Lambda Distribution Research Articles

Statistical modelling of cryptocurrencies

There has been tremendous interest invested by researchers and academics in Bitcoin since it's introduction to the financial market. However, in recent years there has been an advancement of the cryptocurrency market where other cryptocurrencies such as Ethereum, Litecoin and Ripple have grown relatively quickly and could potentially challenge the dominant placement of Bitcoin. These cryprocurrencies have been utilized globally as a virtual currency for multiple transactions. The returns of cryptocurrencies are known to be volatile and have been observed to fluctuate quite a bit in recent times. This study assesses and differentiates the performance of generalized autoregressive score (GAS) models integrated with a few heavy-tailed distributions in Value-at-Risk (VaR) estimation of the four most popular cryptocurrencies' returns, i.e. Bitcoin returns, Ethereum returns, Litecoin returns and Ripple returns. This paper proposed VaR models for Bitcoin, Ethereum, Litecoin and Ripple returns, i.e. GAS models combined with the generalized hyperbolic distribution (GHD), the variance gamma (VG) distribution, the normal inverse Gaussian (NIG) distribution and the generalized lambda distribution (GLD). The Kupiec likelihood ratio test was adopted to evaluate the proposed models' adequacy and Backtesting VaR was used to select the superior set of models.

Small‐sample properties of robust willingness‐to‐pay estimators

AbstractThe small‐sample properties of robust, binary choice willingness‐to‐pay (WTP) estimators are analyzed. A Monte Carlo simulation compares the bias and mean‐squared error of marginal and expected WTP estimates from probit, zero‐centered (“robit”), logit, and a generalized Tukey lambda distribution called a “pregibit” regression under normal and nonnormal distributional assumptions. Robust binary choice estimators allow for variation in tail thickness (the robit and pregibit) or tail asymmetry (the pregibit). No previous studies have compared the performance of these WTP estimators. The findings will interest researchers who use contingent validation methods to estimate WTP for nonmarket or hypothetical goods.

Cosmic evolution of black hole spin and galaxy orientations: Clues from the NewHorizon and Galactica simulations

Black holes (BHs) are ubiquitous components of the center of most galaxies. In addition to their mass, the BH spin, through its amplitude and orientation, is a key factor in the galaxy formation process, as it controls the radiative efficiency of the accretion disk and relativistic jets. Using the recent cosmological high-resolution zoom-in simulations and in which the evolution of the BH spin is followed on the fly, we have tracked the cosmic history of a hundred BHs with a mass greater than $2 For each of them, we have studied the variations of the three-dimensional angle (Psi ) subtended between the BH spins and the angular momentum vectors of their host galaxies (estimated from the stellar component). The analysis of the individual evolution of the most massive BHs suggests that they are generally passing by three different regimes. First, for a short period after their birth, low-mass BHs BH <$3times 10$^4$M$_ are rapidly spun up by gas accretion and their spin tends to be aligned with their host galaxy spin. Then follows a second phase in which the accretion of gas onto low-mass BHs BH is quite chaotic and inefficient, reflecting the complex and disturbed morphologies of forming proto-galaxies at high redshifts. The variations of Psi are rather erratic during this phase and are mainly driven by the rapid changes of the direction of the galaxy angular momentum. Then in a third and long phase, BHs are generally well settled in the center of galaxies around which the gas accretion becomes much more coherent BH >$10$^5$ M$_ In this case, the BH spins tend to be well aligned with the angular momentum of their host galaxy and this configuration is generally stable even though BH merger episodes can temporally induce misalignment. We even find a few cases of BH-galaxy spin anti-alignment that lasts for a long time in which the gas component is counter-rotating with respect to the stellar component. We have also derived the distributions of cos(Psi ) at different redshifts and found that BHs and galaxy spins are generally aligned. Our analysis suggests that the fraction of BH-galaxy pairs with low Psi values reaches maximum at zsim 4-3 and then decreases until zsim 1.5 due to the high BH-merger rate. Afterward, it remains almost constant probably due to the fact that BH mergers becomes rare, except for a slight increase at late times. Finally, based on a Monte Carlo method, we also predict statistics for the 2-d projected spin-orbit angles lambda . In particular, the distribution of lambda traces the alignment tendency well in the three-dimensional analysis. Such predictions provide an interesting background for future observational analyses.

