**Commenced**in January 2007

**Frequency:**Monthly

**Edition:**International

**Paper Count:**2361

# Search results for: Inverse Gaussian distribution

##### 2361 Base Change for Fisher Metrics: Case of the q−Gaussian Inverse Distribution

**Authors:**
Gabriel I. Loaiza O.,
Carlos A. Cadavid M.,
Juan C. Arango P.

**Abstract:**

It is known that the Riemannian manifold determined by the family of inverse Gaussian distributions endowed with the Fisher metric has negative constant curvature κ = −1/2 , as does the family of usual Gaussian distributions. In the present paper, firstly we arrive at this result by following a different path, much simpler than the previous ones. We first put the family in exponential form, thus endowing the family with a new set of parameters, or coordinates, θ1, θ2; then we determine the matrix of the Fisher metric in terms of these parameters; and finally we compute this matrix in the original parameters. Secondly, we define the Inverse q−Gaussian distribution family (q < 3), as the family obtained by replacing the usual exponential function by the Tsallis q−exponential function in the expression for the Inverse Gaussian distribution, and observe that it supports two possible geometries, the Fisher and the q−Fisher geometry. And finally, we apply our strategy to obtain results about the Fisher and q−Fisher geometry of the Inverse q−Gaussian distribution family, similar to the ones obtained in the case of the Inverse Gaussian distribution family.

**Keywords:**
Base of Changes,
Information Geometry,
Inverse
Gaussian distribution,
Inverse q-Gaussian distribution,
Statistical
Manifolds.

##### 2360 An Extension of the Kratzel Function and Associated Inverse Gaussian Probability Distribution Occurring in Reliability Theory

**Authors:**
R. K. Saxena,
Ravi Saxena

**Abstract:**

In view of their importance and usefulness in reliability theory and probability distributions, several generalizations of the inverse Gaussian distribution and the Krtzel function are investigated in recent years. This has motivated the authors to introduce and study a new generalization of the inverse Gaussian distribution and the Krtzel function associated with a product of a Bessel function of the third kind )(zKQ and a Z - Fox-Wright generalized hyper geometric function introduced in this paper. The introduced function turns out to be a unified gamma-type function. Its incomplete forms are also discussed. Several properties of this gamma-type function are obtained. By means of this generalized function, we introduce a generalization of inverse Gaussian distribution, which is useful in reliability analysis, diffusion processes, and radio techniques etc. The inverse Gaussian distribution thus introduced also provides a generalization of the Krtzel function. Some basic statistical functions associated with this probability density function, such as moments, the Mellin transform, the moment generating function, the hazard rate function, and the mean residue life function are also obtained.KeywordsFox-Wright function, Inverse Gaussian distribution, Krtzel function & Bessel function of the third kind.

**Keywords:**
Fox-Wright function,
Inverse Gaussian distribution,
Krtzel function & Bessel function of the third kind.

##### 2359 Statistical Analysis for Overdispersed Medical Count Data

**Authors:**
Y. N. Phang,
E. F. Loh

**Abstract:**

Many researchers have suggested the use of zero inflated Poisson (ZIP) and zero inflated negative binomial (ZINB) models in modeling overdispersed medical count data with extra variations caused by extra zeros and unobserved heterogeneity. The studies indicate that ZIP and ZINB always provide better fit than using the normal Poisson and negative binomial models in modeling overdispersed medical count data. In this study, we proposed the use of Zero Inflated Inverse Trinomial (ZIIT), Zero Inflated Poisson Inverse Gaussian (ZIPIG) and zero inflated strict arcsine models in modeling overdispered medical count data. These proposed models are not widely used by many researchers especially in the medical field. The results show that these three suggested models can serve as alternative models in modeling overdispersed medical count data. This is supported by the application of these suggested models to a real life medical data set. Inverse trinomial, Poisson inverse Gaussian and strict arcsine are discrete distributions with cubic variance function of mean. Therefore, ZIIT, ZIPIG and ZISA are able to accommodate data with excess zeros and very heavy tailed. They are recommended to be used in modeling overdispersed medical count data when ZIP and ZINB are inadequate.

