Generalized Gamma Distribution Research Articles

A proposed method for predicting extreme design forces of wave energy converters

This paper proposes to utilize a Generalized Gamma distribution for fitting the significant wave height data in order to more accurately calculate the sea state parameter distribution tails. The accuracy of the proposed method has been demonstrated based on the fittings to two ocean wave data sets. This proposed method has subsequently been utilized for deriving a 50-year environmental contour line. The engineering significance of using a more reliable contour line such as the one derived using the proposed method for predicting the long-term design force values for wave energy converters has been highlighted.

Adaptive CFAR Method for SAR Ship Detection Using Intensity and Texture Feature Fusion Attention Contrast Mechanism.

Due to the complexity of sea surface environments, such as speckles and side lobes of ships, ship wake, etc., the detection of ship targets in synthetic aperture radar (SAR) images is still confronted with enormous challenges, especially for small ship targets. Aiming at the key problem of ship target detection in the complex environments, the article proposes a constant false alarm rate (CFAR) algorithm for SAR ship target detection based on the attention contrast mechanism of intensity and texture feature fusion. First of all, the local feature attention contrast enhancement is performed based on the intensity dissimilarity and the texture feature difference described by local binary pattern (LBP) between ship targets and sea clutter, so as to realize the target enhancement and background suppression. Furthermore, the adaptive CFAR ship target detection method based on generalized Gamma distribution (GΓD) which can fit the clutter well by the goodness-of-fit analyses is carried out. Finally, the public datasets HRSID and LS-SSDD-v1.0 are used to verify the effectiveness of the proposed detection method. A large number of experimental results show that the proposed method can suppress clutter background and speckle noise and improve the target-to-clutter rate (TCR) significantly, and has the relative high detection rate and low false alarm rate in the complex background and multi-target marine environments.

Crop Classification and Representative Crop Rotation Identifying Using Statistical Features of Time-Series Sentinel-1 GRD Data

Compared with a monoculture planting mode, the practice of crop rotations improves fertilizer efficiency and increases crop yield. Large-scale crop rotation monitoring relies on the results of crop classification using remote sensing technology. However, the limited crop classification accuracy cannot satisfy the accurate identification of crop rotation patterns. In this paper, a crop classification and rotation mapping scheme combining the random forest (RF) algorithm and new statistical features extracted from time-series ground range direction (GRD) Sentinel-1 images. First, the synthetic aperture radar (SAR) time-series stacks are established, including VH, VV, and VH/VV channels. Then, new statistical features named the objected generalized gamma distribution (OGΓD) features are introduced to compare with other object-based features for each polarization. The results showed that the OGΓD σVH achieved 96.66% of the overall accuracy (OA) and 95.34% of the Kappa, improving around 4% and 6% compared with the object-based backscatter in VH polarization, respectively. Finally, annual crop-type maps for five consecutive years (2017–2021) are generated using the OGΓD σVH and the RF. By analyzing the five-year crop sequences, the soybean-corn (corn-soybean) is the most representative rotation in the study region, and the soybean-corn-soybean-corn-soybean (together with corn-soybean-corn-soybean-corn) has the highest count with 100 occurrences (25.20% of the total area). This study offers new insights into crop rotation monitoring, giving the basic data for government food planning decision-making.

Applicable Condition of the Approximate Parameter Estimation Method of the Generalized Gamma Distribution

The generalized Gamma distribution ( <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\text{G}\Gamma \text{D}$ </tex-math></inline-formula> ) has been found accurate for modeling synthetic aperture radar (SAR) data. To facilitate the practical applications of this model, an approximate method for estimating the parameters in the <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\text{G}\Gamma \text{D}$ </tex-math></inline-formula> was recently given by Stacy (1962) and discussed by Krylov et al. (2013) and Abramowitz and Stegun (1972), in which the applicable condition of the method is restrictive and incorrect. This article further derives the analytical condition of the applicability of the method. Examples of theoretical analysis and simulations verify the correctness of the derivations.

