英语词汇“first, second, etc, moment”的英英意思、用法、释义、翻译、读音、例句、短语、词组-英语词典

d. Statistics. Each of a series of quantities ( first, second, etc., moment) that express the average or expected value of the first (second, etc.) powers of the deviation of a random variable from some given value, usually the mean or zero.The first moment (averaging the deviations from zero) is the expected value or mean of the random variable; the second moment (averaging the squares of the deviations from the mean) is the variance (variance n. 5); the third is a measure of skewness; the fourth a measure of kurtosis.product moment: see product n.¹ Compounds 2.

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the world > relative properties > number > probability or statistics > [noun] > variable > observation(s)

observation1559

time series1887

moment1893

variate1899

outlier1907

1893 K. Pearson in Nature 26 Oct. 615/2 Now the centre of gravity of the observation curve is found at once, also its area and its first four moments by easy calculation.

1925 R. A. Fisher Statist. Methods iii. 70 The standard error of the variance is √[(μ₄ − μ₂²)/N], where N is the number of samples, and μ₂ and μ₄ are the second and fourth moments of the theoretical distribution.

1938 A. E. Waugh Elem. Statist. Method vi. 114 The formula for the first moment about the mean involves Σx and..it reduces to zero, since Σx = 0. We can thus say some things about the moments of all curves in advance: (1) v₀ = 1, (2) v₁ = 0, (3) v₂ = σ².

1938 A. E. Waugh Elem. Statist. Method vi. 114 In any symmetrical curve the odd moments, being based on the sums of odd powers of deviations, will equal zero.

1959 G. James & R. C. James Math. Dict. (ed. 2) 257/2 μ_r = ∞−∞ (x − a)^rf(x)dx is the rth moment of x around the point a, where x is a random variable with frequency function f(x).

1961 D. V. Huntsberger Elem. Statist. Inference v. 102 The first moment about the origin is the mean μ of the theoretical distribution... The variance σ² of a random variable Y is defined as the second moment about the mean, the average value of (Y − μ)².

1991 Oxf. Econ. Papers 43 218 Assuming G has finite first moment, both integrals are convergent.

单词	first, second, etc, moment
释义	> as lemmas first, second, etc., moment d. Statistics. Each of a series of quantities ( first, second, etc., moment) that express the average or expected value of the first (second, etc.) powers of the deviation of a random variable from some given value, usually the mean or zero.The first moment (averaging the deviations from zero) is the expected value or mean of the random variable; the second moment (averaging the squares of the deviations from the mean) is the variance (variance n. 5); the third is a measure of skewness; the fourth a measure of kurtosis.product moment: see product n.¹ Compounds 2. ΘΚΠ the world > relative properties > number > probability or statistics > [noun] > variable > observation(s) observation1559 time series1887 moment1893 variate1899 outlier1907 1893 K. Pearson in Nature 26 Oct. 615/2 Now the centre of gravity of the observation curve is found at once, also its area and its first four moments by easy calculation. 1925 R. A. Fisher Statist. Methods iii. 70 The standard error of the variance is √[(μ₄ − μ₂²)/N], where N is the number of samples, and μ₂ and μ₄ are the second and fourth moments of the theoretical distribution. 1938 A. E. Waugh Elem. Statist. Method vi. 114 The formula for the first moment about the mean involves Σx and..it reduces to zero, since Σx = 0. We can thus say some things about the moments of all curves in advance: (1) v₀ = 1, (2) v₁ = 0, (3) v₂ = σ². 1938 A. E. Waugh Elem. Statist. Method vi. 114 In any symmetrical curve the odd moments, being based on the sums of odd powers of deviations, will equal zero. 1959 G. James & R. C. James Math. Dict. (ed. 2) 257/2 μ_r = ∞−∞ (x − a)^rf(x)dx is the rth moment of x around the point a, where x is a random variable with frequency function f(x). 1961 D. V. Huntsberger Elem. Statist. Inference v. 102 The first moment about the origin is the mean μ of the theoretical distribution... The variance σ² of a random variable Y is defined as the second moment about the mean, the average value of (Y − μ)². 1991 Oxf. Econ. Papers 43 218 Assuming G has finite first moment, both integrals are convergent. extracted from momentn. < as lemmas
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> as lemmas