IPO estimation of heaviness of the distribution beyond regularly varying tails

Abstract

We introduce a completely novel method for estimation of the parameter which governs the tail behavior of the cumulative distribution function of the observed random variable. We call it Inverse Probabilities for p-Outside values (IPO) estimation method. We show that this approach is applicable for wider class of distributions than the one with regularly varying tails. We demonstrate that IPO method is a valuable competitor to regularly varying tails based estimation methods. Some of the properties of the estimators are derived. The results are illustrated by a convenient simulation study.     

Books: The college Experience

Abstract

What Matters in College? Four Critical Years Revisited by Alexander W. Astin. San Francisco: Jossey-Bass, 1992, 482 pages, $30.95.     

The optimality conditions for optimization problems with fuzzy-valued objective functions

The optimality conditions for an optimization problem with fuzzy-valued objective function are derived in this article. The solution concept of this optimization problem will follow the similar solution concept, called nondominated solution, in multiobjective programming problem. In order to consider the differentiation of fuzzy-valued function, we invoke the Hausdorff metric to define the distance between two fuzzy numbers and the Hukuhara difference to define the difference of two fuzzy numbers. Under these settings, the optimality conditions for obtaining the nondominated solutions are elicited naturally by introducing the Lagrange multipliers.     

Optimization of Ethanol Supercritical Fluid Extraction of Medicinal Compounds from St. John's Wort by Central Composite Design

Extraction of medicinal compounds from St John's Wort was performed using supercritical ethanol. The supercritical fluid extraction parameters were optimized via response surface methodology which included a central composite design. The independent variables were extraction temperature (ranging from 300°C to 340°C), extraction times (ranging from 60 to 120 min), and plant concentration (ranging from 8% to 12%). The response was the St John's Wort extract yield. The extraction temperature was the most significant factor which affects St John's Wort yields according to statistical results. The coefficient of determination was estimated to be 0.98 which indicates the effectiveness of the model and its adaptability to the experimental data. The extract of St John's Wort was comprised of a wide array of compounds including phenols, acids, acid esters, and alkanes. The most prominent components of the extract of St. John's Wort in terms of their relative concentrations were linoleic acid ethyl ester, oleic acid ethyl ester, hexadecanoic acid ethyl ester, and nonacosane.