**Keywords:**
Zero inflated,
inverse trinomial distribution,
Poisson inverse Gaussian distribution,
strict arcsine distribution,
Pearson’s goodness of fit.

##### 2358 Short-Term Electric Load Forecasting Using Multiple Gaussian Process Models

**Authors:**
Tomohiro Hachino,
Hitoshi Takata,
Seiji Fukushima,
Yasutaka Igarashi

**Abstract:**

This paper presents a Gaussian process model-based short-term electric load forecasting. The Gaussian process model is a nonparametric model and the output of the model has Gaussian distribution with mean and variance. The multiple Gaussian process models as every hour ahead predictors are used to forecast future electric load demands up to 24 hours ahead in accordance with the direct forecasting approach. The separable least-squares approach that combines the linear least-squares method and genetic algorithm is applied to train these Gaussian process models. Simulation results are shown to demonstrate the effectiveness of the proposed electric load forecasting.

**Keywords:**
Direct method,
electric load forecasting,
Gaussian process model,
genetic algorithm,
separable least-squares method.

##### 2357 Multinomial Dirichlet Gaussian Process Model for Classification of Multidimensional Data

**Authors:**
Wanhyun Cho,
Soonja Kang,
Sangkyoon Kim,
Soonyoung Park

**Abstract:**

**Keywords:**
Multinomial dirichlet classification model,
Gaussian
process priors,
variational Bayesian approximation,
Importance
sampling,
approximate posterior distribution,
Marginal likelihood
evidence.

##### 2356 Real-time Tracking in Image Sequences based-on Parameters Updating with Temporal and Spatial Neighborhoods Mixture Gaussian Model

**Abstract:**

**Keywords:**
Gaussian mixture model,
real-time tracking,
sequence image,
gradient.

##### 2355 Variational EM Inference Algorithm for Gaussian Process Classification Model with Multiclass and Its Application to Human Action Classification

**Authors:**
Wanhyun Cho,
Soonja Kang,
Sangkyoon Kim,
Soonyoung Park

**Abstract:**

In this paper, we propose the variational EM inference algorithm for the multi-class Gaussian process classification model that can be used in the field of human behavior recognition. This algorithm can drive simultaneously both a posterior distribution of a latent function and estimators of hyper-parameters in a Gaussian process classification model with multiclass. Our algorithm is based on the Laplace approximation (LA) technique and variational EM framework. This is performed in two steps: called expectation and maximization steps. First, in the expectation step, using the Bayesian formula and LA technique, we derive approximately the posterior distribution of the latent function indicating the possibility that each observation belongs to a certain class in the Gaussian process classification model. Second, in the maximization step, using a derived posterior distribution of latent function, we compute the maximum likelihood estimator for hyper-parameters of a covariance matrix necessary to define prior distribution for latent function. These two steps iteratively repeat until a convergence condition satisfies. Moreover, we apply the proposed algorithm with human action classification problem using a public database, namely, the KTH human action data set. Experimental results reveal that the proposed algorithm shows good performance on this data set.

**Keywords:**
Bayesian rule,
Gaussian process classification model
with multiclass,
Gaussian process prior,
human action classification,
laplace approximation,
variational EM algorithm.

##### 2354 Further Thoughtson a Sequential Life Testing Approach Using an Inverse Weibull Model

**Authors:**
D. I. De Souza,
G. P. Azevedo,
D. R. Fonseca

**Abstract:**

In this paper we will develop further the sequential life test approach presented in a previous article by [1] using an underlying two parameter Inverse Weibull sampling distribution. The location parameter or minimum life will be considered equal to zero. Once again we will provide rules for making one of the three possible decisions as each observation becomes available; that is: accept the null hypothesis H0; reject the null hypothesis H0; or obtain additional information by making another observation. The product being analyzed is a new electronic component. There is little information available about the possible values the parameters of the corresponding Inverse Weibull underlying sampling distribution could have.To estimate the shape and the scale parameters of the underlying Inverse Weibull model we will use a maximum likelihood approach for censored failure data. A new example will further develop the proposed sequential life testing approach.

