Hammou El Barmi

Bio: Hammou El Barmi is an academic researcher from City University of New York. The author has contributed to research in topics: Estimator & Stochastic ordering. The author has an hindex of 12, co-authored 53 publications receiving 448 citations. Previous affiliations of Hammou El Barmi include Baruch College & Kansas State University.

Conditional tests in a competing risks model

Abstract: Testing for equality of competing risks based on their cumulative incidence functions (CIFs) or their cause specific hazard rates (CSHRs) has been considered by many authors The finite sample distributions of the existing test statistics are in general complicated and the use of their asymptotic distributions can lead to conservative tests In this paper we show how to perform some of these tests using the conditional distributions of their corresponding test statistics instead (conditional on the observed data) The resulting conditional tests are initially developed for the case of k = 2 and are then extended to k > 2 by performing a sequence of two sample tests and by combining several risks into one A simulation study to compare the powers of several tests based on their conditional and asymptotic distributions shows that using conditional tests leads to a gain in power A real life example is also discussed to show how to implement such conditional tests

Nonhomogeneous poisson processes as overhaul models

Abstract: Hollander and Proschan (1974) studied nonhomogeneous Poisson processes as models for systems subject to overhauls. They did not postulate a functional form for the intensity, but showed that certain basic assumptions about the deterioration of the system implied that the mean function is superadditive. They studied tests of the null hypothesis that the intensity is constant with the alternative restricted to superadditive mean functions. For estimation purposes, the class of superadditive mean functions is too broad. We assume that the intensity is nondecreasing between overhauls and that at an overhaul it does not fall below its average prior to the overhaul. These two assumptions imply that the mean function is star-shaped. We obtain the restricted maximum-likelihood estimates under these two assumptions and under the star-shaped restriction. The two estimates are compared on a data set.

Empirical likelihood ratio test for symmetry against type I bias with applications to competing risks

Abstract: A random variable X with cumulative distribution function F is said to have a symmetric distribution about θ if and only if X−θ and−X+θ are identically distributed. Different types of partial skewness and one-sided bias are obtained by looking at different types of orderings between the distributions of X−θ and−X+θ. For example, X, or equivalently F, is said to have type I bias about θ if X−θ is stochastically larger than−X+θ. In this paper, we assume that F is continuous, θ is known and develops an empirical likelihood ratio type test for testing for symmetry about θ against this type of alternative. This test is shown to be asymptotically distribution free and the results of a simulation study show that it outperforms in terms of power, a test developed for the same problem in Alfieri and El Barmi [(2005), ‘Nonparametric Estimation of a Distribution Function with Type I Bias with Applications to Competing Risks’, Journal of Nonparametric Statistics, 17, 319–333]. It turns out that the results developed ...

Convergence of Probability Measures

Abstract: Convergence of Probability Measures. By P. Billingsley. Chichester, Sussex, Wiley, 1968. xii, 253 p. 9 1/4“. 117s.

Convergence of probability measures

Abstract: The author's preface gives an outline: "This book is about weakconvergence methods in metric spaces, with applications sufficient to show their power and utility. The Introduction motivates the definitions and indicates how the theory will yield solutions to problems arising outside it. Chapter 1 sets out the basic general theorems, which are then specialized in Chapter 2 to the space C[0, l ] of continuous functions on the unit interval and in Chapter 3 to the space D [0, 1 ] of functions with discontinuities of the first kind. The results of the first three chapters are used in Chapter 4 to derive a variety of limit theorems for dependent sequences of random variables. " The book develops and expands on Donsker's 1951 and 1952 papers on the invariance principle and empirical distributions. The basic random variables remain real-valued although, of course, measures on C[0, l ] and D[0, l ] are vitally used. Within this framework, there are various possibilities for a different and apparently better treatment of the material. More of the general theory of weak convergence of probabilities on separable metric spaces would be useful. Metrizability of the convergence is not brought up until late in the Appendix. The close relation of the Prokhorov metric and a metric for convergence in probability is (hence) not mentioned (see V. Strassen, Ann. Math. Statist. 36 (1965), 423-439; the reviewer, ibid. 39 (1968), 1563-1572). This relation would illuminate and organize such results as Theorems 4.1, 4.2 and 4.4 which give isolated, ad hoc connections between weak convergence of measures and nearness in probability. In the middle of p. 16, it should be noted that C*(S) consists of signed measures which need only be finitely additive if 5 is not compact. On p. 239, where the author twice speaks of separable subsets having nonmeasurable cardinal, he means "discrete" rather than "separable." Theorem 1.4 is Ulam's theorem that a Borel probability on a complete separable metric space is tight. Theorem 1 of Appendix 3 weakens completeness to topological completeness. After mentioning that probabilities on the rationals are tight, the author says it is an

A tutorial on geometric programming

Abstract: A geometric program (GP) is a type of mathematical optimization problem characterized by objective and constraint functions that have a special form. Recently developed solution methods can solve even large-scale GPs extremely efficiently and reliably; at the same time a number of practical problems, particularly in circuit design, have been found to be equivalent to (or well approximated by) GPs. Putting these two together, we get effective solutions for the practical problems. The basic approach in GP modeling is to attempt to express a practical problem, such as an engineering analysis or design problem, in GP format. In the best case, this formulation is exact; when this is not possible, we settle for an approximate formulation. This tutorial paper collects together in one place the basic background material needed to do GP modeling. We start with the basic definitions and facts, and some methods used to transform problems into GP format. We show how to recognize functions and problems compatible with GP, and how to approximate functions or data in a form compatible with GP (when this is possible). We give some simple and representative examples, and also describe some common extensions of GP, along with methods for solving (or approximately solving) them.