# 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 It might be outdated or ideologically biased.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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In order to verify that the coefficients of the quantile regression model ([[beta].sub.0]([tau]) and [[beta].sub.1]([tau]) differ between the equations adjusted for the three quantiles ([tau] = 0.2, 0.5, 0.8) the confidence intervals for the 3 models were obtained.
The estimates across quantiles decreased for individuals with multiple disabilities from 22.6% at 10th quantile to 9.7% at 90th quantile.
Results over control variables related to both recipient-countries and donorcountries are broadly in line with those reported in Table 1 and interpreted above, with the exception here that public debt in donor-countries appear to be alternatively negative and significant, positive and significant, and statistically non-significant, depending on the quantiles.
property liability insurers was collected to examine the determinants of leverage in the lower and higher quantiles. The results of the 2SQR method show that the estimated coefficients for some explanatory variables (e.g., business concentration index and marketing channel) have a different sign for the lower and higher quantiles.
Moreover, this section discusses focus on the influence of sentiment and investor structure on the basis at different quantiles. The basis is more likely to be influenced by the interaction between investor sentiment and structure.
where Q1 and Q3 are the first and the third quantiles. Figure 3 is the representation of [Z.sub.t] and the transformed response variable [X.sup.*.sub.t] defined in (34) at level [tau] = 0.75.
political tie, firm performance, quantile regression, diminishing effect
The black triangle marks the estimated median incubation period for all Zika virus disease cases; the white triangle marks the estimated 95th quantile. The top panel shows the fitted Weibull density function; the blue line represents the distribution for all Zika virus disease cases; and the red line represents only those with confirmed Zika virus disease.
Accuracy of estimated quantiles: Results of statistical analysis were inherently uncertain, and to make the results useful certain criteria for measuring the extent of uncertainty should be used.
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 1.5 percent.

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