**Keywords:**
Sequential Life Testing,
Inverse Weibull Model,
Maximum Likelihood Approach,
Hypothesis Testing.

##### 2353 Approximate Method of Calculation of Inviscid Hypersonic Flow

**Authors:**
F. Sokhanvar,
A. B. Khoshnevis

**Abstract:**

**Keywords:**
Hypersonic flow,
Inverse problem method

##### 2352 Human Action Recognition Using Variational Bayesian HMM with Dirichlet Process Mixture of Gaussian Wishart Emission Model

**Authors:**
Wanhyun Cho,
Soonja Kang,
Sangkyoon Kim,
Soonyoung Park

**Abstract:**

In this paper, we present the human action recognition method using the variational Bayesian HMM with the Dirichlet process mixture (DPM) of the Gaussian-Wishart emission model (GWEM). First, we define the Bayesian HMM based on the Dirichlet process, which allows an infinite number of Gaussian-Wishart components to support continuous emission observations. Second, we have considered an efficient variational Bayesian inference method that can be applied to drive the posterior distribution of hidden variables and model parameters for the proposed model based on training data. And then we have derived the predictive distribution that may be used to classify new action. Third, the paper proposes a process of extracting appropriate spatial-temporal feature vectors that can be used to recognize a wide range of human behaviors from input video image. Finally, we have conducted experiments that can evaluate the performance of the proposed method. The experimental results show that the method presented is more efficient with human action recognition than existing methods.

**Keywords:**
Human action recognition,
Bayesian HMM,
Dirichlet process mixture model,
Gaussian-Wishart emission model,
Variational Bayesian inference,
Prior distribution and approximate posterior distribution,
KTH dataset.

##### 2351 Confidence Interval for the Inverse of a Normal Mean with a Known Coefficient of Variation

**Authors:**
Arunee Wongkha,
Suparat Niwitpong,
Sa-aat Niwitpong

**Abstract:**

In this paper, we propose two new confidence intervals for the inverse of a normal mean with a known coefficient of variation. One of new confidence intervals for the inverse of a normal mean with a known coefficient of variation is constructed based on the pivotal statistic Z where Z is a standard normal distribution and another confidence interval is constructed based on the generalized confidence interval, presented by Weerahandi. We examine the performance of these confidence intervals in terms of coverage probabilities and average lengths via Monte Carlo simulation.

**Keywords:**
The inverse of a normal mean,
confidence interval,
generalized confidence intervals,
known coefficient of variation.

##### 2350 An Iterative Algorithm to Compute the Generalized Inverse A(2) T,S Under the Restricted Inner Product

**Authors:**
Xingping Sheng

**Abstract:**

**Keywords:**
Generalized inverse A(2)
T,
S,
Restricted inner product,
Iterative method,
Orthogonal projection.

##### 2349 Applications of Stable Distributions in Time Series Analysis, Computer Sciences and Financial Markets

**Authors:**
Mohammad Ali Baradaran Ghahfarokhi,
Parvin Baradaran Ghahfarokhi

**Abstract:**

In this paper, first we introduce the stable distribution, stable process and theirs characteristics. The a -stable distribution family has received great interest in the last decade due to its success in modeling data, which are too impulsive to be accommodated by the Gaussian distribution. In the second part, we propose major applications of alpha stable distribution in telecommunication, computer science such as network delays and signal processing and financial markets. At the end, we focus on using stable distribution to estimate measure of risk in stock markets and show simulated data with statistical softwares.

**Keywords:**
stable distribution,
SaS,
infinite variance,
heavy tail networks,
VaR.

##### 2348 An Alternative Method for Generating Almost Infinite Sequence of Gaussian Variables

**Authors:**
Nyah C. Temaneh,
F. A. Phiri,
E. Ruhunga

**Abstract:**

**Keywords:**
Gaussian variable,
statistical analysis,
simulation ofCommunication Network,
Random numbers.

##### 2347 Connectivity Estimation from the Inverse Coherence Matrix in a Complex Chaotic Oscillator Network

**Authors:**
Won Sup Kim,
Xue-Mei Cui,
Seung Kee Han

**Abstract:**

We present on the method of inverse coherence matrix for the estimation of network connectivity from multivariate time series of a complex system. In a model system of coupled chaotic oscillators, it is shown that the inverse coherence matrix defined as the inverse of cross coherence matrix is proportional to the network connectivity. Therefore the inverse coherence matrix could be used for the distinction between the directly connected links from indirectly connected links in a complex network. We compare the result of network estimation using the method of the inverse coherence matrix with the results obtained from the coherence matrix and the partial coherence matrix.

