Quantile


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quantile

[′kwän‚tīl]
(statistics)
A value which divides a set of data into equal proportions; examples are quartile and decile.

Quantile

 

one of the numerical characteristics of random quantities used in mathematical statistics. If a distribution function of a random quantity X is continuous, then the quantile Kp of order p is defined as that number for which the probability of the inequality X < K<p is equal to p. From the definition of quantile it follows that the probability of the inequality Kp < X < K′’p is equal to p′p. The quantile K½ is the median of the random quantity X. The quantiles K¼ and K¾ are called quartiles, and K0.1, K0.2, … E0.9 are called deciles. Knowledge of the quantiles for suitably selected values of p makes it possible to visualize the distribution function.

Figure 1

For example, for the normal distribution (see Figure 1)

the graph of the function Φ (x) may be plotted by means of the deciles K0.1 = −1.28, K0.2 = −0.84, K0.3 = –0.52, K0.4 = –0.25 K0.5 = 0.25, K0.7= 0.52, K0.8 = 0.52, K0.8 = 0.84, and K0.9 =1.28. The quartiles of the normal distribution Φ(x) are K¼ = − 0.67 and K = 0.67.

References in periodicals archive ?
TAXATION AND ECONOMIC GROWTH IN THE EUROPEAN UNION: A QUANTILE APPROACH
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BARROSO et al., (2015) suggested that the following model of quantile regression is used in studies of adaptability and phenotypic stability:
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Moreover, spatial disaggregation/detrended quantile mapping (SD-DQM) and spatial disaggregation/quantile delta mapping (SD-QDM) are also applied to preserve GCM-driven long-term trends.
Of recent, a couple of studies have deviated from the conventional use of the autoregressive (AR) framework in favour of quantile regression framework in capturing the persistence within an inflation process (Tsong & Lee, 2011; Manzan & Zerom, 2015; Wolters & Tillman, 2015; Gupta et al., 2017).
* Second quantile programs were strong and should be maintained.
Based on a database of non-financial A-share listed firms from 2004 to 2012, we study the effects of political ties on firm performance within a quantile regression framework.