Uncertainty quantification with high-dimensional correlated process variations for an in-situ thermal expansion coefficient test structure

The impacts of process variations on the π-shaped thermal expansion coefficient (TEC) in-situ test structure are analyzed. Correlations among high-dimensional design parameters have to be taken into account for this type of structure, while the widely studied polynomial chaos expansion (PCE) technique is incapable of solving such problems. This paper presents a novel method for high-dimensional uncertainty quantification problems with non-Gaussian correlated variants. As a pre-processing method, the Spearman correlation coefficient and generalized lambda distribution are merged to eliminate the correlation. Then a compressed-sensing based Legendre-sparse solver is applied benefiting from the uniformly distributed parameters derived from the pre-processing and thus the cost of rebuilding correlated basis functions is eliminated. This method has demonstrated superior performance over existing methods in the analysis of TEC in-situ test structures. This analysis shows that the measurement accuracy of the test structure demonstrates good performance and is insensitive to process errors, which is consistent with experimental data. The presented technique has the potential to be applied in the design of various microelectromechanical system (MEMS) devices.

Identifying the Probability Distribution of Exchange Rates in Sri Lanka

The exchange rate is one of the main components that represents the status of a country’s economic condition. This study mainly focuses on identifying an appropriate distribution that can capture the asymmetric behaviour of important currency exchange rates related to Sri Lanka. The true behaviour of the exchange rates of USD, EURO, JPY, AUD, GBP, CHF, SGD and CAD in terms of LKR was determined using flexible distributions of generalised lambda distribution (GLD), Normal Inverse Gaussian and Skew-Normal. The parameter estimation was carried out by maximum likelihood estimation (MLE), while for GLD, few more parameter estimation techniques were applied. To understand how well the fitted distributions identify the real behaviour of data, we conducted the goodness-of-fit (GOF) tests. The results from Cramer–Von Mises (CvM) and Anderson–Darling (AD) GOF tests pointed out that the exchange rates data follow a GLD with the parameter estimation of maximum product of spacings (MPS). Further, plots of histograms with theoretical densities, cumulative distribution functions (CDFs) with empirical CDF and Quantile–Quantile plots illustrated the same idea. This study presented the findings based on different suitable parameter estimation techniques and this study is the first investigation on the distribution identification of exchange rates in Sri Lanka. JEL Codes: C12,C13,G10

Extreme Events Analysis Using LH-Moments Method and Quantile Function Family

A direct way to estimate the likelihood and magnitude of extreme events is frequency analysis. This analysis is based on historical data and assumptions of stationarity, and is carried out with the help of probability distributions and different methods of estimating their parameters. Thus, this article presents all the relations necessary to estimate the parameters with the LH-moments method for the family of distributions defined only by the quantile function, namely, the Wakeby distribution of 4 and 5 parameters, the Lambda distribution of 4 and 5 parameters, and the Davis distribution. The LH-moments method is a method commonly used in flood frequency analysis, and it uses the annual series of maximum flows. The frequency characteristics of the two analyzed methods, which are both involved in expressing the distributions used in the first two linear moments, as well as in determining the confidence interval, are presented. The performances of the analyzed distributions and the two presented methods are verified in the following maximum flows, with the Bahna river used as a case study. The results are presented in comparison with the L-moments method. Following the results obtained, the Wakeby and Lambda distributions have the best performances, and the LH-skewness and LH-kurtosis statistical indicators best model the indicators’ values of the sample (0.5769, 0.3781, 0.548 and 0.3451). Similar to the L-moments method, this represents the main selection criterion of the best fit distribution.

Spatial multivariate data imputation using deep learning and lambda distribution

Artificial neural networks (ANNs) are often used to establish a mapping between an input data set and a corresponding output. There are many applications that rely on quantifying the conditional distribution of the output given the input data set. This is often referred to as aleatoric uncertainty associated with variability of the outcome due to inherently random effects. In this paper, deep learning is used to quantify moments of the conditional distribution of a missing variable based on homotopic multivariate observations. The lambda distribution is then used to parametrize the conditional distribution based on the provided moments. Geostatistical quantification of spatial continuity complements the multivariate conditional distribution through Bayesian updating to inform multiple data imputation that accounts for the uncertainty associated with the missing variable(s). Geological data are often incomplete, and data imputation is an essential step to avoid excluding heterotopic data. The proposed data imputation framework trains multi layer perceptron (MLP) neural networks to characterize multivariate relationships inferred from homotopic training data. A case study is conducted using geological data from a lateritic Nickle deposit to demonstrate application of the proposed methodology.