**Keywords:**
Chaotic oscillator,
complex network,
inverse coherence matrix,
network estimation.

##### 2346 An Inverse Heat Transfer Algorithm for Predicting the Thermal Properties of Tumors during Cryosurgery

**Authors:**
Mohamed Hafid,
Marcel Lacroix

**Abstract:**

This study aimed at developing an inverse heat transfer approach for predicting the time-varying freezing front and the temperature distribution of tumors during cryosurgery. Using a temperature probe pressed against the layer of tumor, the inverse approach is able to predict simultaneously the metabolic heat generation and the blood perfusion rate of the tumor. Once these parameters are predicted, the temperature-field and time-varying freezing fronts are determined with the direct model. The direct model rests on one-dimensional *Pennes* bioheat equation. The phase change problem is handled with the enthalpy method. The *Levenberg-Marquardt* Method (LMM) combined to the *Broyden* Method (BM) is used to solve the inverse model. The effect (a) of the thermal properties of the diseased tissues; (b) of the initial guesses for the unknown thermal properties; (c) of the data capture frequency; and (d) of the noise on the recorded temperatures is examined. It is shown that the proposed inverse approach remains accurate for all the cases investigated.

**Keywords:**
Cryosurgery,
inverse heat transfer,
Levenberg-Marquardt method,
thermal properties,
Pennes model,
enthalpy method.

##### 2345 Uncontrollable Inaccuracy in Inverse Problems

**Authors:**
Yu. Menshikov

**Abstract:**

In this paper the influence of errors of function derivatives in initial time which have been obtained by experiment (uncontrollable inaccuracy) to the results of inverse problem solution was investigated. It was shown that these errors distort the inverse problem solution as a rule near the beginning of interval where the solutions are analyzed. Several methods for removing the influence of uncontrollable inaccuracy have been suggested.

**Keywords:**
Inverse problems,
uncontrollable inaccuracy,
filtration.

##### 2344 Propagation of Cos-Gaussian Beam in Photorefractive Crystal

**Authors:**
A. Keshavarz

**Abstract:**

**Keywords:**
Beam propagation,
cos-Gaussian beam,
Numerical
simulation,
Photorefractive crystal.

##### 2343 Investigation of Droplet Size Produced in Two-Phase Gravity Separators

**Authors:**
Kul Pun,
F. A. Hamad,
T. Ahmed,
J. O. Ugwu,
J. Eyers,
G. Lawson,
P. A. Russell

**Abstract:**

Determining droplet size and distribution is essential when determining the separation efficiency of a two/three-phase separator. This paper investigates the effect of liquid flow and oil pad thickness on the droplet size at the lab scale. The findings show that increasing the inlet flow rates of the oil and water results in size reduction of the droplets and increasing the thickness of the oil pad increases the size of the droplets. The data were fitted with a simple Gaussian model, and the parameters of mean, standard deviation, and amplitude were determined. Trends have been obtained for the fitted parameters as a function of the Reynolds number, which suggest a way forward to better predict the starting parameters for population models when simulating separation using CFD packages. The key parameter to predict to fix the position of the Gaussian distribution was found to be the mean droplet size.

**Keywords:**
Two-phase separator,
average bubble droplet,
bubble size distribution,
liquid-liquid phase.

##### 2342 Temperature-Dependent Barrier Characteristics of Inhomogeneous Pd/n-GaN Schottky Barrier Diodes Surface

**Authors:**
K. Al-Heuseen,
M. R. Hashim

**Abstract:**

The current-voltage (I-V) characteristics of Pd/n-GaN Schottky barrier were studied at temperatures over room temperature (300-470K). The values of ideality factor (n), zero-bias barrier height (φB0), flat barrier height (φBF) and series resistance (Rs) obtained from I-V-T measurements were found to be strongly temperature dependent while (φBo) increase, (n), (φBF) and (Rs) decrease with increasing temperature. The apparent Richardson constant was found to be 2.1x10-9 Acm-2K-2 and mean barrier height of 0.19 eV. After barrier height inhomogeneities correction, by assuming a Gaussian distribution (GD) of the barrier heights, the Richardson constant and the mean barrier height were obtained as 23 Acm-2K-2 and 1.78eV, respectively. The corrected Richardson constant was very closer to theoretical value of 26 Acm-2K-2.

