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 ?
But in practice even more samples are required: accurate determination of the quantiles requires an uncorrelated sample from the distribution; samples drawn using the Gibbs sampler often do exhibit serial autocorrelation One way of avoiding this is to thin the sampler output by accepting only a certain fraction of values.
This requires the calculation of four parameters, namely the median, the normalized median absolute deviation (NMAD), and two sample quantiles.
Quantile regression of religious commitment data from the 1998 International Social Survey Program results produces a negative to positive pattern of rising coefficients on civil liberties across quantiles similar to what is found in the regression analysis of the simulation data.
The gender wage gap was falling across all quantiles of the conditional wage distribution between 2001 and 2005; hence women's relative wage gains were experienced across the earnings distribution.
There are 19 distinct quantiles (5% to 95% at intervals of 5%) with the coefficient of each quantile plotted by a filled circle.
When the practitioner feels that "early infant mortality" (in this context of thickness, an undue preponderance of smaller thickness) will have an effect on the distribution chosen for a data set, then induced censoring at the quantiles say between the 0.
This is probably a statistical artifact; the quantile regression models predicted the values of upper quantiles in the response distribution, and these upper values were not dependent on grass cover.
A quantile survival of interest such as the median, can be calculated from the hazard or survival function.
innovations from a Student's t distribution and comparing the estimated quantiles with the ones from the actual distribution.
Vincent and Eastman (2009) fall into the trap of interpreting quantiles as subsets of the data.
We use course and student characteristic data along with program evaluation methods to quantify the effect of this voluntary training program on its participants, both at the mean, as well as the different quantiles of the distribution of students' outcomes.