Mathematical Programming for Statistical Inference

Abstract


 
 
 
 The study is concerned with the transforming theoretical Mathematical models into applied Mathematical programming models that are easy to handle and use. These Mathematical programming models can be applied and used in statistical inference, which used in many applied fields, for example, quality control and its application. The aim of this paper is to suggest two mathematical programming models for hypotheses tests, which make a balance between the high power (1-β), and the probability of a type I error, significance (), of the test. The paper introduces a simulation study to evaluate the performance of the two suggested mathematical programming models for tests hypotheses. The two suggested mathematical programming models solved with different sample sizes and different level of significance. The suggested models calculate the critical values which determine the rejection region exactly and the results are easy to interpret clearly. Then the conclusion for the suggested mathematical programming models makes balance between the power and the significance.
 
 
 
 

Mathematical Nonlinear Goal Programming in Quality Control

“…Both acceptance sampling applications have the basic purpose of classifying a lot as accepted or rejected, given the quality levels required for it [4]. This paper used the goal programming technique to convert the mathematical programming models are going to be introduced by Elrefaey et al [5] to nonlinear goal programming models. This paper also concerned with applying the mathematical programming presented by Elrefaey et al [5] and the suggested nonlinear goal programming models, which determine the producer's risk (α), consumer's risk (β) and acceptance level (c) simultaneously.…”

“…This paper used the goal programming technique to convert the mathematical programming models are going to be introduced by Elrefaey et al [5] to nonlinear goal programming models. This paper also concerned with applying the mathematical programming presented by Elrefaey et al [5] and the suggested nonlinear goal programming models, which determine the producer's risk (α), consumer's risk (β) and acceptance level (c) simultaneously. Real quality control data are used to evaluate the performance of the suggested models, which is used to determine the producer's risk α, consumer's risk β and acceptance level (c).…”

“…Elrefaey et al [5] presented the mathematical programming models which are used to determine power of a statistical test (1-β) and the critical value (c). The suggested nonlinear goal programming models concerned in this paper as modification models for the mathematical programming models are going to be introduced by Elrefaey et al [5]. The suggested nonlinear goal programming models are used to determine level of significance , power of a statistical test (1-β) and the critical value (c) simultaneously.…”

“… The first suggested nonlinear goal programming model depends on the first mathematical programming model Elrefaey et al [5] when binomial distribution is used as probability distribution as follows:…”

“… The suggested nonlinear goal programming model is extension for the mathematical programming model Elrefaey et al [5] by using goal programming technique. Also the suggested model depends on the first suggested nonlinear goal programming model when incomplete Beta distribution, as probability distribution, is used as equivalent to cumulative Binomial distribution as follows:…”