**Keywords:**
Electrical properties,
Gaussian distribution,
Pd-GaN Schottky diodes,
thermionic emission.

##### 2341 Frequency Offset Estimation Schemes Based On ML for OFDM Systems in Non-Gaussian Noise Environments

**Authors:**
Keunhong Chae,
Seokho Yoon

**Abstract:**

In this paper, frequency offset (FO) estimation schemes robust to the non-Gaussian noise environments are proposed for orthogonal frequency division multiplexing (OFDM) systems. First, a maximum-likelihood (ML) estimation scheme in non-Gaussian noise environments is proposed, and then, the complexity of the ML estimation scheme is reduced by employing a reduced set of candidate values. In numerical results, it is demonstrated that the proposed schemes provide a significant performance improvement over the conventional estimation scheme in non-Gaussian noise environments while maintaining the performance similar to the estimation performance in Gaussian noise environments.

**Keywords:**
Frequency offset estimation,
maximum-likelihood,
non-Gaussian noise environment,
OFDM,
training symbol.

##### 2340 Inverse Matrix in the Theory of Dynamic Systems

**Authors:**
R. Masarova,
M. Juhas,
B. Juhasova,
Z. Sutova

**Abstract:**

**Keywords:**
Dynamic system,
transfer matrix,
inverse matrix,
modeling.

##### 2339 Simulation of Propagation of Cos-Gaussian Beam in Strongly Nonlocal Nonlinear Media Using Paraxial Group Transformation

**Authors:**
A. Keshavarz,
Z. Roosta

**Abstract:**

In this paper, propagation of cos-Gaussian beam in strongly nonlocal nonlinear media has been stimulated by using paraxial group transformation. At first, cos-Gaussian beam, nonlocal nonlinear media, critical power, transfer matrix, and paraxial group transformation are introduced. Then, the propagation of the cos-Gaussian beam in strongly nonlocal nonlinear media is simulated. Results show that beam propagation has periodic structure during self-focusing effect in this case. However, this simple method can be used for investigation of propagation of kinds of beams in ABCD optical media.

**Keywords:**
Paraxial group transformation,
nonlocal nonlinear media,
Cos-Gaussian beam,
ABCD law.

##### 2338 Introduction of the Fluid-Structure Coupling into the Force Analysis Technique

**Authors:**
Océane Grosset,
Charles Pézerat,
Jean-Hugh Thomas,
Frédéric Ablitzer

**Abstract:**

**Keywords:**
Fluid-structure coupling,
inverse methods,
naval,
vibrations.

##### 2337 Volterra Filtering Techniques for Removal of Gaussian and Mixed Gaussian-Impulse Noise

**Authors:**
M. B. Meenavathi,
K. Rajesh

**Abstract:**

In this paper, we propose a new class of Volterra series based filters for image enhancement and restoration. Generally the linear filters reduce the noise and cause blurring at the edges. Some nonlinear filters based on median operator or rank operator deal with only impulse noise and fail to cancel the most common Gaussian distributed noise. A class of second order Volterra filters is proposed to optimize the trade-off between noise removal and edge preservation. In this paper, we consider both the Gaussian and mixed Gaussian-impulse noise to test the robustness of the filter. Image enhancement and restoration results using the proposed Volterra filter are found to be superior to those obtained with standard linear and nonlinear filters.

