Statistical Analysis Stack Exchange
Statistical Analysis Stack Exchange

Questions tagged [quantiles]

The quantiles of a distribution refer to points on its cumulative distribution function. Some common quantiles are quartiles and percentiles.

The quantiles of a distribution refer to points on its cumulative distribution function. Some common quantiles are quartiles and percentiles. Quantiles are used in quantile-normal and quantile-quantile plots, which can be useful for examining the shape of distributions.

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Percentile vs quantile vs quartile

What is the difference between the three terms below? percentile quantile quartile
luciano
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Help me understand the quantile (inverse CDF) function

I am reading about the quantile function, but it is not clear to me. Could you provide a more intuitive explanation than the one provided below? Since the cdf $F$ is a monotonically increasing function, it has an inverse; let us denote this by…
Inder Gill
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Estimate quantile of value in a vector

I have a set of real numbers. I need to estimate the quantile of a new number. Is there any clean way to do this in R? in general? I hope this is not ultra-trivial ;-) Much appreciated for your response. PK
polarise
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Finding Quartiles in R

I'm working through a statistics textbook while learning R and I've run into a stumbling block on the following example: After looking at ?quantile I attempted to recreate this in R with the following: > nuclear <- c(7, 20, 16, 6, 58, 9, 20, 50,…
user60305
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Quantile regression: Loss function

I am trying to understand the quantile regression, but one thing that makes me suffer is the choice of the loss function. $\rho_\tau(u) = u(\tau-1_{\{u<0\}})$ I know that the minimum of the expectation of $\rho_\tau(y-u)$ is equal to the…
CDO
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Algorithm to dynamically monitor quantiles

I want to estimate the quantile of some data. The data are so huge that they can not be accommodated in the memory. And data are not static, new data keep coming. Does anyone know any algorithm to monitor the quantiles of the data observed so far…
sinoTrinity
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Are there 99 percentiles, or 100 percentiles? And are they groups of numbers, or dividers or pointers to individual numbers?

Are there 99 percentiles, or 100 percentiles? And are they groups of numbers, or divider lines, or pointers to individual numbers? I suppose the same question would apply for quartiles or any quantile. I have read that the index of a number at a…
barlop
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Estimating a distribution based on three percentiles

What methods can I use to infer a distribution if I know only three percentiles? For example, I know that in a certain data set, the fifth percentile is 8,135, the 50th percentile is 11,259, and the 95th percentile is 23,611. I want to be able to…
Mark Eichenlaub
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How to determine quantiles (isolines?) of a multivariate normal distribution

I'm interested in how one can calculate a quantile of a multivariate distribution. In the figures, I have drawn the 5% and 95% quantiles of a given univariate normal distribution (left). For the right multivariate normal distribution, I am…
Marc in the box
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How does the inverse transform method work?

How does the inversion method work? Say I have a random sample $X_1,X_2,...,X_n$ with density $f(x;\theta)={1\over \theta} x^{(1-\theta)\over \theta}$ over $0
clarkson
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Is it possible to accumulate a set of statistics that describes a large number of samples such that I can then produce a boxplot?

I must clarify immediately that I am a practicing software developer, not a statistician, and that my college stats class was a very long time ago… That said, I would like to know if there is a method for accumulating a set of descriptive statistics…
Kaelin Colclasure
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How to obtain a confidence interval for a percentile?

I have a bunch of raw data values that are dollar amounts and I want to find a confidence interval for a percentile of that data. Is there a formula for such a confidence interval?
GeoffDS
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Why use extreme value theory?

I'm coming from Civil Engineering, in which we use Extreme Value Theory, like GEV distribution to predict the value of certain events, like The biggest wind speed, i.e the value that 98.5% of the wind speed would be lower to. My question is that…
cqcn1991
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Computing percentile rank in R

How can I add new variable into data frame which will be percentile rank of one of the variables? I can do this in Excel easily, but I really want to do that in R. Thanks
user333
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Does a univariate random variable's mean always equal the integral of its quantile function?

I just noticed that integrating a univariate random variable's quantile function (inverse cdf) from p=0 to p=1 produces the variable's mean. I haven't heard of this relationship before now, so I'm wondering: Is this always the case? If so, is this…
Tyler Streeter
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