Likelihood and Quadratic Distance Methods for the Generalized Asymmetric Laplace Distribution for Financial Data

Maximum likelihood (ML) estimation for the generalized asymmetric Laplace (GAL) distribution also known as Variance gamma using simplex direct search algorithms is investigated. In this paper, we use numerical direct search techniques for maximizing the log-likelihood to obtain ML estimators instead of using the traditional EM algorithm. The density function of the GAL is only continuous but not differentiable with respect to the parameters and the appearance of the Bessel function in the density make it difficult to obtain the asymptotic covariance matrix for the entire GAL family. Using M-estimation theory, the properties of the ML estimators are investigated in this paper. The ML estimators are shown to be consistent for the GAL family and their asymptotic normality can only be guaranteed for the asymmetric Laplace (AL) family. The asymptotic covariance matrix is obtained for the AL family and it completes the results obtained previously in the literature. For the general GAL model, alternative methods of inferences based on quadratic distances (QD) are proposed. The QD methods appear to be overall more efficient than likelihood methods infinite samples using sample sizes n ≤5000 and the range of parameters often encountered for financial data. The proposed methods only require that the moment generating function of the parametric model exists and has a closed form expression and can be used for other models.

Generalized Minimum Perpendicular Distance Square Method of Estimation

In case of heteroscedasticity, a Generalized Minimum Perpendicular Distance Square (GMPDS) method has been suggested instead of traditionally used Generalized Least Square (GLS) method to fit a regression line, with an aim to get a better fitted regression line, so that the estimated line will be closest one to the observed points. Mathematical form of the estimator for the parameters has been presented. A logical argument behind the relationship between the slopes of the lines and has been placed.

Red clump stars from the LAMOST dataⅠ: identification and distance

We present a sample of about 120 000 red clump candidates selected from the LAMOST DR2 catalog based on the empirical distribution model in the effective temperature vs. surface gravity plane. Although, in general, red clump stars are considered as standard candles, they do not exactly stay in a narrow range of absolute magnitude, but may have a range of more than one magnitude depending on their initial mass. Consequently, conventional oversimplified distance estimations with the assumption of a fixed luminosity may lead to systematic bias related to the initial mass or age, which can potentially affect the study of the evolution of the Galaxy with red clump stars. We therefore employ an isochrone-based method to estimate the absolute magnitude of red clump stars from their observed surface gravities, effective temperatures and metallicities. We verify that the estimation removes the systematics well and provides initial mass/age estimates that are independent of distance with accuracy better than 10%.

Modified Generalized Degree Distance of Some Graph Operations

The modified generality degree distance, is defined as: ,?which is a modification of the generality degree distance. In this paper, we give some computing formulas of the modified generality degree distance of some graph operations, such as, composition, join, etc.

Some Results on Generalized Degree Distance

In [1], Hamzeh, Iranmanesh and Hossein-Zadeh and M. V. Diudea recently introduced the generalized degree distance of graphs. In this paper, we present explicit formulas for this new graph invariant of the Cartesian product, composition, join, disjunction and symmetric difference of graphs and introduce generalized and modified generalized degree distance polynomials of graphs, such that their first derivatives at x = 1 are respectively, equal to the generalized degree distance and the modified generalized degree distance. These polynomials are related to Wiener-type invariant polynomial of graphs.

<i>d-Distance</i>Coloring of Generalized Petersen Graphs <i>P(n, k)</i>

A coloring of G is d-distance if any two vertices at distance at most d from each other get different colors. The minimum number of colors in d-distance colorings of G is its d-distance chromatic number, denoted by χd(G). In this paper, we give the exact value of χd(G) (d = 1, 2), for some types of generalized Petersen graphs P(n, k) where k = 1, 2, 3 and arbitrary n.

Generalized nested logit-based stochasticuser equilibrium model with distance constraint of electric vehicles

Considering the range anxiety issue caused by the limited driving range and the scarcity of battery charging stations,the conventional multinomial logit(MNL)model with the overlapping path issue was used in route choice modeling to describe the route choice behavior of travelers effectively.Furthermore,the generalized nested logit-based stochastic user equilibrium(GNL-SUE)model with the constraints of multiple user classes and distance limits was proposed.A mathematical model was developed and solved by the method of successive averages.The mathematical model was proven to be analytically equivalent to the modified GNL-SUE model,and the uniqueness of the solution was also confirmed.The proposed mathematical model was tested and compared with the GNL-SUE model without a distance limit and the MNL-SUE model with a distance limit.Results show that the proposed mathematical model can effectively handle the range anxiety and overlapping path challenges.

Calibration of parallel kinematics machine using generalized distance error model

This paper focus on the accuracy enhancement of parallel kinematics machine through kinematics calibration. In the calibration processing, well-structured identification Jacobian matrix construction and end-effector position and orientation measurement are two main difficulties. In this paper, the identification Jacobian matrix is constructed easily by numerical calculation utilizing the unit virtual velocity method. The generalized distance errors model is presented for avoiding measuring the position and orientation directly which is difficult to be measured. At last, a measurement tool is given for acquiring the data points in the calibration processing. Experimental studies confirmed the effectiveness of method. It is also shown in the paper that the proposed approach can be applied to other typed parallel manipulators.

