# 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