of its parameter. Several properties of the proposed distribution including the mode, moments and index of dispersion, mean residual life, mean past life, order statistics and L- moment statistics have been established. Two actuarial or risk measures were derived. The numerical computations for these measures are conducted for several parametric values of the model parameter. The parameter of the introduced distribution is estimated using eight frequentist estimation methods. Detailed Monte Carlo simulations are conducted to explore the performance of the studied estimators. The performance of the proposed distribution has been examined by three over-dispersed real data sets from biological sciences.

A Two-Filter Approach for State Estimation Utilizing Quantized Output Data

Filtering and smoothing algorithms are key tools to develop decision-making strategies and parameter identification techniques in different areas of research, such as economics, financial data analysis, communications, and control systems. These algorithms are used to obtain an estimation of the system state based on the sequentially available noisy measurements of the system output. In a real-world system, the noisy measurements can suffer a significant loss of information due to (among others): (i) a reduced resolution of cost-effective sensors typically used in practice or (ii) a digitalization process for storing or transmitting the measurements through a communication channel using a minimum amount of resources. Thus, obtaining suitable state estimates in this context is essential. In this paper, Gaussian sum filtering and smoothing algorithms are developed in order to deal with noisy measurements that are also subject to quantization. In this approach, the probability mass function of the quantized output given the state is characterized by an integral equation. This integral was approximated by using a Gauss–Legendre quadrature; hence, a model with a Gaussian mixture structure was obtained. This model was used to develop filtering and smoothing algorithms. The benefits of this proposal, in terms of accuracy of the estimation and computational cost, are illustrated via numerical simulations.

Design and Performance Analysis of Probabilistically Shaped QAM Signals for Coherent FSO Systems with Gamma-Gamma Turbulence Channels

Probabilistic shaping (PS) is a promising technique to approach the Shannon limit. In this paper, we design a practical coded modulation scheme based on PS to improve the capacity of coherent free-space optical (FSO) links with quadrature amplitude modulation (QAM), where the fading channel follows the Gamma-Gamma distribution. The aim of this paper is to optimize the probability mass function (PMF) of the QAM signal points to achieve the maximum channel capacity. Due to the complexity of the objective function, the heuristic algorithm was employed to solve the optimization problem. To the best of the authors’ knowledge, the closed-form pairwise error probability (PEP) is first derived with the non-uniform signals under the turbulence channel. In addition, we measure the average symbol error rate (SER) and post-FEC bit error rate (BER) by the Monte Carlo simulation method. The numerical simulation results of both capacity and BER show that the proposed PS scheme is better than the uniform distribution. The post-FEC BER results show that the proposed PS scheme provides significant gains compared with the uniform scheme.

Efficient Welding Defect Detectionand Classification of Phased Array C-Scan Images Using Modified Fast Fuzzy C Means Andradial Bias Function Neural Network

In the recent past, phased array technology is one of the most important methodologies used for inspection of welding. The welding defect identification is a difficult task due to noise content and uneven illumination and contrast on phased array 2D image. Artificial Neural Network (ANN) is a recent Machine Learning (ML) technology that has been achieved a lot of attention over the recent years. The saliency feature extraction for representing image has become complex due to quality of 2D image. The proper image restoration and enhancement techniques should be applied in order to improve the quality of 2D phased array image. The 2D-Adaptive Anisotropic Diffusion Filter (2D AADF) is applied to eliminate noises such as impulse noise and speckle noise. The Adaptive Mean Adjustment-Contrast Limited Adaptive Histogram Equalization (AMA-CLAHE) is the enhancement technique that is applied to improve contrast and brightness of the phased array 2D image. The welding defect region can be exactly segmented using saliency mapping to contour boundaries of defects in welding. In this paper, a novel methodology for welding defect detection is applied based on Modified Fast Fuzzy C Means (MFFCM) clustering technique by integrating Probability Mass Function (PMF) threshold technique for higher range of efficient and accurate segmentation. The Gray Level Co-Occurrence Matrix (GLCM) and 2D Band-let Transform (2D BT) are applied to extract features on segmented image. TheRadial Bias Function Neural Network (RBFNN) classifier is one of the ANN classifier for classifying welding defects. Most of image classification techniques utilize RBFNN as they will provide great range of accuracy and precision while compared to existing techniques. The localized generation error model is implemented in RBFNN in order to minimize Mean Square Error (MSE). The efficiency and accuracy of the proposed methodology has been evaluated with the help of experimental results in terms of graphical representation and numerical analysis.

A Probability Mass Function for Various Shapes of the Failure Rates, Asymmetric and Dispersed Data with Applications to Coronavirus and Kidney Dysmorphogenesis

In this article, a discrete analogue of an extension to a two-parameter half-logistic model is proposed for modeling count data. The probability mass function of the new model can be expressed as a mixture representation of a geometric model. Some of its statistical properties, including hazard rate function, moments, moment generating function, conditional moments, stress-strength analysis, residual entropy, cumulative residual entropy and order statistics with its moments, are derived. It is found that the new distribution can be utilized to model positive skewed data, and it can be used for analyzing equi- and over-dispersed data. Furthermore, the hazard rate function can be either decreasing, increasing or bathtub. The parameter estimation through the classical point of view has been performed using the method of maximum likelihood. A detailed simulation study is carried out to examine the outcomes of the estimators. Finally, two distinctive real data sets are analyzed to prove the flexibility of the proposed discrete distribution.