Some Properties of the New Mixture of Generalized Gamma Distribution

Some Properties of the New Mixture of Generalized Gamma Distribution

Design of Multiple Deferred State Repetitive Group Sampling Plans for Life Tests based on Generalized Gamma Distribution

Reliability sampling plans is a procedure to determine the acceptance or non-acceptance of the lot(s) of finished products by performing tests on the sampled items. Lifetime of individual items is a quality characteristic that can be treated as a continuous random variable and can be modeled by an appropriate continuous probability distribution. In this article, Multiple Deferred State Repetitive Group Sampling (MDSRGS) Plans for life tests under hybrid censoring with a provision to draw a random sample and to admit a maximum of one failure in the sample is formulated assuming that the lifetime random variable follows a Generalized Gamma (GG) distribution. A methodical procedure for the selection of the plan parameters using mean life criterion with the desired discrimination protecting the interests of the producer and the consumer in terms of the acceptable mean life and unacceptable mean life is evolved.

Energy Efficient Resource Allocation for eHealth Monitoring Wireless Body Area Networks With Backscatter Communication

Electronic Health (eHealth) monitoring systems with wireless body area networks (WBANs) have recently emerged as promising solutions to provide sustainable and high-quality health services. In this paper, we propose an optimization framework to maximize the energy efficiency (EE) of a WBAN assisted by backscatter communication (BackCom) and energy harvesting technologies, subject to quality-of-service and power budget constraints. More specifically, the optimization problem jointly optimizes the transmit power of the aggregator, transmission time, and backscatter time of the WBAN consisting of energy-constrained sensor nodes (SNs) which have the ability to harvest energy from the signals transmitted by the aggregator. A generalized gamma distribution is adopted to characterize the channel propagation characteristics of patients under different arbitrary body movements and their corresponding transmission requirements during daily life activities. It is shown that the formulated EE optimization problem is a quasi-concave nonlinear fractional program, and it is transformed to an equivalent parametric problem by using the Dinkelbach algorithm to obtain the solution. We exploit the structure of the optimization problem and propose a low-complexity iterative-based suboptimal heuristic with performance fairly close to the optimized solution. Simulation results demonstrate the effectiveness of the proposed schemes in maximizing EE of the WBAN, whereas the comparisons with the related work from the literature reaffirm the superiority of the proposed algorithms.

Approximation of Long-Term Survival with Polatuzumab Vedotin Plus Bendamustine and Rituximab for Patients with Relapsed/Refractory Diffuse Large B-Cell Lymphoma: Results Based on The GO29365 Trial.

To inform healthcare professionals, payers and health technology organisations of estimated survival benefits of new treatments, statistical methods can be used to model the projected clinical benefits versus costs of new interventions. This is particularly relevant for new treatments where data describing all progression events are incomplete and long-term survival outcomes are not yet established. In patients with the fast-growing B-cell cancer, diffuse large B-cell lymphoma (DLBCL), heterogeneous clinical efficacy outcomes are observed with the presence of both 'cured' (long-term survivors [LTS]) and 'non-cured' patients. Mixture cure rate models represent an alternative approach to traditional standard parametric survival models as they capture this heterogeneity. The aim of this analysis was to use progression-free survival (PFS) as an intermediate endpoint to estimate long-term survival with polatuzumab vedotin (Pola) + bendamustine (B) + rituximab (R) treatment (Pola+BR); these survival estimates will be utilised to inform future economic analyses. Using data from the Phase II randomised cohort of the GO29365 trial (NCT02257567), we estimated the overall survival (OS) benefit and proportion of LTS with Pola+BR versus BR alone in patients with relapsed/refractory (R/R) DLBCL. Alongside standard parametric survival models, a mixture cure rate model was evaluated for each treatment arm, exploring both OS and OS informed by PFS. The estimated mean OS was 3.78 years for Pola+BR versus 1.07 years for BR using standard parametric methods and 4.00 years versus 1.02 years using a mixture cure rate model (OS informed by PFS). The proportion of LTS using the mixture cure rate model was 23.0% (95% confidence interval: 9.3, 45.36) for Pola+BR versus 0% for BR (assuming a generalised gamma distribution). Of the extrapolation methods tested, mixture cure rate model predictions were best aligned with the observed survival data in GO29365. These models suggest that compared with BR alone, Pola+BR is associated with a higher proportion of LTS ranging from 22.0 to 26.6%, depending on the distribution assumed. However, the upper and lower limits of the confidence intervals of the point estimates are reaching from 9 to 45%.

