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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6 views

How to robustly present a min and a max value?

I have a set of measurements from an air polution sensor. I want to determine the min and the max value in a period of time (let's say in a day). The min and the max don't have to be the true ...
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How does AWS Forecast make probabilistic forecasts at a given quantile?

I would like to know which method is used by AWS Forecast to generate lower bound and upper bound time series forecasts at a given quantile? More generally, what is the method employed to make ...
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Why does median() differ from quantile()[“50%”] in R and doesn't honor the type? Is this an estimator or sample quantile?

I just found, that when I want a specific type of quantile in R, say the number 3, it doesn't agree with median calculated in the "traditional way" in R. ...
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Descriptive measures

What is the percentage of people who earned between Rs 75 and Rs 125? If the given frequency table is below:
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Interpretation of a figure: mismatching confidence intervals and percentiles

I found a figure as follows, showing distributions of some scores at three time points: Considering the with of 25th-75th percentiles, how can 95% CIs be so narrow? Is this erroneous?
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Which of the 3 given exact methods of calculating the confidence interval for median is better (correct)?

I want to calculate CI for the median in R. I found a number of packages and functions doing that and noticed something interesting. I think the problem can be generalized to any statistical software. ...
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How is that possible, that in R, SAS or other packages there are so many ways to calculate quantiles? Isn't median just median?

As in the topic. I always thought, that we have a clear, well established definition of a quantile over a vector of numbers. For example - median is such observation, that splits the data set in so, ...
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25 views

Normalize skewed distribution

My data is right-skewed. Log-transform data only shifts it, not changing the distribution shape. Tried to use QuantileTransformer but output seems to be really messy. Any suggestions on how to ...
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Convert percentile change to Cohen's d

tl;dr: How do I convert from percentile change to Cohen's d for the whole distribution? A common measure of effect size is Cohen's d: the mean difference between an experiment and control group ...
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M estimator confidence intervals for quantiles

I try to understand the M estimator and make some quantiles estimation. I think I can see how we get the best theta (minimum point): I need to minimize the: $ \sum \rho_\tau(\epsilon_i) = \sum \tau \...
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1answer
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Nonparametric Confidence Intervals from Sample Quantiles - Sample Estimate Outside Upper and Lower Confidence Limits

The Approach Say I have a 95% confidence interval $(l, u)$ for some true parameter of interest $\theta$ computed from the 2.5th percent and 97.5th percent quantiles of a given set of continuously-...
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Estimating user percentile using mean, min, max and previous percentile for multiple tests

I have a set of tests that a group of people take. The same people take all tests. I am given one person's score, along with the highest score, lowest score, and mean score and must estimate the ...
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Computing percentile rank best way to compare?

The following is a sample dataset, I'm only providing a snippet but there is more data than this. I need to know how compare each company is doing in terms of the different measures ( measure_1 and ...
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Quantile regression categorical data

I am planning to do an analysis on socio economic determinants of women health status. For health status, being my dependent variables, I have taken anemia as one of the variable. I want to do see ...
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If I have interval (binned) data from a D.G.P. with a truncated Pareto distribution, can I estimate the truncation point?

Suppose I have high-income data that I believe to be reasonably approximated by a Pareto distribution above some income level. I have mean and total income for several income ranges, including the &...
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1answer
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Why is the Hyndman and Fan 1996 recommendation for sample quantile definition to standardize on not more accepted? [closed]

The 1996 paper Sample quantiles in statistical packages is often cited as the comprehensive source of sample quantile definitions and many a software package refers to the paper in the description of ...
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2answers
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Small sample size fails to approach inverse CDF

When sample size $n$ gets large, we know that a sorted set of the $n$ samples approaches the inverse cumulative distribution function (CDF) sampled at $\frac{1}{n}, \frac{2}{n}, \dots, \frac{n}{n}$. ...
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Is $z_{0.025}$ equal to -1.96, or 1.96?

