# 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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### Combining information from different quantiles

I have a number of "mostly" Gaussian distributions (in truth a Gauss core and longer tails). I am interested in the width of this distributions. Given that I do not know the amount of tails ...
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### Assessing whether a dataset follows a distribution using Q-Q Plot

I recently found myself answering a question on Stack Overflow about adjusting a dataset to a unknown distribution. Adding my two cents to the community, I have provided a script to draw a Q-Q Plot in ...
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### Calculating the mean and error for correlated measurements involving different estimators and quantiles

My goal is to find a way to report a mean $\pm$ error for different estimators and quantiles of the same distribution (same measurement). I am measuring the width of a distribution (Gaussian core and ...
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Suppose that I have two arbitrary random variables $Y,X$ with strictly increasing CDF. Let $\omega(X)$ be a known function of $X$ that is known in advance and $\mu$ be a scalar parameter. Assume that ...
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### Calculate mu and sigma of a log normal distribution from p50 and p99 in javascript

I'd like to generate realistic sample data in javascript for monetary donations. I've chosen to model them as following the log normal distribution. I think a fairly intuitive way for a lay person to ...
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### How can I reconstruct a normal distribution from a set of percentiles?

I have the 3rd, 10th, 50th, 90th, and 97th percentile values of a normally distributed variable, and I wish to generate a dataset that will allow me to query for other percentile values (say, the 67th....
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### What is the formula for the conditional inverse function for the Ali-Mikhail-Haq and the Farlie-Gumbel-Morgenstern Copulas?

I am trying to do a Monte Carlo simulation and want to define a function for the conditional inverse function for the the Ali-Mikhail-Haq and the Farlie-Gumbel-Morgenstern Copula. Here is an example ...
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### Numpy implementation of the Quantile function [duplicate]

I am trying to wrap my head around the implementation of the quantile function for finite samples and, specifically, in numpy (main reason to do this: I am working ...
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### Why divide data into 4 parts for IQR, and not into parts of 20 or 10 percentages each?

Why divide data into 4 parts for IQR, versus into more parts, such as 20 or 10 percent per part? I know that interquartile range by definition means 25%, but that is not my question. I think that ...
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### How to resolve the residual versus predicted quantile devation (Dharma plot)?

I have been trying to perform beta regression modeling with random effects. I have sex ratio (0.561, 0.765 etc) as the response variable, and climatic variables + years (1970-2021) as predictor ...
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### Percentiles of a distribution of weighted summary statistics

Suppose I have a collection of different independent probability distributions, $\{ P_i(X)\}_{i=1}^N$, each with their own support $I_i$. I know that the $10^{th}$ percentile of a given distribution ...
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### How can I calculate the standard deviation when knowing the P10, P25, P75, P90, mean and median? [duplicate]

I'm trying to find the standard deviation from some simulated task duration results. The results provided the following: Mean - 430 Median - 374 P10 - 371.8 P25 - 372.4 P75 - 440.5 P90 - 588.6 From my ...
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### Median of a set with even number of elements

Consider the following sample of numbers: 9,18,11,14,15,17,10,69,11,13 Since there are 10 elements, the median of the set would be (13+14)/2 = 13.5 However, is it wrong to say that median is one of 13 ...
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### Distribution of $F_n^{-1}(3/4)-F_n^{-1}(1/4)$ [closed]

Given $X_1,X_2,...X_n\overset{\text{iid}}{\sim}F$, find the distribution of the sample inter quartile range, $F_n^{-1}(3/4)-F_n^{-1}(1/4)$ in terms of $F$ where, $F_n$ is the emperical distribution ...
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### Bootstrapping moderately extreme quantile regression

Let $(Y_1, X_1), \dots, (Y_n, X_n)$ be iid sequence drawn from $F$. For a fixed $q\in (0,1)$, consider the linear q-quantile regression $Q_Y(q|x) = \beta_qx$, where $Q_Y(\cdot\mid x)$ is the ...
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### Calculating VaR from copula-GARCH using rmgarch

I'm new to both R and copula, nevertheless I want to compare VaR estimations for 25 days ahead using a GARCH and a copula-GARCH model in R. To calculate VaR for the GARCH model seems pretty straight ...
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### Why does creation of a Q–Q plot in Excel need an adjustment by 0.5?

I am aware that different statistical packages provide Q–Q plots using code or via a black box. For example, minitab with R integration for Q–Q plot from here. I am trying to do this manually via ...
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### Determining percentile of a salary within a survey of salaries

I am not a statistics expert, so forgive me if this question is too simplistic. I have the following salary survey for a position: Someone internally is making: What is the easiest way to calculate ...
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### What is the quantile function of a Skellam distribution?

Reading Is there a formula for the 95% confidence interval for the Skellam distribution or difference of two Poisson r.v.'s?, I realized that I would rather have the quantile function. Unfortunately ...
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### How to calculate quantiles for a gamma distribution?

I would like to compute quantiles for a gamma distribution. I found a purported example here given as $$\text{quantile}(a, b, p) = \frac{\gamma^{-1}(a, \Gamma(a) p )}{b}$$ where $\gamma^{-1}$ is the ...
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### Are sample quantiles consistent with population quantiles?

