“kurtosis”的概念、定义、翻译、参考文献-科学参考

kurtosis

Mathematics

Let m₂ = E((X−μ‎)²) and m₄ = E((X−μ‎)⁴), where μ‎ = E(X), be the second and fourth moments about the mean. Then $\frac{m_{4}}{{(m_{2})}^{2}}$ is the kurtosis of the distribution. For a normal distribution this has the value 3, which can be taken as a standard for comparison and hence a value of 3 is termed mesokurtic—from ‘meso’ meaning ‘middle’. For values less than 3 the distribution is termed platykurtic, and for values greater than 3 it is leptokurtic.

Statistics

A measure of the peakedness of a distribution. The measure (usually denoted by β₂ or κ), was introduced by Karl Pearson before 1905. The measure is given by $kurtosis$
where μ₄ is the fourth central moment of the distribution and μ₂ is the variance. It is invariant under a change of scale or origin.
An alternative definition uses (β₂−3) to give a value of 0 for the normal distribution. With this definition, a distribution having negative kurtosis is described as being platykurtic (flatter), and a distribution having positive kurtosis is described as being leptokurtic (more peaked). A distribution having kurtosis zero is described as mesokurtic.

Geology and Earth Sciences

The degree of peakedness in a distribution curve. If kurtosis (K) is 1, the curve is said to be mesokurtic; if K is greater than 1 it is leptokurtic; if K is less than 1 it is platykurtic.

Economics

A measure of how ‘humped’ a probability distribution is, compared to a normal distribution with the same mean and variance. The kurtosis of a variable x with mean μ‎ is defined by K = E [(x − μ‎)⁴]/[E(x − μ‎)²]². A variable with a normal distribution has K = 3. A distribution with K > 3 is slim and long-tailed, with more weight in its centre and extremes and less at medium distances from the mean than a normal distribution. A distribution with K < 3 is fat and short-tailed, with less weight in its centre and extremes and more at medium distances from the mean than a normal distribution.

单词	kurtosis
释义	kurtosis Mathematics Let m₂ = E((X−μ‎)²) and m₄ = E((X−μ‎)⁴), where μ‎ = E(X), be the second and fourth moments about the mean. Then $\frac{m_{4}}{{(m_{2})}^{2}}$ is the kurtosis of the distribution. For a normal distribution this has the value 3, which can be taken as a standard for comparison and hence a value of 3 is termed mesokurtic—from ‘meso’ meaning ‘middle’. For values less than 3 the distribution is termed platykurtic, and for values greater than 3 it is leptokurtic. Statistics A measure of the peakedness of a distribution. The measure (usually denoted by β₂ or κ), was introduced by Karl Pearson before 1905. The measure is given by $kurtosis$ where μ₄ is the fourth central moment of the distribution and μ₂ is the variance. It is invariant under a change of scale or origin. An alternative definition uses (β₂−3) to give a value of 0 for the normal distribution. With this definition, a distribution having negative kurtosis is described as being platykurtic (flatter), and a distribution having positive kurtosis is described as being leptokurtic (more peaked). A distribution having kurtosis zero is described as mesokurtic. Geology and Earth Sciences The degree of peakedness in a distribution curve. If kurtosis (K) is 1, the curve is said to be mesokurtic; if K is greater than 1 it is leptokurtic; if K is less than 1 it is platykurtic. Economics A measure of how ‘humped’ a probability distribution is, compared to a normal distribution with the same mean and variance. The kurtosis of a variable x with mean μ‎ is defined by K = E [(x − μ‎)⁴]/[E(x − μ‎)²]². A variable with a normal distribution has K = 3. A distribution with K > 3 is slim and long-tailed, with more weight in its centre and extremes and less at medium distances from the mean than a normal distribution. A distribution with K < 3 is fat and short-tailed, with less weight in its centre and extremes and more at medium distances from the mean than a normal distribution.
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