Aydin Ozturk

Least Squares Estimation of the Parameters of the Generalized Lambda Distribution

Nonlinear least squares estimation procedures are proposed for estimating the parameters of the generalized lambda distribution. The procedures are compared with other methods by making Monte Carlo experiments. A numerical example is also given to illustrate the proposed method.

On determining the radar threshold for non-Gaussian processes from experimental data

The problem of detecting radar signals embedded in clutter is an area of great interest. In many radar applications, it is important to set thresholds to achieve a false alarm probability (P/sub F/) of 10/sup -5/ or lower. Using conventional Monte Carlo techniques, where thresholds are set based on raw percentiles, an extremely large number of samples is required. We use the generalized Pareto distribution to approximate the extreme tail of the distributions and propose the ordered sample least squares (OSLS) method for estimating its parameters.

A new method for assessing multivariate normality with graphical applications

A new methodology for assessing distributional assumptions of multivariate data, with graphical applications, is developed. The underlying procedure is based on transforming the multivariate sample into a set of uncorrelated samples and representing the order statistics of each transformed sample by linked vectors in a two dimensional space. The multivariate normality tests are reviewed in detail, the proposed method is described and its properties are discussed.

Technical Section: Linear approximation of Bidirectional Reflectance Distribution Functions

Various empirical and theoretical models of the surface reflectance have been introduced so far. Most of these models are based on functions with non-linear parameters and therefore faces some computational difficulties involved in non-linear optimization processes. In this paper, we introduce a new approach for approximating Bidirectional Reflectance Distribution Functions (BRDF) by employing response surface methodology. The proposed model employs principal component transformations of the explanatory variables which are essentially functions of incoming and outgoing light directions. The resulting model is linear and can be used to represent both isotropic and anisotropic reflectance for diffuse and glossy materials. Considering some widely used reflection models including the Ward model, the Ashikhmin-Shirley model and the Lafortune model, we demonstrate empirically that satisfactory approximations can be made by means of the proposed general, simple and computationally efficient linear model.

An application of a distribution identification algorithm to signal detection problems

A computer program based on a new algorithm for univariate and multivariate distribution identification is presented. The underlying algorithm is proposed as a useful tool for the analysis of the signal detection problems. A computationally simple method for parameter estimation is considered and a general method for generating correlated non-Gaussian noise is also provided. >A computer program based on a new algorithm for univariate and multivariate distribution identification is presented. The underlying algorithm is proposed as a useful tool for the analysis of the signal detection problems. A computationally simple method for parameter estimation is considered and a general method for generating correlated non-Gaussian noise is also provided.<<ETX>>

A general algorithm fob, univariate and multivariate goodness of pit tests based on graphical representation

This paper presents a general algorithm tor assessing the distributional assumptions. Empirical distributions of the corresponding test statistics are obtained and examples are given to illustrate various applications of the proposed test. By using the squared radii and angles, it is shown that the problem of assessing multivariate normality can be reduced to that of testing for a univariate distribution. A limited comparison is made to investigate the power of the proposed test. This work was supported in part by the National Science Foundation under Grant NO.G88135. Support from the Computer Applications ami Software Engineering (CASE) Center of Syracuse University is also gratefully acknowledged

A new test for the extreme value distribution

In this paper a test statistic which is a modification of the W statistic for testing the goodness of fit for the two paremeter extreme value (smallest element) distribution is proposed. The test statistic Is obtained as the ratio of two linear estimates of the scale parameter. It Is shown that the suggested statistic is computationally simple and has good power properties. Percentage points of the statistic are obtained by performing Monte Carlo experiments. An example is given to illustrate the test procedure.

A histogram smoothing method for digital subtraction radiography

Digital subtraction radiography is a powerful technique for the detection of changes in serial radiographs. Among the others, contrast correction is a basic step for comparing the radiographs. Ruttimanns algorithm is widely used for contrast correction. In this study we propose a technique which is based on smoothing the empirical distribution of the reference image to improve Ruttimanns algorithm. Cardinal splines were used for smoothing the empirical distribution. Results based on clinical and simulated data showed that the proposed technique has outperformed the Ruttimanns algorithm. Relationship between the color depth and contrast differences was also investigated in terms of peak to signal ratio metric.

A New Graphical Test for Multivariate Normality

SYNOPTIC ABSTRACTA new methodology for assessing distributional assumptions of multivariate data, with graphical applications, is presented. The underlying procedure is based on transforming the multivariate sample into a set of uncorrelated samples and representing the order statistics of each transformed sample by linked vectors in a two dimensional space. The proposed method is described and its properties discussed. The multivariate normality tests are reviewed and a new classification scheme for them is proposed. The new test is then compared with a selection of the “best” competing ones under an exhaustive Monte Carlo study. A selection of “best” tests for several non normal alternatives, with advantages and disadvantages, is given. Graphical aspects of the new procedure are discussed.

On determining the radar threshold from experimental data

To set the radar threshold for small false alarm probabilities, it is necessary to know the tail of the probability density function for the test statistic under the no target assumption. It is shown that the generalized Pareto distribution (GPD) can be used to approximate the extreme tail of the density function. As a result, fixing the threshold is equivalent to estimating the two parameters of the GPD. For a variety of probability density functions it is demonstrated that accurate results can be obtained with orders of magnitude fewer samples than are required by Monte Carlo simulation. The thresholds required for very low false alarm probabilities were obtained with a good deal of accuracy.<<ETX>>