Superpixel Generation for Polarimetric SAR Images with Adaptive Size Estimation and Determinant Ratio Test Distance

Superpixel generation of polarimetric synthetic aperture radar (PolSAR) images is widely used for intelligent interpretation due to its feasibility and efficiency. However, the initial superpixel size setting is commonly neglected, and empirical values are utilized. When prior information is missing, a smaller value will increase the computational burden, while a higher value may result in inferior boundary adherence. Additionally, existing similarity metrics are time-consuming and cannot achieve better segmentation results. To address these issues, a novel strategy is proposed in this article for the first time to construct the function relationship between the initial superpixel size (number of pixels contained in the initial superpixel) and the structural complexity of PolSAR images; additionally, the determinant ratio test (DRT) distance, which is exactly a second form of Wilks’ lambda distribution, is adopted for local clustering to achieve a lower computational burden and competitive accuracy for superpixel generation. Moreover, a hexagonal distribution is exploited to initialize the PolSAR image based on the estimated initial superpixel size, which can further reduce the complexity of locating pixels for relabeling. Extensive experiments conducted on five real-world data sets demonstrate the reliability and generalization of adaptive size estimation, and the proposed superpixel generation method exhibits higher computational efficiency and better-preserved details in heterogeneous regions compared to six other state-of-the-art approaches.

Single-Leg Squat and Reported Pain in Collegiate Softball Pitchers.

Single-leg squat (SLS) performance is related to altered mechanics related to injury during the windmill softball pitch; however, it is unknown if SLS kinematics differ between softball pitchers with and without upper extremity pain. The purpose of this study was to compare knee valgus, trunk rotation, trunk lateral flexion, and trunk flexion during an SLS in collegiate softball pitchers with and without self-reported upper extremity pain. It was hypothesized that those who reported upper extremity pain would show increased compensatory trunk and knee kinematics compared with those without pain. Controlled laboratory study. A total of 75 collegiate softball players (mean age, 20.4 ± 1.7 years; mean height, 173.3 ± 7.7 cm; mean weight, 79.1 ± 11.6 kg) participated and were placed in pain (n = 20) or no-pain (n = 55) groups. Participants performed an SLS once per side. Kinematic data were collected at 100 Hz using an electromagnetic tracking system. A 2 (pain vs no pain) × 2 (descent vs ascent) × 2 (drive leg vs stride leg) mixed-design multivariate analysis of variance with Wilks lambda distribution was used to determine differences in drive-leg and stride-leg lower body mechanics between the descent and ascent phases of the SLS between the pitchers in the current study with and without pain. There was no significant effect in the 3-way interaction between upper extremity pain, side, and phase (Λ = 0.960; F[4, 70] = 0.726; P = .577; η2 = 0.04). However, there were large effects for the phase × side interaction (Λ = 0.850; P = .021; η2 = 0.150). There was a main effect of phase (Λ = 0.283; P < .001; η2 = 0.717). Study findings indicated that SLS mechanics do not differ between collegiate softball pitchers with and without reported upper extremity pain. Drive-leg mechanics showed more stability in the SLS than stride-leg mechanics. Softball pitchers are at risk of upper extremity injury. It is important to identify mechanisms that may lead to pain in order to mitigate the risk of injury.

Large-Eddy Simulation Analysis of Flow and Combustion in a Pre-Chamber Ignited Gasoline Engine

ABSTRACT Multi-cycle large eddy simulations were conducted to resolve the turbulent flow field spatially and temporally in a pre-chamber ignited gasoline engine. The numerical models were validated by comparing with both the passive and active pre-chamber experimental data. Correlation analysis results of the two pressure peaks during combustion inside the pre-chamber showed that the combustion inside the pre-chamber directly influences the timing and strength of the turbulent jets, which would ignite the mixture inside the main chamber. Then, the flow field evolution and fuel/air mixture formation inside both the main chamber and pre-chamber during intake and compression strokes were investigated numerically. Results of the passive pre-chamber showed that mixture distribution near the orifices during the compression stroke affects the averaged lambda of the gas inside the pre-chamber. By using the orifices with a tilted orientation, the fuel inside the pre-chamber could be stratified. When the mixture near electrodes is rich, the development of ignition kernel and the consequent flame propagation would benefit. In the case of active pre-chamber, although the lambda distribution patterns of mixture before the spark plug ignition are similar between different cycles, the magnitude of velocity would affect the early flame propagation inside the pre-chamber.