Statistical properties of the off-diagonal matrix elements of observables in eigenstates of integrable systems.

We study the statistical properties of the off-diagonal matrix elements of observables in the energy eigenstates of integrable quantum systems. They have been found to be dense in the spin-1/2 XXZ chain, while they are sparse in noninteracting systems. We focus on the quasimomentum occupation of hard-core bosons in one dimension and show that the distributions of the off-diagonal matrix elements are well described by generalized Gamma distributions, in both the presence and absence of translational invariance but not in the presence of localization. We also show that the results obtained for the off-diagonal matrix elements of observables in the spin-1/2 XXZ model are well described by a generalized Gamma distribution.

Generalized gamma distribution for biomedical signals denoising

A wide range of signs are acquired from the human body called biomedical signs or biosignals, and they can be at the cell level, organ level, or sub-atomic level. Electroencephalogram is the electrical activity from the cerebrum, the electrocardiogram is the electrical activity from the heart, electrical action from the muscle sound signals referred to as electromyogram, the electroretinogram from the eye, and so on. Studying these signals can be so helpful for doctors, and it can help them examine and predict and cure many diseases.However, these signals are often affected by various types of noise. It is important to denoise the signals to get accurate information from them. The denoising process is solved by proposing an entirely novel family of flexible score functions for blind source separation, based on a family of generalized Gamma densities. To blindly extract the independent source signals, we resort to the popular fast independent component analysis (FastICA) approach; to adaptively estimate the parameters of such score functions, we use an efficient method based on maximum likelihood. The results obtained using generalized Gamma densities in our technique are better than those obtained by other distribution functions.

A novel full-polarization SAR image ship detector based on scattering mechanisms and wave polarization anisotropy

Synthetic aperture radar (SAR) is suitable for earth observation due to its unique advantages. In this study, we constructed an adaptive ship detector using full-polarization SAR images. First, we thoroughly investigated the differences in scattering characteristics between ships, their background, and the wave polarization anisotropy. We then constructed a novel ship detector that incorporates scattering and anisotropy (known as joint scattering–anisotropy [joint-SA]). We found that joint-SA is an effective physical quantity representing the difference between the ship and its background; thus, joint-SA can be used for ship detection using full-polarization image data. Second, we used generalized gamma distribution to characterize joint-SA statistics of sea clutter with a large homogeneity range. Third, an adaptive constant false alarm rate (CFAR) method was implemented based on joint-SA. Finally, RADARSAT-2 and GF-3 data in the C-band and ALOS data in the L-band were used for verification. We tested five datasets, and the experimental results verified the correctness and superiority of the CFAR method based on joint-SA. The results show that the signal–clutter ratio of the proposed ship detector (33.17 dB, 35.98 dB, and 57.25 dB) was higher than that of DBSP (8.92 dB, 3.43 dB, and 25.40 dB) and RsDVH (17.28 dB, 11.17 dB, and 54.55 dB). Furthermore, the proposed detector has a higher detection accuracy and lower false alarm rate than those of the other two other methods.

