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 ?
The quantile estimates (5%-95%) for these patients were similar to those for all travelers; however, among travelers with shorter travel durations and confirmed Zika virus infections, symptoms developed within 11.
One of the advantages (Coad & Rao, 2008; Wu & Liu, 2009; Ohlson & Kim, 2015) of using quantile regression--in addition to not assuming the normality of the residuals--is that it is possible to estimate regressions without "correcting" the problem of outliers because quantiles are not very sensitive to them; in contrast, OLS regression has a high sensitivity to extreme data because it is a conditional mean.
The graphic representation of estimates of growth curves were shown in figure 6 (a) and 6 (b) by measuring return periods based on non-exceedance probability along horizontal axis and quantiles of regional frequency distribution (growth curves) on vertical axis.
Machado and Mata (2001) provided evidence of increasing returns to schooling over the period 1982-1994 for Portugal, claiming that education is more valued for highly paid jobs because the impact of education at the tails of the distribution was distinct, the return at the 90th quantile increased by 3 percent, and the returns at the low quantiles decreased by 1.
In the actual process of analysis, this paper adopts bootstrap algorithm technology intensive quantile regression coefficients were estimated, and the sampling frequency is set to 400, that is to say by constantly with confidence interval sampling and sample, thus to infer the coefficient.
The estimation of regression quantiles coefficients, [[beta].
For each simulation, we solved for all quantiles from 0.
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This method thus aims to study the causes of the wage differential at different quantiles of the ln([W.
The correlation is negative at lower quantiles and turns positive at upper quantiles.
Table 5: Estimated Quantiles (hundered mm) for different Return Periods based on L-moments