I'm unsure about the interpretation of $z_{\alpha}$. I've seen some source claim that $z_{\alpha}$ is equal to the z value with $\alpha$ of the area to the right of it. Under this view, $z_{0.025}$ is ...
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Characteristic Function and Quantile Function?

Characteristic functions (cf) are closely related to cdfs and pdfs of random variables, for example cf is the Fourier transform of the pdf Inversion formulae from Lévy and Gil-Pelaez Question: Is ...
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Is it possible to interchange the quantile operator and a measurable monotone function? $Q_\theta(f(X)) = f(Q_\theta(X))$

Let $Q_\theta(X)$ is the $\theta^{th}$ quantile of a random variable $X$, and if $f$ is a measurable strictly increasing function. I want to know if $Q_\theta(f(X)) = f(Q_\theta(X))$. I know that for ...
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Can the sum of these two quantiles be negative?

We already know that in a two sample t test, given alpha and beta, we can compute sample size: $$ N=\frac{4 \sigma^{2}\left(z_{1-\frac{\alpha}{2}}+z_{1-\beta}\right)^{2}}{\Delta^{2}} $$ Now if we want ...
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Model that takes two percentiles as input - what is the percentile of the output value

For some analysis I have two input variables with some (unknown) probabilities distributions. Of both the input variables I know the (assumed) 10th, 50th and 90th percentile. I have some simple model ...
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Should You Take the Average of Two Test Score Percentiles?

I have two different tests that measure the skill of participants in two different fields, leading to two different test scores for each participant. I want to combine both test scores to get an ...
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1answer
11 views

finding median of multiple samples [duplicate]

I have the following problem: (1) I get a package with many samples with values (2) I have reasonable time to calculate whatever i want and keep in memory any info i want, but not all of the samples (...
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quantile regression parameter for desired confidence interval

I want to plot C% confidence intervals for a regressor (GradientBoosting in my case). I found this example on scikit-learn documentation https://scikit-learn.org/stable/auto_examples/ensemble/...
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39 views

Uncertainty and distribution of a percentile

In a Bayesian analysis (Normal case), it is possible to obtain a posterior distribution of the mean and variance. We can also obtain quantiles, median,... of these distributions. My question now is: ...
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Testing the statistical difference of two quantile parameters in a quantile regression

I have estimated a quantile regression at 15 different quantiles, I'd like to iterate a test to check that the most important quantiles are statistically different from each other. From "Roger ...
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1answer
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Can we sample from both pdf and cdf?

my question is quite generic. I am currently studying the algorithms calculating random numbers from distributions: In inverse transform method we get the cumulative distribution function in the end ...
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Median from two unmergable datasets

I am trying to calculate the "overall" median of a variable that is spread across two datasets. I have access to the raw data in each dataset but can't bring their raw data together. What ...
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1answer
42 views

The meaning of upper 100 alpha(th) percentile

Recently, I learned about the chi-square distribution. In my class, I was told about the upper $100\alpha^{th}$ percentile $\chi^{2}_{\alpha}(k)$ and given the following definition: $$P(X<\chi^{2}_{...
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Equality in distribution involving a uniform random variable and quantile function

I'm trying to show the following statement: "if $U$ is a random variable with uniform law over $[0,1]$, then $Q^2(U)$ has the same law as $X^2$". Here $Q(x)=\inf\{z\in\mathbb{R}:P(\lvert X\...
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Is minimizing Koenker-Bassett error the only optimization problem that gives sample quantile? [duplicate]

Sample quantile can be estimated by solving $\min_\theta \sum_{x \in X}f_\alpha(x-\theta)$ $f_\alpha = \alpha |x|$ when $x>0$, $f_\alpha = (1-\alpha) |x|$ when $x\leq0$. Sample expectile can be ...
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How to find the Percentile of this distribution?

