Inverse Gaussian Model Research Articles

가우시안 혼합모델을 이용한 강인한 실시간 곡선차선 검출 알고리즘

ADAS (Advanced Driver Assistance Systems) requires not only real-time robust lane detection, both straight and curved, but also predicting upcoming steering direction by detecting the curvature of lanes. In this paper, a curvature lane detection algorithm is proposed to enhance the accuracy and detection rate based on using inverse perspective images and Gaussian Mixture Model (GMM) to segment the lanes from the background under various illumination condition. To increase the speed and accuracy of the lane detection, this paper used template matching, RANSAC and proposed post processing method. Through experiments, it is validated that the proposed algorithm can detect both straight and curved lanes as well as predicting the upcoming direction with 92.95% of detection accuracy and 50fps speed.

Advective transport in heterogeneous aquifers: Are proxy models predictive?

AbstractWe examine the prediction capability of two approximate models (Multi‐Rate Mass Transfer (MRMT) and Continuous Time Random Walk (CTRW)) of non‐Fickian transport, by comparison with accurate 2‐D and 3‐D numerical simulations. Both nonlocal in time approaches circumvent the need to solve the flow and transport equations by using proxy models to advection, providing the breakthrough curves (BTC) at control planes at any x, depending on a vector of five unknown parameters. Although underlain by different mechanisms, the two models have an identical structure in the Laplace Transform domain and have the Markovian property of independent transitions. We show that also the numerical BTCs enjoy the Markovian property. Following the procedure recommended in the literature, along a practitioner perspective, we first calibrate the parameters values by a best fit with the numerical BTC at a control plane at x1, close to the injection plane, and subsequently use it for prediction at further control planes for a few values of . Due to a similar structure and Markovian property, the two methods perform equally well in matching the numerical BTC. The identified parameters are generally not unique, making their identification somewhat arbitrary. The inverse Gaussian model and the recently developed Multi‐Indicator Model (MIM), which does not require any fitting as it relates the BTC to the permeability structure, are also discussed. The application of the proxy models for prediction requires carrying out transport field tests of large plumes for a long duration.

Inverse Gaussian Model to Describe the Distribution of Age Specific Fertility Rates of Nepal

This paper attempts to formulate Inverse Gaussian probability model to describe the distribution of the age specific fertility rates among Nepalese mothers. The average age of child bearing has been found to be 26.12 years whereas child bearing starts at the age of 15.82 years. Estimated total fertility rate (TFR) has been found to be 2.60 against the observed value of 2.6 per woman. The coefficient of determination and chi-square values suggest that the model found to be good fit to the Nepal Demographic and Health Surveys data. Findings may help researchers and policy makers for applying the model in order to obtain the descriptive statistics for policy interventions.Journal of Institute of Science and Technology, 2015, 20(2): 80-83

A Hybrid Algorithm for Non-negative Matrix Factorization Based on Symmetric Information Divergence.

The objective of this paper is to provide a hybrid algorithm for non-negative matrix factorization based on a symmetric version of Kullback-Leibler divergence, known as intrinsic information. The convergence of the proposed algorithm is shown for several members of the exponential family such as the Gaussian, Poisson, gamma and inverse Gaussian models. The speed of this algorithm is examined and its usefulness is illustrated through some applied problems.

Bayesian analysis of covariance under inverse Gaussian model

This paper considers the problem of analysis of covariance (ANCOVA) under the assumption of inverse Gaussian distribution for response variable from the Bayesian point of view. We develop a fully Bayesian model for ANCOVA based on the conjugate prior distributions for parameters contained in the model. The Bayes estimator of parameters, ANCOVA model and adjusted effects for both treatments and covariates along with predictive distribution of future observations are developed. We also provide the essentials for comparing adjusted treatments effects and adjusted factor effects. A simulation study and a real world application are also performed to illustrate and evaluate the proposed Bayesian model.

