Questions tagged [quantiles]

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

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Median zero in the multivariate case

I have a question about the definition of the median of a (continuous) random vector $X\equiv (X_1,..., X_r)$. As suggested here and by other discussions in this forum (e.g., here and here) there are ...
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Bias in percentiles: what summary statistic will not be systematically different from the true value?

It is known that for non-symmetric distributions, sample percentiles are biased estimators. I took the Log-normal distribution as a template. I take a small sample size (say 10 samples) and estimate ...
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Why does linearly interpolating the quantile work?

I am working on the following exercise: In the lecture we required a quantile $Q_p$ to suffice the condition $$F_n(Q_p^{-}) \le p \le F_n(Q_p) \tag 1,$$ where $F_n$ is the empirical distribution ...
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Test whether expected shortfalls of two distributions are equal

I have paired samples of size 1000 from two distributions. I would like to test a null hypothesis that the 2.5% expected shortfalls1 of the two distributions are equal. How can I do that? (This is a ...
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Test whether expected shortfalls of two portfolios are equal

I have about 2000 daily observations of historical share prices for a handful of companies. I use a rolling window of 1000 observations to model their joint distribution. From each of the windows, I ...
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What statistics are good for measuring the tail?

We're working with latency data and people are concerned with the worst case latencies. They're using the 99th and 99.9th percentile as KPIs (key performance indicators). We know that an unbiased ...
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Test whether or not quantile values belong to a distribution

I have a list of 23 values for the following quantiles: ...
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What does 0.5sigma mean?

I want to ask about a term about "this data is within 0.5 sigma". If I understand correctly the person first calculates standart deviation(sigma) of his data and multiples his/her std ...
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The inverse cumulative distribution function evaluated at Halton draws [duplicate]

Sandor and Train (2004, Quasi-random simulation of discrete choice models) mention that "A randomized Halton sequence is a set of draws from the uniform distribution. To obtain draws from density ...
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Estimating quantiles for posterior predictive distribution

Let's say I have a parametrised distribution $X|\theta$ and a sample from the posterior distribution of $\theta$, $\hat{\theta}_1,...,\hat{\theta}_k$. If I was interested in the CDF of the predictive ...
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The simulated $((1-\alpha )\times 100)^{th}$ percentiles of the null distribution of a specific statistic [closed]

I've written this algorithm in R program: as following ...
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If I know all the parameters of a distribution (mean, deviation, skewness, kurtosis,...) how do I calculate what quantile a certain data is at?

I have a game with levels. I am tracking the time (in seconds) each of my users took to complete a certain level. What I want to accomplish is to show the user how their time compares to others (i.e. &...
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Creating an Index by summing percentiles

This is probably a basic concept but i want to understand if it makes sense mathematically. I want to create an index on how much somebody spends at grocery stores. So for each person I calculate the ...
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measuring distance between distributions by using distance between CDF estimate with CIs?

I'm working on an machine learning-related project that compares distributions of features and alerts user when a feature's distribution changed over time. I have been thinking about the best way to ...
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Confused about inverse function (quantile function)

I read a post that says: "Math definition is that the quantile function is the inverse of the distribution function at α. It specifies the value of the random variable such that the probability ...
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Why type 8 quantile function is the best?

https://www.researchgate.net/publication/222105754_Sample_Quantiles_in_Statistical_Packages ...
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About the definition of quantile from empirical data? [duplicate]

R> quantile(c(1,2,3), 0.01) 1% 1.02 The above is an example output from the quantile() function in R. The problem with it ...
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How many points fall below quantile regression-line?

I am sorry for the relatively easy question regarding quantile regression. I am a little stuck, and reading these resources I can't resolve this problem right now: (1) http://www.econ.uiuc.edu/~roger/...
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Extract slopes for all fitted quantile regression models with different tau-values, R

I wonder how I can get the slopes of all the models that were fitted when I do the following: library(quantreq) z =rq(mpg ~ wt, data=mtcars, tau=-1) Putting the <...
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How to make conditional quantiles?

I have a dataset consisting two variables X and Y. Both of them are of length 250. Now, I want to make conditional quantiles of X and Y. I have been reading the papers of Koenker and Basset (1978) and ...
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Self-study: Comparing Uniform and Normal CDF/quantiles for a given range

Not sure if the title is perfect. Nevertheless, there are two persons drawing $\alpha$. ‘A’ draws from $N(0,1)$ and ‘B’ from $U(-2\sqrt{2\pi}, 2\sqrt{2\pi})$. For which person is it more likely that ...
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