Reliability Evaluation Method of Pseudo-failure Life Distribution for Industrial Robot Servo System Based on The Generalized Lambda Distribution

A reliability evaluation method of pseudo-failure life distribution for Industrial Robot Servo System (IRSS) based on The Generalized Lambda Distribution (GLD) was proposed in the paper. The IRSS pseudo-failure life GLD distribution was established. Quantile estimation method was applied to estimate the GLD parameters. The proposed method had no need of presetting specific distribution morphology, and thus improve the accuracy of IRSS pseudo-failure reliability modeling. In the application experiment, the IRSS pseudo-failure life distribution reliability evaluation method based on GLD was used to obtain the IRSS failure life, the reliability evaluation result was consistent with the design failure life, which indicated the validity of the proposed method.

Distribution of angle lambda and pupil offset as measured by combined Placido Scheimpflug Topography

BackgroundAngle lambda is the angle between the pupillary axis and the line of sight. It is important for accurate centration during anterior segment surgery. The purpose of this study is to identify the distribution of angle lambda and pupil center offset as measured by a combined placido disc Scheimpflug topography system.MethodsA prospective non-randomized study was performed on 2178 eyes in Eye World Hospital, Giza, Egypt. Sirius device (CSO, Costruzione Strumenti Oftalmici, Florence, Italy, version 3.2.1.60) was used to measure average keratometry (K), anterior chamber depth (ACD), central corneal thickness (CCT), horizontal visible iris diameter (HVID), pupil radius (PR), pupil center intercept x-component (PCI-x), and pupil center intercept y-component (PCI-y). Axial length (AL) was measured by immersion A-scan Eyecube Ultrasonography device (Ellex, Adelaide, South Australia, Australia). Angle lambda was calculated by a trigonometrical equation. Pearson correlation was used to analyze the correlation between angle lambda and age and refraction.ResultsAverage angle lambda in all eyes was 3.32° ± 1.99. Mean angle lambda was significantly smallest in myopia and largest in hyperopia. Age correlation to angle lambda was insignificant. Average PCI-x and PCI-y in all eyes was − 0.047 mm and + 0.091 mm, respectively.ConclusionsAngle λ is significantly larger in hyperopia than myopia, and the effect of age is insignificant. Pupil center offset was horizontally greater in hyperopia than in myopia. We therefore encourage the preoperative assessment of angle λ to avoid decentered ablation, especially when treating hyperopia.

On the goodness-of-fits of the generalized lambda distribution on high-frequency stock index returns

On the goodness-of-fits of the generalized lambda distribution on high-frequency stock index returns

From monocular photograph to angle lambda: A new clinical approach for quantitative assessment

ABSTRACT Angle lambda assessment is essential in pediatric and strabismus practice. An abnormal angle lambda will modify the visual appearance of a strabismus or mimic one. Currently, angle lambda can be assessed by corneal topographs. Unfortunately, the use of these devices remains limited in the context of a strabismus clinic. Herein, we propose an easy, low cost, and reproducible method for angle lambda quantification, based on monocular photographs. Monocular pictures were taken by using a camera with a ring flash, centered by a fixation point. A digital evaluation analyzed the position of the corneal reflex on the pupil diameter. Using a trigonometric formula, the resulting ratio was converted into the value of angle lambda. This method was tested on 20 healthy eyes, on two successive couples of pictures, to evaluate its repeatability. Assessment using Pentacam was performed for comparison. The mean value of angle lambda was +2.61° ± 2.92° and 2.63° ± 2.85° in both picture series, respectively, and Lin’s repeatability coefficient was 0.99 – with a systematic deviation of −0.071° compared to Pentacam assessment. Angle lambda distribution was in range with values from the literature. This new method allows for angle lambda assessment without requiring a specific device and can be used in strabismus and pediatric clinics.

Modified information criterion for testing changes in generalized lambda distribution model based on confidence distribution

Modified information criterion for testing changes in generalized lambda distribution model based on confidence distribution

Quantile based modeling of diurnal temperature range with the five‐parameter lambda distribution

AbstractDiurnal temperature range is an important variable in climate science that can provide information regarding climate variability and climate change. Changes in diurnal temperature range can have implications for hydrology, human health and ecology, among others. Yet, the statistical literature on modeling diurnal temperature range is lacking. In this article we propose to model the distribution of diurnal temperature range using the five‐parameter lambda (FPL) distribution. Additionally, in order to model diurnal temperature range with explanatory variables, we propose a distributional quantile regression model that combines quantile regression with marginal modeling using the FPL distribution. Inference is performed using the method of quantiles. The models are fitted to 30 years of daily observations of diurnal temperature range from 112 weather stations in the southern part of Norway. The flexible FPL distribution shows great promise as a model for diurnal temperature range, and performs well against competing models. The distributional quantile regression model is fitted to diurnal temperature range data using geographic, orographic, and climatological explanatory variables. It performs well and captures much of the spatial variation in the distribution of diurnal temperature range in Norway.

