“quantile”的概念、定义、翻译、参考文献-科学参考

quantile

Mathematics

Let X be a continuous random variable. For 0<p<1, the p-th quantile is the value x_p such that Pr(X ≤ x_p) = p. In other words, the fraction of the population less than or equal to x_p is p. For example, x_0.5 is the (population) median.

Often percentages are used. The n-th percentile is the value x_n/100 such that n per cent of the population is less than or equal to x_n/100. For example, 30% of the population is less than or equal to the 30th percentile. The 25th, 50th, and 75th percentiles are the quartiles.

Alternatively, the population may be divided into tenths. The n-th decile is the value x_n/10 such that n-tenths of the population is less than or equal to x_n/10. For example, three-tenths of the population is less than or equal to the 3rd decile.

The terms can be modified, though not always very satisfactorily, to be applicable to a discrete random variable or to a large sample ranked in ascending order.

Statistics

The qth quantile of the distribution of a random variable, X, is that value x such that P(X<x)=q. If q=0.5, the value is called the median. The cases q=0.25 and q=0.75 correspond to the lower quartile and upper quartile, respectively. See also decile; percentile.

Economics

For any number p between 0 and 1, the pth population quantile is the number x such that the probability of a value below x occurring equals p; in other words, population quantile is the inverse cumulative distribution function. In a sample of size N, the pth quantile is the observation such that approximately Np of the observations are less than this observation and N(1−p) of the observations are larger. The pth quantile is also referred to as the (100p)th percentile. The 0.5th quantile is the median; the 0.25th and the 0.75th quantiles are called the lower and the upper quartiles. The distance between the lower and upper quartiles, called the interquartile range, is sometimes used as a measure of dispersion.

单词	quantile
释义	quantile Mathematics Let X be a continuous random variable. For 0<p<1, the p-th quantile is the value x_p such that Pr(X ≤ x_p) = p. In other words, the fraction of the population less than or equal to x_p is p. For example, x_0.5 is the (population) median. Often percentages are used. The n-th percentile is the value x_n/100 such that n per cent of the population is less than or equal to x_n/100. For example, 30% of the population is less than or equal to the 30th percentile. The 25th, 50th, and 75th percentiles are the quartiles. Alternatively, the population may be divided into tenths. The n-th decile is the value x_n/10 such that n-tenths of the population is less than or equal to x_n/10. For example, three-tenths of the population is less than or equal to the 3rd decile. The terms can be modified, though not always very satisfactorily, to be applicable to a discrete random variable or to a large sample ranked in ascending order. Statistics The qth quantile of the distribution of a random variable, X, is that value x such that P(X<x)=q. If q=0.5, the value is called the median. The cases q=0.25 and q=0.75 correspond to the lower quartile and upper quartile, respectively. See also decile; percentile. Economics For any number p between 0 and 1, the pth population quantile is the number x such that the probability of a value below x occurring equals p; in other words, population quantile is the inverse cumulative distribution function. In a sample of size N, the pth quantile is the observation such that approximately Np of the observations are less than this observation and N(1−p) of the observations are larger. The pth quantile is also referred to as the (100p)th percentile. The 0.5th quantile is the median; the 0.25th and the 0.75th quantiles are called the lower and the upper quartiles. The distance between the lower and upper quartiles, called the interquartile range, is sometimes used as a measure of dispersion.
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