Statistical method of dividing data into equal-sized intervals for analysis
Probability density of a normal distribution, with quantiles shown. The area below the red curve is the same in the intervals (−∞,Q1), (Q1,Q2), (Q2,Q3), and (Q3,+∞).
In statistics and probability, quantiles are cut points dividing the range of a probability distribution into continuous intervals with equal probabilities, or dividing the observations in a sample in the same way. There is one fewer quantile than the number of groups created. Common quantiles have special names, such as quartiles (four groups), deciles (ten groups), and percentiles (100 groups). The groups created are termed halves, thirds, quarters, etc., though sometimes the terms for the quantile are used for the groups created, rather than for the cut points.
q-quantiles are values that partition a finite set of values into q subsets of (nearly) equal sizes. There are q − 1 partitions of the q-quantiles, one for each integer k satisfying 0 < k < q. In some cases the value of a quantile may not be uniquely determined, as can be the case for the median (2-quantile) of a uniform probability distribution on a set of even size. Quantiles can also be applied to continuous distributions, providing a way to generalize rank statistics to continuous variables (see percentile rank). When the cumulative distribution function of a random variable is known, the q-quantiles are the application of the quantile function (the inverse function of the cumulative distribution function) to the values {1/q, 2/q, …, (q − 1)/q}.
In statistics and probability, quantiles are cut points dividing the range of a probability distribution into continuous intervals with equal probabilities...
predictor variables, quantile regression estimates the conditional median (or other quantiles) of the response variable. Quantile regression is an extension...
In probability and statistics, the quantile function outputs the value of a random variable such that its probability is less than or equal to an input...
In statistics, quantile normalization is a technique for making two distributions identical in statistical properties. To quantile-normalize a test distribution...
In statistics, quartiles are a type of quantiles which divide the number of data points into four parts, or quarters, of more-or-less equal size. The...
{e^{-n^{2}/2}}{n{\sqrt {\pi /2}}}}} . The quantile function of a distribution is the inverse of the cumulative distribution function. The quantile function of the standard...
function (quantile function) of the logistic distribution is a generalization of the logit function. Its derivative is called the quantile density function...
statistic that can be used in conjunction with the histogram and the normal quantile plot to characterize the data or distribution. Skewness indicates the direction...
In statistics, the logit (/ˈloʊdʒɪt/ LOH-jit) function is the quantile function associated with the standard logistic distribution. It has many uses in...
represents 1/10 of the sample or population. A decile is one possible form of a quantile; others include the quartile and percentile. A decile rank arranges the...
Quantile Regression Averaging (QRA) is a forecast combination approach to the computation of prediction intervals. It involves applying quantile regression...
function of those values; less commonly, the conditional median or some other quantile is used. Like all forms of regression analysis, linear regression focuses...
ease of fitting to data with linear least squares; simple, closed-form quantile function (inverse CDF) equations that facilitate simulation; a simple,...
of the Q–Q probability plot for a normal distribution. The theoretical quantiles are generally chosen to approximate either the mean or the median of the...
{\displaystyle F(x)=p} . This defines the inverse distribution function or quantile function. Some distributions do not have a unique inverse (for example...
different procedures to estimate alternative location parameters (e.g., quantile regression or Necessary Condition Analysis) or estimate the conditional...
bounded quantile-parameterized distributions, which are highly shape-flexible and can be parameterized with data using linear least squares (see Quantile-parameterized...
continuous, symmetric probability distribution defined in terms of its quantile function. It is typically used to identify an appropriate distribution...
malleolus (above ankle outer side of leg). Any value measured below the 0.05 Quantile IENFD values per age span, is considered a reliable positive diagnosis...
1947) is an American econometrician mostly known for his contributions to quantile regression. He is currently a Honorary Professor of Economics at University...
one thousandth of a dollar. Permille may also be used to express a 1000-quantile ("999th permille"), but this usage is rare and largely obsolete. Modern...
inverse of the cumulative distribution function. Percentiles are a type of quantiles, obtained adopting a subdivision into 100 groups. The 25th percentile...
probability density function (pdf) cumulative distribution function (cdf) quantile function raw moment central moment mean variance standard deviation skewness...
Median regression may refer to: Quantile regression, a regression analysis used to estimate conditional quantiles such as the median Repeated median regression...
\ 2\!\ }}\ } quantile of a standard normal distribution, vs. z α / 2 , {\displaystyle \ z_{\alpha /2}\ ,} which is the upper quantile. Since the test...
/2;k+1,1),} where χ 2 ( p ; n ) {\displaystyle \chi ^{2}(p;n)} is the quantile function (corresponding to a lower tail area p) of the chi-squared distribution...
probability density function (pdf) cumulative distribution function (cdf) quantile function raw moment central moment mean variance standard deviation skewness...
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