Optimality conditions are derived for problems of minimizing a generalized measure of deviation of a random variable, with special attention to situations where the random variable could be the rate of return from a portfolio of financial instruments. Generalized measures of deviation go beyond standard deviation in satisfying axioms that do not demand symmetry between ups and downs. The optima...

Optimality conditions are derived for problems of minimizing a general measure of deviation of a random variable, with special attention to situations where the random variable could be the rate of return from a portfolio of financial instruments. General measures of deviation go beyond standard deviation in satisfying axioms that do not demand symmetry between ups and downs. The optimality con...

in this paper, we propose a new method for fuzzy numbers. in this method, we assume that ai= (ai1, ai2, ai3, ai4) is to be a fuzzy number. so, the convex combination of ai1 and ai2 and also the convex combination of ai3 and ai4 are obtained separately. then, mic and mis that are to be the convex combinations and the standard deviation respectively we acquire them from these components. finally,...

Why process at all? Of course, the answer is ultimately feed efficiency, producing the most milk, eggs, meat or fiber at the lowest possible cost. Particle size reduction as the first step in the feed manufacturing process works toward the goal of improved feed efficiency by increasing the surface area of the materials being processed. This increases the amount of materials exposed to the anima...

Standard deviation (SD) and standard error (SE) are quietly but extensively used in biomedical publications. These terms and notations are used as descriptive statistics (summarizing numerical data), and they are used as inferential statistics (estimating population parameters from samples). I review the use and misuse of SD and SE in several authoritative medical journals and make suggestions ...