# Quantile

quantilesquintiletertileEstimating quantiles from a samplequintilestercile4th quantiledecilefractile bandssample quantiles
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.wikipedia
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### Quantile function

quantileinverse distribution functionnormal quantile function
-quantiles are the application of the quantile function (the inverse function of the cumulative distribution function) to the values
In probability and statistics, the quantile function, associated with a probability distribution of a random variable, specifies the value of the random variable such that the probability of the variable being less than or equal to that value equals the given probability.

### Quartile

quartileslower quartilelower and upper quartiles
Thus quartiles are the three cut points that will divide a dataset into four equal-sized groups. The 4-quantiles are called quartiles → Q; the difference between upper and lower quartiles is also called the interquartile range, midspread or middle fifty → IQR = Q 3 − Q 1
A quartile is a type of quantile.

### Quintile

the quintile
The 5-quantiles are called quintiles → QU
In statistics, a quantile for the case where the sample or population is divided into fifths

### Decile

deciles
The 10-quantiles are called deciles → D
A decile is one possible form of a quantile; others include the quartile and percentile.

### Percentile

percentiles50th percentile85th percentile speed
The 100-quantiles are called percentiles → P
In general, percentiles and quartiles are specific types of quantiles.

### Quantile regression

QuantileQuantile Regressions
Quantile regression
Whereas the method of least squares results in estimates of the conditional mean of the response variable given certain values of the predictor variables, quantile regression aims at estimating either the conditional median or other quantiles of the response variable.

### Standard error

SEstandard errorsstandard error of the mean
The standard error of a quantile estimate can in general be estimated via the bootstrap.
If the sampling distribution is normally distributed, the sample mean, the standard error, and the quantiles of the normal distribution can be used to calculate confidence intervals for the true population mean.

### Q–Q plot

plotting positionnormal quantile plotprobability plot correlation coefficient
Q–Q plot
In statistics, a Q–Q (quantile-quantile) plot is a probability plot, which is a graphical method for comparing two probability distributions by plotting their quantiles against each other.

### Quantile normalization

normalized
Quantile normalization
To quantile normalize two or more distributions to each other, without a reference distribution, sort as before, then set to the average (usually, arithmetic mean) of the distributions.

### Empirical distribution function

statistical distributionempirical distributiondistribution
Estimating quantiles from a sample

### Flashsort

Flashsort – sort by first bucketing by quantile
If numbered 1 to m, the class of an item A_i is the quantile, computed as:

### Quantization (signal processing)

quantizationquantization errorquantized
Quantization
Quantile

### Probability distribution

distributioncontinuous probability distributiondiscrete probability distribution
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.

### Median

averagesample medianmedian-unbiased estimator
. 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.

### Ranking

rankrankedrankings
Quantiles can also be applied to continuous distributions, providing a way to generalize rank statistics to continuous variables.

### Cumulative distribution function

distribution functionCDFcumulative probability distribution function
-quantiles are the application of the quantile function (the inverse function of the cumulative distribution function) to the values When the cumulative distribution function of a random variable is known, the

### Random variable

random variablesrandom variationrandom
When the cumulative distribution function of a random variable is known, the

### Inverse function

inverseinvertibleinvertible function
-quantiles are the application of the quantile function (the inverse function of the cumulative distribution function) to the values

### Interquartile range

inter-quartile rangebelowinterquartile
The 4-quantiles are called quartiles → Q; the difference between upper and lower quartiles is also called the interquartile range, midspread or middle fifty → IQR = Q 3 − Q 1

### Sextile

The 6-quantiles are called sextiles → S

### Ventile

The 20-quantiles are called ventiles, vigintiles, or demi-deciles → V

### Per mille

permilleper mil
The 1000-quantiles are called permilles → Pr

### Standard deviation

standard deviationssample standard deviationsigma
As in the computation of, for example, standard deviation, the estimation of a quantile depends upon whether one is operating with a statistical population or with a sample drawn from it. For a population, of discrete values or for a continuous population density, the

### Statistical population

populationsubpopulationsubpopulations
As in the computation of, for example, standard deviation, the estimation of a quantile depends upon whether one is operating with a statistical population or with a sample drawn from it. For a population, of discrete values or for a continuous population density, the

### Sample (statistics)

samplesamplesstatistical sample
As in the computation of, for example, standard deviation, the estimation of a quantile depends upon whether one is operating with a statistical population or with a sample drawn from it. For a population, of discrete values or for a continuous population density, the