Concentration inequalities from monotone couplings for graphs, walks, trees and branching processes

Generalized gamma distributions arise as limits in many settings involving random graphs, walks, trees, and branching processes. Peköz et al. (2016) exploited characterizing distributional fixed point equations to obtain uniform error bounds for generalized gamma approximations using Stein’s method. Here we show how monotone couplings arising with these fixed point equations can be used to obtain sharper tail bounds that, in many cases, outperform competing moment-based bounds and the uniform bounds obtainable with Stein’s method. Applications are given to concentration inequalities for preferential attachment random graphs, branching processes, random walk local time statistics and the size of random subtrees of uniformly random binary rooted plane trees.

Channel Modeling for Orbital Angular Momentum Based Underwater Wireless Optical Systems

The underwater turbulence channel is modelled and a unified statistical distribution is applied for characterizing orbital angular momentum (OAM) propagation in underwater wireless optical communication (UWOC) systems. Based on Monte-Carlo simulations, the effects of turbulences are characterized by the multiple phase screens model considering both the coherence width and scintillation index. The phase screen samples are processed by the randomized spectral sampling discrete Fourier transform (DFT) technique. To validate the propagated field distribution, both the phase structure function and optical transfer function are derived and evaluated with the aid of ensemble-averaged results. The Generalized Gamma Distribution (GGD) enriched by an additional independent parameter is applied for modelling the probability density function (PDF) of both the reference-channels, fluctuating irradiance as well as the intermodal crosstalk irradiance between different OAM modes. Furthermore, based on the PDF, the performance metrics of both single input multiple output (SISO) and multiple input multiple output (MIMO) systems are analyzed, based on the average capacity, the bit-error rate and the outage probability.

Generalized Gamma-Laguerre Polynomial Chaos to Model Random Bending of Wearable Antennas

A novel generalized Gamma-Laguerre polynomial chaos expansion is proposed to account for the effect of random variations in lower bounded design parameters on antenna performance. After fitting a shifted generalized Gamma distribution to datasets of such random variables, a predistorted polynomial chaos expansion is generated based on a set of orthogonal generalized Laguerre polynomials. The new statistical methodology is applied to assess the random change in resonance frequency when bending a wearable antenna around different parts of the human body, such as a leg, an arm, and a head. For different datasets, an excellent statistical fit is found to both the estimated probability density function of the bending radius and the resulting statistical distribution of the resonance frequency, while requiring up to 480 times fewer sample evaluations.

The Generalized Gamma Distribution as a Useful RND under Heston’s Stochastic Volatility Model

We present the Generalized Gamma (GG) distribution as a possible risk neutral distribution (RND) for modeling European options prices under Heston’s stochastic volatility (SV) model. We demonstrate that under a particular reparametrization, this distribution, which is a member of the scale-parameter family of distributions with the mean being the forward spot price, satisfies Heston’s solution and hence could be used for the direct risk-neutral valuation of the option price under Heston’s SV model. Indeed, this distribution is especially useful in situations in which the spot’s price follows a negatively skewed distribution for which Black–Scholes-based (i.e., the log-normal distribution) modeling is largely inapt. We illustrate the applicability of the GG distribution as an RND by modeling market option data on three large market-index exchange-traded funds (ETF), namely the SPY, IWM and QQQ as well as on the TLT (an ETF that tracks an index of long-term US Treasury bonds). As of the writing of this paper (August 2021), the option chain of each of the three market-index ETFs shows a pronounced skew of their volatility ‘smile’, which indicates a likely distortion in the Black–Scholes modeling of such option data. Reflective of entirely different market expectations, this distortion in the volatility ‘smile’ appears not to exist in the TLT option data. We provide a thorough modeling of the option data we have on each ETF (with the 15 October 2021 expiration) based on the GG distribution and compare it to the option pricing and RND modeling obtained directly from a well-calibrated Heston’s SV model (both theoretically and also empirically, using Monte Carlo simulations of the spot’s price). All three market-index ETFs exhibited negatively skewed distributions, which are well-matched with those derived under the GG distribution as RND. The inadequacy of the Black–Scholes modeling in such instances, which involves negatively skewed distribution, is further illustrated by its impact on the hedging factor, delta, and the immediate implications to the retail trader. Similarly, the closely related Inverse Generalized Gamma distribution (IGG) is also proposed as a possible RND for Heston’s SV model in situations involving positively skewed distribution. In all, utilizing the Generalized Gamma distributions as possible RNDs for direct option valuations under the Heston’s SV is seen as particularly useful to the retail traders who do not have the numerical tools or the know-how to fine-calibrate this SV model.