Inverse Gaussian mixtures models of bearing vibrations under local faults

Repetitive impacts performed by damaged spot on a component of the rolling element bearing specific statistical properties, due to the constant angular distance between the roller elements. Under (almost) constant rotational speed the successive impacts are regarded as almost periodic with small random fluctuations due to slippage. Often these random components are modelled as normally distributed, which is unrealistic since physically impossible events, such as negative time between two consecutive impacts, become likely by the nature of the distribution. Motivated by this deficiency we propose a new model that describes the occurrence of repetitive vibrational patterns as realisation of a point process with the (mixture) inverse Gaussian distribution of the inter-event times. Such a model is applicable to both constant and variable rotational speeds. Additionally, the proposed model inherently describes the quasi-cyclostationarity of the impact times under almost constant rotational speed. The applicability of the model was evaluated using vibrational signals generated by bearings with localised surface fault.

Option Pricing for Symmetric Lévy Returns with Applications

This paper considers options pricing when the assumption of normality is replaced with that of the symmetry of the underlying distribution. Such a market affords many equivalent martingale measures (EMM). However we argue (as in the discrete-time setting of Klebaner and Landsman in Methodology and Computing in Applied Probability, 2007, doi: 10.1007/s11009-007-9038-2 ) that an EMM that keeps distributions within the same family is a “natural” choice. We obtain Black–Scholes type option pricing formulae for symmetric Variance-Gamma and symmetric Normal Inverse Gaussian models.

CALIBRATING THE SMILE WITH MULTIVARIATE TIME-CHANGED BROWNIAN MOTION AND THE ESSCHER TRANSFORM

In this study, we investigate two multivariate time-changed Brownian motion option pricing models in which the connection between the historical measure P and the risk-neutral measure Q is given by the Esscher transform. The models incorporate skewness, kurtosis and more complex dependence structures among stocks log-returns than the simple correlation matrix. The two models can be seen as a multivariate extension of the normal inverse Gaussian (NIG) model and the variance gamma (VG) model, respectively. We discuss two possible approaches to estimate historical asset returns and calibrate univariate option implied volatilities. While the first approach considers only time series of log-returns, the second approach makes use of both time series of log-returns and univariate observed volatility surfaces. To calibrate the models, there is no need of liquid multivariate derivative quotes.

Efficiency combined with simplicity: new testing procedures for Generalized Inverse Gaussian models

The standard efficient testing procedures in the Generalized Inverse Gaussian (GIG) family (also known as Halphen Type A family) are likelihood ratio tests, and hence rely on Maximum Likelihood (ML) estimation of the three parameters of the GIG. The particular form of GIG densities, involving modified Bessel functions, prevents in general form a closed-form expression for ML estimators, which are obtained at the expense of complex numerical approximation methods. On the contrary, Method of Moments (MM) estimators allow for concise expressions, but tests based on these estimators suffer from a lack of efficiency as compared to likelihood ratio tests. This is why, in recent years, trade-offs between ML and MM estimators have been proposed, resulting in simpler yet not completely efficient estimators and tests. In the present paper, we do not propose such a trade-off but rather an optimal combination of both methods, our tests inheriting efficiency from an ML-like construction and simplicity from the MM estimators of the nuisance parameters. This goal shall be reached by attacking the problem from a new angle, namely via the Le Cam methodology. Besides providing simple efficient testing methods, the theoretical background of this methodology further allows us to write out explicitly power expressions for our tests. A Monte Carlo simulation study shows that, also at small sample sizes, our simpler procedures do at least as good as the complex likelihood ratio tests. We conclude the paper by applying our findings on two real-data sets.

Bayesian Inference for Transportation Origin–Destination Matrices: the Poisson–Inverse Gaussian and Other Poisson Mixtures

SummaryTransportation origin–destination analysis is investigated through the use of Poisson mixtures by introducing covariate-based models which incorporate different transport modelling phases and also allow for direct probabilistic inference on link traffic based on Bayesian predictions. Emphasis is placed on the Poisson–inverse Gaussian model as an alternative to the commonly used Poisson–gamma and Poisson–log-normal models. We present a first full Bayesian formulation and demonstrate that the Poisson–inverse Gaussian model is particularly suited for origin–destination analysis because of its desirable marginal and hierarchical properties. In addition, the integrated nested Laplace approximation is considered as an alternative to Markov chain Monte Carlo sampling and the two methodologies are compared under specific modelling assumptions. The case-study is based on 2001 Belgian census data and focuses on a large, sparsely distributed origin–destination matrix containing trip information for 308 Flemish municipalities.