Testing the distance-duality relation with a combination of cosmological distance observations

We propose an accurate test of the distance-duality （DD） relation, η = DL（z）（1 ＋ z）^-2/DA（z） = 1 （where DL and DA are the luminosity distances and angular diameter distances, respectively）, with a combination of cosmological observational data of Type Ia Supernovae （SNe Ia） from the Union2 set and the galaxy cluster sample under an assumption of the spherical model. In order to avoid bias brought on by redshift non-coincidence between observational data and to consider redshift error bars of both clusters and SNe Ia in the analysis, we carefully choose the SNe Ia points which have the minimum acceptable redshift difference of the galaxy cluster sample （│△Z│min = σz,SN ＋σz,cluster）. By assuming η to be a constant and defined as functions of the redshift parameterized by six different expressions, we find that there exists no observable evidence for variations in the DD relation based on the collected data, since related statistical tests are well satisfied within the 1σ confidence level for most cases. Further, considering different values of △z as constraints, we also find that the choice of △z may play an important role in this model-independent test of the DD relation for the spherical sample of galaxy clusters.

On the ErdÖs Distance Conjecture in Geometry

Erd&#214;s asks if it is possible to have n points in general position in the plane (no three on a line or four on a circle) such that for every i (1≤i≤n-1 ) there is a distance determined by the points that occur exactly i times. So far some examples have been discovered for 2≤n≤8 [1] [2]. A solution for the 8 point is provided by I. Palasti [3]. Here two other possible solutions for the 8 point case as well as all possible answers to 4 - 7 point cases are provided and finally a brief discussion on the generalization of the problem to higher dimensions is given.

Testing the distance-duality relation with data from galaxy clusters and type Ia supernovae

We test the distance-duality （DD） relation by combining the angular diameter distance DA provided by two galaxy cluster samples compiled by De Filippis et al. （the elliptical β model） and Bonamente et al. （the spherical β model）, and the luminosity distance DL from Constitution and Union2 type Ia supernova （SNe Ia） datasets. To obtain DL associated with the observed DA at the same redshift, we smooth the noise of the SNe Ia in a model-independent way, obtain the evolutionary curve of DL and, finally, test the DD relation. We find that the elliptical β model, when compared with the SNe Ia from the Constitution compilation, is only consistent with the DD relation at the 3σ confidence level （CL）, while the spherical β model is incompatible with the DD relation at the 3σ CL. For the Union2 compilation, the De Filippis and Bonamente samples are marginally compatible with the validity of the DD relation at the 1σ and 2σ CLs, respectively.

The distance duality relation test from the ACT cluster and type Ia supernova data

The validity of the cosmic distance-duality （DD） relation is investigated by using 91 measure- ments of the gas mass fraction of galaxy clusters recently reported by the Atacama Cosmology Telescope （ACT） and the luminosity distance from the Union2.1 type Ia supernova （SNIa） sample independent of any cosmological models and the value of the Hubble constant. We consider four different approaches to derive the gas mass function and two different parameterizations of the DD relation, and find that they have very slight influences on the DD relation test and the relation is valid at the la confidence level. We also discuss the constraints on a andβ, which represent the effects of the shapes and colors of the light curves of SNIa, respectively. Our results on a and β are different from those obtained from the ACDM model and the galaxy cluster plus SNIa data.

Testing X-ray measurements of galaxy cluster gas mass fraction using the cosmic distance-duality relation

We propose a consistency test for some recent X-ray gas mass fraction （fgas） measurements in galaxy clusters, using the cosmic distance-duality relation, Ttneory = DL（1 ＋ Z）-2/DA, with luminosity distance （DL） data from the Union2 compilation of type Ia supernovae. We set Z/theory = 1, instead of assigning any red- shift parameterizations to it, and constrain the cosmological information preferred by fga8 data along with supernova observations. We adopt a new binning method in the reduction of the Union2 data, in order to minimize the statistical errors. Four data sets of X-ray gas mass fraction, which are reported by Allen et al. （two samples）, LaRoque et al. and Ettori et al., are analyzed in detail in the context of two theoretical models of fgas. The results from the analysis of Alien et al.＇s samples demonstrate the feasibility of our method. It is found that the preferred cosmology by LaRoque et al.＇s sample is consistent with its reference cosmology within the 1σ confidence level. However, for Ettori et al.＇s fgas sample, the inconsistency can reach more than a 3σ confidence level and this dataset shows special preference to an ΩA = 0 cosmology.

Induction of Forces at Distance Performed by Piezoelectric Materials

We describe the phenomenon of generation of an external field of forces from piezoelectric materials subjected to the application of electric fields or mechanical stress. We show that piezoelectric materials are capable of producing nonlocal forces of induction in external objects and we conclude that the nature of the forces generated is not originated from traditional interactions. Further we specifically assert that the generation of forces by the piezoelectric materials is ruled by the hypothesis of preexisting condition of generalized quantum entanglement between the molecular structure of the material bulk and the surrounding environment. In addition, the widely spread coupling of the molecules with the environment can be manifested from the so-called direct effect or the converse effect in piezoelectric materials and this coupling is not intermediated by acoustic waves or electromagnetic fields. We show that the novel effect has a theoretical explanation consistent with the generalized quantum entanglement framework and the direction of the induced forces depends on either the direction of the mechanical force or the electric field applied in these materials.