Benfordness of the Generalized Gamma Distribution

The generalized gamma distribution shows up in many problems related to engineering, hydrology as well as survival analysis. Earlier work has been done that estimated the deviation of the exponential and the Weibull distribution from Benford's Law. We give a mathematical explanation for the Benfordness of the generalized gamma distribution and present a measure for the deviation of the generalized gamma distribution from the Benford distribution.

Parametric Landmark Estimation of the Transition Probabilities in Survival Data with Multiple Events

Multi-state models are a useful tool for analyzing survival data with multiple events. The transition probabilities play an important role in these models since they allow for long-term predictions of the process in a simple and summarized manner. Recent papers have used the idea of subsampling to estimate these quantities, providing estimators with superior performance in the case of strong violations of the Markov condition. Subsampling, also referred to as landmarking, leads to small sample sizes and usually heavily censored data, which leads to estimators with higher variability. Here, we use the flexibility of the generalized gamma distribution combined with the same idea of subsampling to obtain estimators free of the Markov condition with less variability. Simulation studies show the good small sample properties of the proposed estimators. The proposed methods are illustrated using real data.

Performance analysis of spatial multiplexing MIMO-MFSK based on energy detection for fast-fading environments

In fast-fading scattering environments such as high-speed rail and low-altitude communications, mobile communication systems need to quickly and robustly estimate and equalize fast-fading, time-varying channels. Under these circumstances, noncoherent multiple-input multiple-output (MIMO) has received attention in recent years, since it is less influenced by factors such as phase fluctuations and has fewer requirements for channel estimation and synchronization. Spatial multiplexing MIMO-MFSK based on energy detection is different from conventional noncoherent MIMO in that it can achieve higher spatial multiplexing gain in the independent distribution of channel fading statistics. At the receiver, partial real channel state information (CSI) is available, which can improve the capacity while ensuring the reliability of the link. With partial real CSI replacing instantaneous CSI, the system performance is inferior to conventional coherent MIMO under the influence of noise. As a result, it is necessary to analyze its theoretical detection performance. By energy detection, the noise of the MIMO-MFSK system conforms to the generalized gamma distribution. On the basis of this distribution, the optimal decision rule of the system and the symbol error rate (SER) formula are derived. Additionally, we investigate the signal-dependent noise problem of minimum Euclidean distance detection. Numerical results show that the SER formula fits well with the simulation results under the condition of a high signal-to-noise ratio.

Retinal Blood Vessel Segmentation Using a Generalized Gamma Probability Distribution Function (PDF) of Matched Filtered

Retinal images contain information about the retina's blood vessel structure to predict retinal diseases such as diabetics, obesity, glaucoma, etc. Segmentation of accurate retinal blood vessels is a challenging task in the low background of retinal images. Therefore, we proposed a Generalized Gamma Distribution probability distribution function (pdf) to extract the accurate vascular structure on the retinal images. The proposed approach is divided into processing steps, the Generalized Gamma distribution kernel, and the postprocessing step. In pre-processing, the conversion of a color retinal image into a grayscale image using PCA followed by the CLAHE method and the Toggle Contrast method enhances the grayscale images of the retina. The proposed matched filter of Generalized Gamma distribution generates the MFR images. The postprocessing step extracts the thick vessels and thin retinal blood vessels using the optimal thresholding technique. The results obtained on DIRVE database average accuracy 95.00% and the STARE database 93.85%, respectively.

Reliability Analysis of a Bridge Deck Utilizing Generalized Gamma Distribution

Reliability Analysis of a Bridge Deck Utilizing Generalized Gamma Distribution