Omar A. Kittaneh

Average Entropy: A New Uncertainty Measure with Application to Image Segmentation

Various modifications have been suggested in the past to extend Shannon entropy to continuous random variables. This article investigates these modifications, and suggests a new entropy measure with the name of average entropy (AE). AE is more general than Shannon entropy in the sense that its definition encompasses both continuous as well as discrete domains. It is additive, positive and attains zero only when the distribution is uniform. The main characteristic of the suggested measure lies in its consistency behavior. Many properties of AE, including its relationship with Kullback–Leibler information measure, are studied. Precise theorems about the vanishing of the conditional AE for both continuous and discrete distributions are provided. Toward the end, the measure is tested for its effectiveness in image segmentation. [Received March 2014. Revised June 2015.]

A Measure of Discrimination Between two Double Truncated Distributions

On the basis of Kullback-Leibler discrimination information, and of discrimination measures introduced by Ebrahimi and Kirmani (1996a) and by Di Crescenzo and Longobardi (2004), we propose a measure of discrepancy between double truncated distributions. Some properties of this measure are studied and some mistakes in the preceding literature are corrected.

Deriving the efficiency function for type I censored sample from Pareto distribution using sup-entropy

This paper utilizes information theory to quantify Efficiency of Type I Censored sample drawn from Exponential Distribution and the consequent information loss due to Censoring. Based on Awad Sup-Entropy, an Efficiency Function for Censored sample is derived explicitly. The properties of the derived Efficiency Function are explained as a function of the Exponential Parameter and the termination time of the experiment. The estimation for the termination time of the experiment for a given Efficiency is discussed. Furthermore, under certain Efficiency, the Maximum Likelihood and Interval Estimation for the Exponential Parameter are also introduced.

Testing the Equality of Two Exponential Distributions

This paper proposes an overlapping-based test statistic for testing the equality of two exponential distributions with different scale and location parameters. The test statistic is defined as the maximum likelihood estimate of the Weitzmans overlapping coefficient, which estimates the agreement of two densities. The proposed test statistic is derived in closed form. Simulated critical points are generated for the proposed test statistic for various sample sizes and significance levels via Monte Carlo Simulations. Statistical powers of the proposed test are computed via simulation studies and compared to those of the existing Log likelihood ratio test.

Deriving scale normalisation factors for a GLoG detector

In computer vision, blob detection is used to obtain regions of interest that could signal the presence of objects or parts with application to object recognition and object tracking. One of the more common blob detectors is based on the Laplacian of Gaussian (LoG). However, most blob detectors developed in the past assume circular blobs, and these detectors do not perform as well with elliptical blobs, a more prevalent scenario in real images. A generalised LoG (GLoG) detector was proposed recently to deal specifically with elliptical blobs. To formulate the GLoG in a multi-scale framework, its response must be made scale invariant. Toward that end, necessary and sufficient conditions are presented here, with the normalisation factors derived for a scale-invariant GLoG detector. The factors are validated with a synthetic example and are further tested with two real-world images.

Efficiency estimation of type-I censored sample from the weibull distribution based on sup-entropy

ABSTRACT On the basis of Awad sup-entropy, the efficiency function for type-I censored sample from the Weibull distribution is numerically introduced. The properties of the derived efficiency are discussed. Furthermore, for a given efficiency, the termination time of the experiment, and the maximum likelihood estimates for the Weibull parameters, are proposed. Simulation results are tabulated and discussed. Censored and complete samples are compared for a wide range of the efficiency. The comparisons show the quality of the developed algorithms and the effectiveness of using censoring in estimating with the Weibull distribution.