Effects of Wind Turbines Equipped with Doubly-fed Induction Generators on Distance Protection

Nowadays wind energy is the fastest growing renewable energy resource in the world.The problems of integrating wind farms are caused by changes of wind speed during a day.Moreover,the behaviors of wind turbines equipped with doubly-fed induction generators differ fundamentally from synchronous generators.Therefore,more considerations are needed to analyze the performances of the distance protection relays.The protection of a wind farm with distance relay is inspected.By changing the conditions of the wind farm,the characteristics of the distance relay are studied.

Learning distance effect on lignite quality variables at global and local scales

Determining scale and variable effects have critical importance in developing an energy resource policy.This study aims to explore the relationships in heterogeneous lignite sites using different scale models,spatial weighting as well as error-based pair-wise identification.From a statistical learning framework,the relationships among the quality variables such as geochemical variables and the contributions of the coordinates to quality measures have been exhibited by generalized additive models.In this way,the critical roles of spatial weights provided by the coordinates have been specified at a global scale.The experimental studies reveal that incorporating the geological weighting in the models as the additional information improves both accuracy and transparency.Because relationships among lignite quality variables and sampling locations are spatially non-stationary,the local structure and interdependencies among the variables were analyzed by geographically weighting regression.The local analyses including spatial patterns of bandwidths,search domains as well as residual-based areal dependencies provided not only the critical zones but also availability of pair-wise model alternatives by calibrating a model at each point for location-specific parameter learning.The results completely show that the weighting models applied at different scales can take spatial heterogeneity into consideration and these abilities provide some meta-data and specific information using in sustainable energy planning.

Are Type Ia Supernovae Reliable Distance Indicators?

Recent applications of type Ia supernovae （SNe Ia） in cosmology have successfully revealed the accelerating expansion of the universe. However, as distance indicators used in measuring the expansion history of the universe and probing the nature of dark energy, these objects must pass more strict tests. We propose a K-S test to investigate if there exists any systematic bias when deriving the luminosity distances under the standard candle assumption. Two samples, one comprising 71 high-redshift SNe Ia and the other, 44 nearby ones, are used in our investigation. We find that it is likely there exists a bias in the adopted samples, which is probably caused by a systematic error, e.g. in the color parameter used in the luminosity calibration and a bias may be caused by the SN evolution or by varying properties of the dust surrounding the SNe Ia.

Resistance Distance and Kirchhoff Index of a Class of Join Graphs

For some complicated graphs obtained by graph operations,it is very difficult to compute resistance distance and Kirchhoff index.Define a new graph operation,and obtain a class of new join graphs:the subdivision-vertex-vertex join G_1* G_2.Then,describe the Laplacian matrix of the graph G_1 * G_2 and use generalized inverse of the Laplacian matrix to get formulas for resistance distance and Kirchhoff index.Through the obtained formulas,the resistance distance of any pairs of vertices and Kirchhoff index of the join graph can be computed.

A Harmonic Approach to Handwriting Style Synthesis Using Deep Learning

The challenging task of handwriting style synthesis requires capturing the individuality and diversity of human handwriting.The majority of currently available methods use either a generative adversarial network(GAN)or a recurrent neural network(RNN)to generate new handwriting styles.This is why these techniques frequently fall short of producing diverse and realistic text pictures,particularly for terms that are not commonly used.To resolve that,this research proposes a novel deep learning model that consists of a style encoder and a text generator to synthesize different handwriting styles.This network excels in generating conditional text by extracting style vectors from a series of style images.The model performs admirably on a range of handwriting synthesis tasks,including the production of text that is out-of-vocabulary.It works more effectively than previous approaches by displaying lower values on key Generative Adversarial Network evaluation metrics,such Geometric Score(GS)(3.21×10^(-5))and Fréchet Inception Distance(FID)(8.75),as well as text recognition metrics,like Character Error Rate(CER)and Word Error Rate(WER).A thorough component analysis revealed the steady improvement in image production quality,highlighting the importance of specific handwriting styles.Applicable fields include digital forensics,creative writing,and document security.

Diagnostics in generalized nonlinear models based on maximum L_q-likelihood estimation

In order to detect whether the data conforms to the given model, it is necessary to diagnose the data in the statistical way. The diagnostic problem in generalized nonlinear models based on the maximum Lq-likelihood estimation is considered. Three diagnostic statistics are used to detect whether the outliers exist in the data set. Simulation results show that when the sample size is small, the values of diagnostic statistics based on the maximum Lq-likelihood estimation are greater than the values based on the maximum likelihood estimation. As the sample size increases, the difference between the values of the diagnostic statistics based on two estimation methods diminishes gradually. It means that the outliers can be distinguished easier through the maximum Lq-likelihood method than those through the maximum likelihood estimation method.