The Wikipedia page about quantiles describes two approaches to the definition of quantiles: population quantiles, and sample quantiles. The section on sample quantiles lists nine different flavors of ...
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### Seaborn Boxplot's quartiles

I'm trying to understand how to properly interpret seaborn-generated boxplots. Consider the following code: ...
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### Can the 90th percentiles of two sub populations both be lower than the overall?

Consider two populations, $A$ and $B$. $A + B = C$. Meaning $A$ and $B$ are mutually exclusive and collectively exhaustive of $C$. Given the above if I calculate the 90th percentile of some metric for ...
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### Real-world example of quantile loss used for evaluation

We can use quantile loss (a.ka. tick or pinball loss) for training a model or for evaluating predictions. (It is helpful to distinguish the two clearly, e.g. as done here.) I am interested in the ...
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### Statistical significance of percentile (quantile) difference

I want to test for statistical significance of the difference between two independent samples of normally distributed measurement. However instead of comparing means or overall distributions I want ...
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### How do quantile time series forecasts work?

My office leadership is interested adopting “quantile time series forecasting”, the idea is query the model to predict the 5th, 25th, 50th, 75th and 95th percentiles of an RV given features such as ...
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### Is there a way to estimate or calculate the expected P99 of a sum of distributions?

Suppose I have an event X whose latency I cannot measure directly, but X consists of a bunch of sub-events X_0, X_1, X_2, ..., X_n whose latency I can measure individually only in isolation. ...
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### Versatility and validity of aggregate algorithm for a multiple criteria decision problem (averaging)

I'm trying to aggregate different variables in multiple scales and distributions. The distributions are not known beforehand, but I want to generate a general statistical value that represents all the ...
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### Compare 90th percentiles of two samples (confidence interval, test)

I have a dataset of ambulance response times before and after a quality improvement change. I'm looking to see if there is a difference in response times before and after the change. Specifically, I'm ...
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### Formal testing for differences in kurtosis between two samples when bootstrapping suggests a difference

My question is similar to Testing difference in kurtosis between two samples where a comment suggested Unless you are looking for an enormous difference in kurtosis, it's unlikely any physically ...
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### Can I estimate the mean of a dataset if I have its standard deviation and a portion of the full data that is higher than some threshold?

I have a partial set of measurement data that is limited due to my tool's sensitivity. I know that the data is approximately normally distributed and I have a standard deviation from another data set ...
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### Z score comparison in longitudinal studies

I have a longitudinal study with two time points (before/after), whereas a particular score was standardized across all individuals and time points, and thus provided only in terms of z-scores. (Edit: ...
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### Is my intuition behind the weight matrix correct for quantile regression?

Motivating Question I was asked by a colleague today why one would run a quantile regression on quantiles that are "extreme" (such as $.10$, $.90$, etc.), if there are too few observations ...
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### Algorithm to determine sufficient range for numerical integration of PDF to get quantiles

Given a probability density function (PDF), we want to use numerical integration to find a quantile at $\alpha \in (0,1)$. Are there standard algorithms for determining a sufficient and optimal range ...
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### Quartiles as interaction term in regression analysis

Hello to everyone in this community. I am feeling like fish out of water writing in this community, but I know that I am at the right place. Currently, I am conducting a research to assess the impact ...
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### Percentile calculation for binary attributes

Assume I have the following dataset: ...
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### Bivariate normal covering circles and ellipses

I am looking at covering circles for cartesian coordinates given by independent bivariate random variables $X, Y \sim N(0, \sigma)$. The radius of a circle that will cover proportion p of these ...
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### Lower bound on distance between ordered statistic

I have found the following inequality in a manuscript: Let $S_{t}^{i}$ and $S_{t}^{i^{\prime }}$ denote the $i/N$-th and $i^{\prime }/N$-th cross sectional order statistics. We require: \begin{align} \...
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### Boostrapping from Exponential Sample to estimate the quantiles

I have the problem where I want to estimate the quantiles of a distribution by bootstrapping. Fortunately I do know the original DGP which I chose to be an Exp(1/4) distribution and so the theoretical ...
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### Credible interval for a quantile from log-normally distributed data

Both reviewers of my latest article suggested better to work with credible intervals instead confidence intervals. Unfortunately, I am not familiar with Bayesian statistics. Until today, I was (...
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### Calculating the mean and sd of a lognormal distribution from the log mean and log 5th percentile [duplicate]

I have a mean and 5th percentile value from river flow data that are assumed to follow a log-normal distribution. From these, I need to calculate the the mean and SD of the underlying normal ...
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### If I have the 1st to 99th percentile of height of men for example, can this information be used to get the probability of a certain height?

Let's just say we know 1st to 99th percentiles of the height of men in country X. Could I use this data to answer the question: What is the probability of a male in this country being greater than 6ft?...
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### Evaluate Value at Risk (VaR) models with different VaR backtesting approaches - averaging p-values?

I estimated the Value at Risk of a time series of log returns with different approaches and models. Now I want to compare the models and choose the model that most accurately estimated the Value at ...
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### Choosing one method for modeling Value at Risk (VaR) over another - determining the "best" model

I estimated the Value at Risk of a time series of log returns with different approaches and models. Now I want to compare the models and chose the model that most accurately estimated the Value at ...
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