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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Non-parametric test for two sample quantiles

I would like to know if there is a non-parametric test on quantiles. In a general setting we define quantiles as $Q_X(p) = inf \{x \in \mathbf{R}: p \leq P(X\leq x)\}$. I would like to test $H_0: Q_X(...
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How to define 2d-quantiles?

I need to group the values of two distributions into n groups of equal size by using quantiles (remark: I know that quantiles do not always result in exactly same ...
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Nonparametric Methods for Two Sample Quantile Test

Background I want to compare two populations' quantile, e.g. 99.99% quantile, 95% quantile. So I am searching for methods for two sample quantile testing. Unfortunately, the population does not obey ...
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Approximate Posterior Predictive Quantiles with Numerical Methods

I have a posterior function which is easy to approximate using numerical methods (the posterior has only 2 parameters, and is approximately Gaussian because of the large sample). However, I need to ...
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Standard Formula for Calculating Percentiles

I have the following question about calculating percentiles (to illustrate my example, I will use the R programming language). Suppose I have the following data: ...
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How to estimate probable response times, from previous samples?

I'm a IT manager that deals with delays from various departments in a purchase process. In a given phase we have 25 handovers and thus 25 response times. So many variable times (and without SLA) ...
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How would one measure consistent high values for a dataset? Is it the same as measuring a high variance for a low percentile?

For a numerical dataset, you can measure the consistency of the data using variance, where lower variance means the data is closer to the mean/median, while higher variance means the data is spread ...
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Is this formula for percentile from z-score correct?

Preface: I am not a mathematician. I have a basic understanding of statistics but am not familiar with mathematical notation beyond high school algebra. I am a software developer maintaining medical ...
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I have data from an unknown, continuous probability distribution. How do I calculate a percentile/quantile?

I'm going to collect a sample of data that comes from an unknown, likely continuous, probability distribution. I don't really know anything about the data other than that it's somewhat chaotic. I want ...
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Why do Quartile, Decile, Percentile have plus 1 in their formula? [duplicate]

I searched this on the internet, but barely found anything, and what I found was not satisfactory. Quartile divides the data into 4 equal parts. Qi = i * (n+1)/4 where i=1, 2, 3 Decile divides the ...
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What determines y-axis scaling on a normal probability plot?

I've been investigating Q-Q plots, specifically the normal probability plot, to determine if a set of data I have is approximately normal. I.e., a plot of the data should be approximately a straight ...
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Probabilistic interpretation of sum of quantile functions

We know that the weighted sum of CDF $$ F(x) = w_1 F_1(x) + w_2 F_2(x), \,\, w_1 + w_2 = 1 $$ is the CDF of the mixture distribution. Is there a probabilistic interpretation for weighted sum of ...
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"Representative" percentile across series of batches

I am running a workload in a typical client-server setup with latency as my metric. My workload generator tools output the percentiles of latency metrics for a batch of transactions every 5 mins. I ...
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Find a function that is closer to the true quantile function than the empirical quantile function

Suppose we have a distribution whose quantile function is $Q(p)$, $p \in [0,1]$. With $n$ ordered samples $\{\bar{x}_1,\bar{x}_2,\cdots,\bar{x}_n\}$, we can build the empirical quantile function $\bar{...
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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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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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Proving convergence in distribution between order statistics and quantiles

The random variable of continuous type $X$ has CDF $F(x)$ $X_1, X_2, \cdots, X_n$ is a random sample of size $n$ from the distribution of $X$ Function $h(y)$ is defined as $h(y) = F^{-1}{(1-e^{-y})}I_{...
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Converting 2-D Quantiles to 2-D CDF

I've been given some data in a format I've not encountered before - quantiles and associated values in 2-D, e.g. height and weight as: For the 10th quantile in the height range, the 50th quantile in ...
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Can you find a confidence interval from a set of percentile samples?

Let's say we run a simulation where thousands of measurements happen, each measurement has a numeric value. For each simulation we output a single aggregate value of all the measurements in the form ...
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Estimate population mean from "best of N" samples

If I have a data set for which I know all measurements represent the largest of N observations, is there a good method for estimating the mean of all observations? So for example if N=10 and I have 3 ...
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About the Normal distribution

I'm having troubles understanding the following problem Problem The volume of daily transactions (in millions of shares) in the New York Stock Exchange is a random variable that is distributed ...
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Regression with percentile independent variable

I am running a simple regression with average standardized exam scores at the school-level, and weekly household income at the neighborhood-level where the school is located. The two variables look as ...
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How does ordinal regression compare to quantile regression?

I am familiar with ordinal regression and quantile regression at a high level, but would like a deeper understanding of the two beginning on how they differ. Can someone compare and contrast the two, ...
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Understanding relationship between T-Score and percentile

Suppose I am told that a person's raw score on a certain test was 26, the T-Score is 45, and the percentile is 31. From what I know about T-Scores, I'm having trouble understanding whether such ...
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Inverse of cumulative density function for Multivariate Normal Distribution

How do I calculate the inverse of the cumulative distribution function (CDF) of a multivariate normal distribution? Does it even exist for the multivariate case? I know this is possible for a ...
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How to best name the interval between two adjacent quantiles? Explained with the example of quartiles

Officially, there are three quartiles: They are the boundaries that divide any distribution into four equally populated intervals. Confusingly, people also refer to these 4 intervals as quartiles! Now,...
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Distribution of percentile rank of largest value in sample

Let's imagine that I sample 100 values from some probability distribution $Distribution$ over the real numbers. Out of these samples, I pick the maximum value $m$. It seems intuitive (and apparently ...
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Quantile regression on a constant: is this different from unconditional quantile?

With a linear model, estimating an OLS regression of y on a constant only will give us the mean of y. I was wondering whether ...
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How to estimate with confidence the quantiles of an unknown random variable using sample mean and variance?

Let $X$ be a uniform distribution of inputs to be used for sampling. Let $f(x)$ be an expensive function. If we take samples from $X$ and give them as input to $f$ we get outputs $y_1, y_2, \ldots, ...
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What caused change in percentile?

We report 95th percentile and 50th percentile of the time series data for every week. The data is time-series data in the following format date. sensor_id. sensor_location. hardware_version. ...
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Best way to construct a QQ-plot

I want to assess the normality of a dataset (which is log-normally distributed data transformed back to normal) using a Q-Q plot. I stumbled on the fact that there are many ways to build such a plot, ...

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