Distribution of Interferon Lambda 4 Single Nucleotide Polymorphism rs11322783 Genotypes in Patients with COVID-19.

Type III interferons (IFN-III), also known as IFN-Lambda, have a pivotal role during SARS-CoV-2 infection. IFN-Lambda response among individuals is heterogeneous and its association with COVID-19 symptoms severity needs to be further clarified. We analyzed the genotype frequencies of IFNL4 single nucleotide polymorphism (SNP) rs11322783 in patients with COVID-19 (n = 128), in comparison with a validated data set of European healthy controls (n = 14152). The IFNL4 SNP was also analyzed according to the haematological and clinical parameters of patients with COVID-19. The distributions of IFNL4 genotypes among SARS-CoV-2 positive patients [TT/TT 41.4% (n = 53), TT/ΔG 47.7% (n = 61) and ΔG/ΔG 10.9% (n = 14)] and healthy controls were comparable. Different levels of white blood cells (p = 0.036) and neutrophils (p = 0.042) were found in the IFNL4 different genotypes in patients with COVID-19; the ΔG/ΔG genotype was more represented in the groups with low white blood cells and neutrophils. There were no differences in major inflammation parameters (C-reactive protein, D-dimer, Albumin, and Lactate-dehydrogenase (LDH)] and survival rate according to the IFNL4 genotypes. In conclusion, although patients with COVID-19 did not exhibit a different distribution of the IFNL4 SNP, the ΔG/ΔG genotype was associated with a lower count of immune cell populations. These findings need to be confirmed in larger groups of patients with COVID-19 and the role of IFNL4 SNP needs to be also investigated in other respiratory viral infections.

Sparse simulation-based estimator built on quantiles

The method of simulated quantiles is extended to a general multivariate framework and to provide sparse estimation of the scaling matrix. The method is based on the minimisation of a distance between appropriate statistics evaluated on the true and synthetic data simulated from the postulated model. Those statistics are functions of the quantiles providing an effective way to deal with distributions that do not admit moments of any order like the α–Stable or the Tukey lambda distribution. The lack of a natural ordering represents the major challenge for the extension of the method to the multivariate framework, which is addressed by considering the notion of projectional quantile. The SCAD ℓ1–penalty is then introduced in order to achieve sparse estimation of the scaling matrix which is mostly responsible for the curse of dimensionality. The asymptotic properties of the proposed estimator have been discussed and the method is illustrated and tested on several synthetic datasets simulated from the Elliptical Stable distribution for which alternative methods are recognised to perform poorly.

Evaluating risk in precious metal prices with generalised lambda, generalised pareto and generalised extreme value distributions

In this study we investigate the performance of the generalised lambda distribution (GLD), the generalised Pareto distribution (GPD) and the generalised extreme value distribution (GEVD) in modelling daily platinum, gold and silver price log-returns. Our primary goal is to compare GLD against GPD, and GEVD, in the estimation of Value-at-Risk (VaR) and expected shortfall (ES) as per the international Basel regulatory framework. Our analyses show that GPD and GLD generally outperform GEVD for VaR and ES estimation for negative precious metal returns. For gold, the GPD stands out as the most suitable model. For platinum, GPD and GLD are equally adequate, especially at the 1% VaR level. For silver, GLD is the most suitable at 1% VaR level, whereas GPD is the best model at 0.1%. This study has shown that GLD is a suitable model for extreme risk in precious metal prices and can be used for the estimation of VaR and ES values. Keywords: Expected shortfall, Generalised extreme value, Generalised lambda, Generalised Pareto, Precious metal returns, Value-at-Risk

Probabilistic power flow computation using nested point estimate method

The probabilistic power flow (PPF) computation involves quantifying and propagating uncertainty over hundreds of variables. Zhao's point estimate method (PEM) has been widely used for PPF computation, and the computational burden increases linearly with respect to the number of PPF inputs. In this paper, Zhao's PEM is reformulated as the Kronecker product of Gauss-Hermite quadrature and an identity matrix. Following this formulation, a new PEM termed Nested PEM is developed based on Hadamard matrix, which can reduce the computational burden nearly by half relative to Zhao's PEM. In order to consider the dependence among PPF inputs, the extended generalized lambda distribution (EGLD) is employed to model marginal distributions of correlated PPF inputs, and the t-copula is introduced to map PPF problem to the independent standard normal space. Finally, case studies are conducted on a modified IEEE 118-bus system to illustrate the proposed PEM.