Modelling follow up time at a single-lane roundabout

The follow up time is an important parameter for estimating the entry capacity of roundabouts. However, its variability and contributing factors have long been ignored in the literatures. In this study, 171 follow up samples and contributing factors (traffic volume, vehicle position, waiting vehicles behind, vehicle type, and drivers’ gender) are collected at a roundabout in Pacific Pines, Australia. It is found that the follow up time is indeed significantly affected by traffic volume, waiting vehicles behind, vehicle type, and drivers’ gender. In order to establish the relationship between the follow up time and its contributing factors, an inverse Gaussian regression model is further developed. This relationship could be applied to estimate the entry capacities by taking into account the variability of follow up samples. According to the model, the traffic volume and vehicle types are the most important contributing factors.

On normal stable Tweedie models and power-generalized variance functions of only one component

As an extension to normal gamma and normal inverse Gaussian models, all normal stable Tweedie (NST) models are introduced for getting a simple form of the determinant of the covariance matrix, so-called generalized variance. As alternatives to the standard normal model, multivariate NST models are composed by a fixed univariate stable Tweedie variable having a positive value domain, and the remaining random variables given the fixed one are real independent Gaussian variables with the same variance equal to the fixed component. Within the framework of exponential dispersion models, a new form of variance functions is firstly established. Then, their generalized variance functions are shown to be powers of only the fixed mean component. Their modified Levy measures are generally of the normal gamma type, which is connected to NST models through some Monge–Ampere equations. Two kinds of generalized variance estimators are discussed and variance modelling under only observations of normal terms is evoked. Finally, reasonable extensions of NST to multiple stable Tweedie models and corresponding problems are presented.

Analysis of covariance under inverse Gaussian model

This paper considers the problem of analysis of covariance (ANCOVA) under the assumption of inverse Gaussian distribution for response variable. We develop the essential methodology for estimating the model parameters via maximum likelihood method. The general form of the maximum likelihood estimator is obtained in color closed form. Adjusted treatment effects and adjusted covariate effects are given, too. We also provide the asymptotic distribution of the proposed estimators. A simulation study and a real world application are also performed to illustrate and evaluate the proposed methodology.

Valuation of European and American Option Prices Under the Levy Processes with a Markov Chain Approximation

This paper suggests a numerical method for valuation of European and American options under the two L<TEX>$\acute{e}$</TEX>vy Processes, Normal Inverse Gaussian Model and the Variance Gamma model. The method is based on approximation of underlying asset price using a finite-state, time-homogeneous Markov chain. We examine the effectiveness of the proposed method with simulation results, which are compared with those from the existing numerical method, the lattice-based method.

A causal continuous-time stochastic model for the turbulent energy cascade in a helium jet flow

We discuss continuous cascade models and their potential for modelling the energy dissipation in a turbulent flow. Continuous cascade processes, expressed in terms of stochastic integrals with respect to Lévy bases, are examples of ambit processes. These models are known to reproduce experimentally observed properties of turbulence: the scaling and self-scaling of the correlators of the energy dissipation and of the moments of the coarse-grained energy dissipation. We compare three models: a normal model, a normal inverse Gaussian model, and a stable model. We show that the normal inverse Gaussian model is superior to both, the normal and the stable models, in terms of reproducing the distribution of the energy dissipation; and that the normal inverse Gaussian model is superior to the normal model and competitive with the stable model in terms of reproducing the self-scaling exponents. Furthermore, we show that the presented analysis is parsimonious in the sense that the self-scaling exponents are predicted from the one-point distribution of the energy dissipation, and that the shape of these distributions is independent of the Reynolds number.

