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A value which divides a set of data into equal proportions; examples are quartile and decile.



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 ?
Middle quantile programs were strong and might have areas that could be improved.
By suitable distribution did not mean only the distribution provided best fit to the selected region but also the distribution which provided accurate quantile estimates for different return periods.
k,[gamma]]] represents the quantile y of the chi-square distribution with "k" degrees of freedom ([[ji al cuadrado].
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.
However, most traditional EVT-based methods for quantile estimation yields VaR estimates which neglect the current volatility background.
As pointed out in Machado and Mata (2005) the estimated Quantile Regression coefficients can be interpreted as rates of return of labor market skills at different points of the conditional wage distribution.
Banker (1988) provides the foundation for an SDEA model where the user pre-specifies the quantile but does not provide a way to choose the optimal quantile.
Because we measured each outcome of interest repeatedly for 77% of the participants, we fit quantile regressions for longitudinal data (Koenker 2004).
Kandil (2009) supports the glass-ceiling hypothesis by showing that both the gender wage differential and the discrimination factor escalate towards the top quantile of the wage distribution.
In this paper we adopt a novel statistical method proposed by Koenker and Xiao [5], the quantile autoregression (QAR) model, to examine the influence of lagged returns on the current return over the whole spectrum of return distribution.
To be able to model and simulate the extreme losses of major accidents, the following sections provide a theoretical procedure for practical use of quantile function and order statistics for the simulation of extreme losses.