Let say, we have 2 IIDs $X, Y \sim N \left( 0, 1 \right) + \eta $ Now $\eta$ has a discrete distribution with values 0(-10) with probabilities 0.991 & 0.009 respectively. Also assume that $Z = X+Y$...
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82 views

Max Likelihood Estimator of the quantile

Let $(X_1, \dots, X_n) \sim Exp(\theta)$ and so $$f(x; \theta) = \theta e^{-\theta x}$$ where $x>0$ and $\theta > 0$. I need to find the quantile $q_p$ as a function of $\theta$, the max-...
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1answer
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How does one test the difference between two uniform distributions with only a median and confidence intervals?

If I have two uniform distributions characterized by a median and two percentiles, how should I go about hypothesis testing if they are different? For example, let's say I have the following ...
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1answer
38 views

Confidence interval determination for skewed bootstrap parameter distribution

I have been reading around the literature and have been trying to work out the correct way (or most accurate way) to calculate a 68.3% confidence interval using bootstrapping for my particular data ...
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1answer
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Removing outliers renders a new distribution that has its own outliers

I'm trying to remove all the outliers from a data set. However, after removing them, data points that weren't outliers before are now outliers due to the new distribution. What is the correct ...
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Best method of quantifying probability of new datum belonging to either of two distanced normal distributions?

I have two samples A and B from two separate normally distributed populations. The population mean of B is higher than that of A, but both are unknown. My aim is to find a threshold value between the ...
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Creating a Probability Plot of a Custom Distribution

Let's say we have some icdf function, which I will paste below: ...
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1answer
56 views

Difference between quantiles

As far as I understood from its definition, quantile borders should divide a dataset into equal parts (or at least into almost equal parts, if the dataset doesn't have enough entries or has an odd ...
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What is the ppf of the truncated normal distribution?

What is the percent point function (ppf), or inverse cdf, of the truncated normal distribution? The distribution and cdf is defined here: https://en.wikipedia.org/wiki/Truncated_normal_distribution $$...
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Confidence Interval of p-Quantile from Empirical CDF

I am trying to provide an interval estimate for the 0.8-quantile of some numeric data, which is assumed to be an IID sample from some unknown, continuous distribution. I constructed an Empirical CDF ...
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Is “critical quantile” equivalent to “critical value”?

I'm reading an article about Ripley's K function and it mentions the concept "critical quantiles". Here's some context (emphasis added): Thus, the two major goals when building a ...
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1answer
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Inverse CDF (Quantile) of Piecewise Function [duplicate]

This question may be insanely simple, but I'm unsure. Let's say we have the following function: $$ f(x) = \begin{cases} x & 0 \leq x < 1 \\ x-1 & 1 \leq x < 2 \\ 0 & \text{otherwise} ...
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Constructing inversion method from a given pdf by finding inverse of cdf

The p.d.f. of the random variable $X$ is given by $f(x) = \begin{cases} e^{x-2} & \mbox{for $0 \leq x \leq 2$}, \\ e^{-x} & \mbox{for $x > 2$}, \\ 0 & \mbox{otherwise,} \end{cases}...
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Calculating the quantile of random forest test cases

I want to calculate the quantile of the observed value of a test case with respect to the prediction interval generated from a random forest, so for each test case I want the proportion of the ...
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1answer
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Quantiles applied to two separate evaluation components vs applying to sum

Our school has a mandate that in any evaluation component (say quiz1, quiz2, etc.), the grades to be given are A, B, C and D to students. There is a further mandate that in any evaluation component (...
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Formula of Expected Shortfall for Generalized extreme value distribution (GEV)

i found the formula ofthe ES for GEV here: https://en.wikipedia.org/wiki/Expected_shortfall#Generalized_extreme_value_distribution_(GEV) My problem is that there is no citation, but I need the formula ...
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1answer
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R function to give me $P(X<x)$

I have this empirical discrete distribution with the respective percentiles (picture below). I want to know a R function which gives me $P(X\lt0.58)$ instead of $P(X\le 0.58)$ (given by ECDF function)....
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Any known approximations of summing quantiles from joint (bernoulli / lognormal) distributions

This is my first post to this site! For an insurance-like scenario, I have several independent risks which I want to sum together and find a 95% percentile. Currently I do this by Monte Carlo but I ...

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