Spiegelman Clifford H
National Bureau of Standards, Washington, D.C. 20234.
J Res Natl Bur Stand (1977). 1980 Sep-Oct;85(5):363-366. doi: 10.6028/jres.085.021.
The result in this paper explains some of the qualitative nature of Jensen's inequality. It is shown that the more disperse the distribution of a random variable is, the smaller is the expectation of any concave function of it. This result can be used to show the inadequacy of some current methods of reporting environmental data by using geometric means, and it extends the result of I. Billick, D. Shier, and C. H. Spiegelman, where symmetry of the error in environmental measurements is assumed.
本文的结果解释了詹森不等式的一些定性性质。结果表明，随机变量的分布越分散，其任何凹函数的期望就越小。这一结果可用于表明当前一些使用几何平均数报告环境数据的方法存在不足，并且它扩展了I. Billick、D. Shier和C. H. Spiegelman的结果，后者假设了环境测量误差的对称性。