Risk Adjustments of Option Prices under Time-Changed Dynamics

We derive a closed-form expansion of option prices in terms of Black-Scholes prices and higher-order Greeks. We show how the true price of an option less its Black-Scholes price is given by a series of premiums on higher-order risks that are not priced under the Black-Scholes model assumptions. The expansion can be used for a broad class of option pricing models with dynamics governed by time-changed Brownian motions. Specifically, we study expansions for exponential Levy models such as the Variance Gamma and the Normal Inverse Gaussian models as well as their stochastic volatility counterparts, e.g., the VGSV and NIGSV models. Moreover, we consider extensions of the expansion to a more general subclass of affine jump-diffusion models for which the pricing transform may not be known in closed form.

Risk adjustments of option prices under time-changed dynamics

We derive a closed-form expansion of option prices in terms of Black–Scholes prices and higher-order Greeks. We show how the true price of an option less its Black–Scholes price is given by a series of premiums on higher order risks that are not priced under the Black–Scholes model assumptions. The expansion can be used for a broad class of option pricing models with dynamics governed by time-changed Brownian motions. Specifically, we study expansions for exponential Lévy models such as the Variance Gamma and the Normal Inverse Gaussian models as well as their stochastic volatility counterparts, e.g. the VGSV and NIGSV models. Moreover, we consider extensions of the expansion to a more general subclass of affine jump-diffusion models for which the pricing transform may not be known in closed form.

Identification and control of Hammerstein systems via wireless networks

This article investigates a systematic approach for the identification and control of Hammerstein systems over a physical IEEE 802.11b wireless channel. Three major factors which may affect system stability and stabilisation are concerned: wireless network-induced delays, nonlinearity and model mismatch. First the network-induced delays are characterised by an inverse Gaussian distribution model according to IEEE 802.11b protocol and a model-based compensation method is used to estimate the delayed samples. Then an inverse function of nonlinear part of the identified model is used to attenuate the influence of nonlinearity, while the model mismatch is regarded as disturbance which is then dealt with by H ∞ control approach. A sufficient condition for mean-square asymptotic stability is obtained and expressed by a set of linear matrix inequalities, enabling direct controller design. Finally, numerical simulation examples are used to confirm the efficacy of the proposed approach.

Modeling and Bayes Estimation of Battery Lifetime for Smart Grids Under an Inverse Gaussian Model

An efficient use of many power systems, from smart grids to mobile devices, requires a careful assessment of the lifetime of the employed batteries. In this paper, a stochastic method for estimating the probability di¬stributions of the battery lifetime is illustrated, which is in particular focused on smart grid applications. The method is based upon a Poisson random process for describing the current load, as motivated by the intermittent supply capability of renewable resources, and uses an advanced battery model, with a proper stochastic input, for deducing the battery lifetime. Extensive numerical experiments performed by means of such battery model and laboratory tests have shown that the best fitting reliability model of a generic battery is the Inverse Gaussian model. This model is thoroughly discussed in the paper and, in order to address the problem of the parameter estimation of such reliability model, a novel practical Bayes approach is proposed, based upon an Inverted Generalized Gamma Distribution. Then, the feasibility and efficiency of such estimation method is illustrated by extensive stochastic simulations. An insight on some key aspects on reliability model identification closes the paper, focusing the attention on hazard rate function characteristics, remarking that it is a decreasing function for large mission times.

Inverse Gaussian process-based corrosion growth modeling and its application in the reliability analysis for energy pipelines

This paper describes an inverse Gaussian process-based model to characterize the growth of metal-loss corrosion defects on energy pipelines. The model parameters are evaluated using the Bayesian methodology by combining the inspection data obtained from multiple inspections with the prior distributions. The Markov Chain Monte Carlo (MCMC) simulation techniques are employed to numerically evaluate the posterior marginal distribution of each individual parameter. The measurement errors associated with the ILI tools are considered in the Bayesian inference. The application of the growth model is illustrated using an example involving real inspection data collected from an in-service pipeline in Alberta, Canada. The results indicate that the model in general can predict the growth of corrosion defects reasonably well. Parametric analyses associated with the growth model as well as reliability assessment of the pipeline based on the growth model are also included in the example. The proposed model can be used to facilitate the development and application of reliability-based pipeline corrosion management.