# 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.
McGraw-Hill Dictionary of Scientific & Technical Terms, 6E, Copyright © 2003 by The McGraw-Hill Companies, Inc.
The following article is from The Great Soviet Encyclopedia (1979). It might be outdated or ideologically biased.

## 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.

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* 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.

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