**Keywords:**
Gaussian noise,
Image enhancement,
Imagerestoration,
Linear filters,
Nonlinear filters,
Volterra series.

##### 2336 Use of Gaussian-Euclidean Hybrid Function Based Artificial Immune System for Breast Cancer Diagnosis

**Authors:**
Cuneyt Yucelbas,
Seral Ozsen,
Sule Yucelbas,
Gulay Tezel

**Abstract:**

Due to the fact that there exist only a small number of complex systems in artificial immune system (AIS) that work out nonlinear problems, nonlinear AIS approaches, among the well-known solution techniques, need to be developed. Gaussian function is usually used as similarity estimation in classification problems and pattern recognition. In this study, diagnosis of breast cancer, the second type of the most widespread cancer in women, was performed with different distance calculation functions that euclidean, gaussian and gaussian-euclidean hybrid function in the clonal selection model of classical AIS on Wisconsin Breast Cancer Dataset (WBCD), which was taken from the University of California, Irvine Machine-Learning Repository. We used 3-fold cross validation method to train and test the dataset. According to the results, the maximum test classification accuracy was reported as 97.35% by using of gaussian-euclidean hybrid function for fold-3. Also, mean of test classification accuracies for all of functions were obtained as 94.78%, 94.45% and 95.31% with use of euclidean, gaussian and gaussian-euclidean, respectively. With these results, gaussian-euclidean hybrid function seems to be a potential distance calculation method, and it may be considered as an alternative distance calculation method for hard nonlinear classification problems.

**Keywords:**
Artificial Immune System,
Breast Cancer Diagnosis,
Euclidean Function,
Gaussian Function.

##### 2335 Numerical Inverse Laplace Transform Using Chebyshev Polynomial

**Authors:**
Vinod Mishra,
Dimple Rani

**Abstract:**

In this paper, numerical approximate Laplace transform inversion algorithm based on Chebyshev polynomial of second kind is developed using odd cosine series. The technique has been tested for three different functions to work efficiently. The illustrations show that the new developed numerical inverse Laplace transform is very much close to the classical analytic inverse Laplace transform.

**Keywords:**
Chebyshev polynomial,
Numerical inverse Laplace transform,
Odd cosine series.

##### 2334 The Effect of Measurement Distribution on System Identification and Detection of Behavior of Nonlinearities of Data

**Authors:**
Mohammad Javad Mollakazemi,
Farhad Asadi,
Aref Ghafouri

**Abstract:**

In this paper, we considered and applied parametric modeling for some experimental data of dynamical system. In this study, we investigated the different distribution of output measurement from some dynamical systems. Also, with variance processing in experimental data we obtained the region of nonlinearity in experimental data and then identification of output section is applied in different situation and data distribution. Finally, the effect of the spanning the measurement such as variance to identification and limitation of this approach is explained.

**Keywords:**
Gaussian process,
Nonlinearity distribution,
Particle
filter.

##### 2333 More on Gaussian Quadratures for Fuzzy Functions

**Authors:**
Shu-Xin Miao

**Abstract:**

In this paper, the Gaussian type quadrature rules for fuzzy functions are discussed. The errors representation and convergence theorems are given. Moreover, four kinds of Gaussian type quadrature rules with error terms for approximate of fuzzy integrals are presented. The present paper complements the theoretical results of the paper by T. Allahviranloo and M. Otadi [T. Allahviranloo, M. Otadi, Gaussian quadratures for approximate of fuzzy integrals, Applied Mathematics and Computation 170 (2005) 874-885]. The obtained results are illustrated by solving some numerical examples.

**Keywords:**
Guassian quadrature rules,
fuzzy number,
fuzzy integral,
fuzzy solution.

##### 2332 Reductive Control in the Management of Redundant Actuation

**Authors:**
Mkhinini Maher,
Knani Jilani

**Abstract:**

We present in this work the performances of a mobile omnidirectional robot through evaluating its management of the redundancy of actuation. Thus we come to the predictive control implemented.

The distribution of the wringer on the robot actions, through the inverse pseudo of Moore-Penrose, corresponds to a « geometric ›› distribution of efforts. We will show that the load on vehicle wheels would not be equi-distributed in terms of wheels configuration and of robot movement.

Thus, the threshold of sliding is not the same for the three wheels of the vehicle. We suggest exploiting the redundancy of actuation to reduce the risk of wheels sliding and to ameliorate, thereby, its accuracy of displacement. This kind of approach was the subject of study for the legged robots.

**Keywords:**
Mobile robot,
actuation,
redundancy,
omnidirectional,
inverse pseudo Moore-Penrose,
reductive control.