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 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 ...
Albert Paradek's user avatar
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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 ...
hehan123's user avatar
10 votes
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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 ...
Tryer's user avatar
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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 ...
stryped's user avatar
7 votes
1 answer
259 views

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 ...
Galen's user avatar
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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 ...
Evan Aad's user avatar
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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 ...
Richard Hardy's user avatar
1 vote
0 answers
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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 ...
considerate_shrimp's user avatar
3 votes
1 answer
439 views

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. ...
merlin2011's user avatar
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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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5 answers
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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 ...
Jeff Jarvis's user avatar
3 votes
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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 ...
StrongBad's user avatar
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2 answers
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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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1 answer
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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: ...
Jonathan Bar's user avatar
7 votes
1 answer
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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 ...
Shawn Hemelstrand's user avatar
1 vote
1 answer
15 views

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 ...
Sblaie's user avatar
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1 answer
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Percentile calculation for binary attributes

Assume I have the following dataset: ...
Adham Enaya's user avatar
4 votes
1 answer
188 views

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 ...
feetwet's user avatar
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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} \...
NC520's user avatar
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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 ...
jjjcjjj893's user avatar
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53 views

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 (...
chenge's user avatar
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1 answer
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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 ...
Pau's user avatar
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2 votes
1 answer
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Quantile function of multivariate distributions from empirical samples

Let's say I have a k-dimensional multivariate normal distribution $MVN(0,\Sigma)$. Denote random vector $X \sim MVN(0,\Sigma)$ as $X = (x_1, x_2, \dots, x_k)$. It is trivial to find $P(x_1 \leq c_1, ...
David Wang's user avatar
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0 answers
66 views

What does it mean to have symmetric quantiles?

I'm using quantile regression for my paper, and my results are symmetric i don't understand what that means. Please explain the symmetry of quantiles and how does this effect the results and how to ...
Helpplease's user avatar
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0 answers
195 views

Understanding usage of quantile function (norm.ppf), passing p vs 1-p

I was given a question related to the quantile function using scipy.stats.norm.ppf, along with its solution - which I don't understand. I'm changing the question ...
HeyJude's user avatar
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0 answers
220 views

Deriving 99th percentile in log-normal data using transformed normal distribution?

My aim is to calculate the 99th percentile of the log-normally distributed data on the left-hand side. There are various approaches described to do this, e.g. ranking data and then selecting the value ...
wptmdoorn's user avatar
4 votes
2 answers
370 views

Estimating quantiles using quantile regression

I understand that quantile regression estimates the conditional quantile of some measured variable (call the variable $y$), but can you use quantile regression to estimate an unconditional quantile of ...
John Smith's user avatar
9 votes
1 answer
3k views

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?...
SCool's user avatar
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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 ...
Isabel's user avatar
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0 votes
0 answers
16 views

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 ...
Isabel's user avatar
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0 votes
1 answer
49 views

How do you determine the 1st quartile? Answer differing from what R outputs [duplicate]

I get that the definition of the first quartile is the value of the data set in which it is greater than 25% of the data set; below I have defined a vector in R (which is already ordered) ...
Wallace's user avatar
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2 votes
1 answer
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Definition of quantiles (e.g., decile, quintile) [duplicate]

The field of research I'm in uses ranked data a lot. We often refer to deciles to mean the group of units that make up one-tenth of a population or sample. Recently I saw a paper which made the point ...
Bradford's user avatar
1 vote
1 answer
34 views

Comparing different methods for modeling Value at Risk (VaR) - understanding VaR backtesting results

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 find the model that most accurately estimated the Value at Risk....
Isabel's user avatar
  • 31
0 votes
0 answers
46 views

Is there a connection between sample quantile distribution and Gaussian processes?

It is known that sample quantiles from any distribution are Gaussian-distributed: $\sqrt{n} (X_{[np]} - q_p) \sim \mathcal{N}(0, \frac{p(1-p)}{(F'(q_p))^2 })$ Here sample size is $n$, $X_{(np)}$ is ...
Boris Burkov's user avatar
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0 answers
31 views

I have weekly averages, and weekly 2-minute peaks, can I estimate 30-second peaks?

I have been given weekly averages and weekly 2-minute peaks of flow to a process. I'd like to predict the 30-second peak. To clarify: By “weekly averages”, I mean that once a week, I get the average ...
Nathan Bevan's user avatar
0 votes
1 answer
111 views

Question about the inversion method for simulation of random variables [closed]

In the method called inversion we have : Let $U$ ~ unif(0,1) denote a uniform random variable on $(0,1)$. Then : $\mathbb{P}(F^{-1}(U))$ = $\mathbb{P}(U \leq F(x))=F(x)$ so $F^{-1}(U)$ has ...
John john's user avatar
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0 answers
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Is this proof correct that the following quantiles are equal?

Let me take $Z\sim \mathcal{N}(0,1)$. Then I know that $Z^2\sim \chi^2_1$. Now I want to show that the quantiles $\left(z_{1-\frac{\alpha}{2}}\right)^2=\chi_{1,1-\alpha}^2$ are equal. We know by ...
user1294729's user avatar
1 vote
1 answer
39 views

How can I find the value $Q$ for which the given region is a confidence region for $\mu$ with confidence level $1-\alpha$?

Let $X_{11},...,X_{1n}\sim \mathcal{N}(\mu_1,\sigma^2)$ and $X_{21},...,X_{2n}\sim \mathcal{n}(\mu_2,\sigma^2)$ be iid distributed and such that $\{X_{i1}\}$ are independent from $\{X_{i2}\}$ and $\...
user1294729's user avatar
0 votes
1 answer
66 views

How can I find a confidence intervall for $\theta$?

We have given a sample $X_1,...,X_n$ which is distributed with respect to $f(x;\theta)=e^{\theta-x} \Bbb{1}_{\theta\leq x<\infty}$. We want to use the statistic $T:=\min\{X_1,...,X_n\}$ to find a ...
user1294729's user avatar
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0 answers
115 views

Why Quantile Regression Forest grows trees in standard way (i.e. using MSE to decide splits)?

I'm interested in training a Random Forrest model to predict conditional quantiles (e.g., P75, P90) given the features instead of the conditional mean. Sklearn's RandomForestRegression has a mean ...
Samir Char's user avatar
1 vote
0 answers
51 views

Is there a package/function in R, Matlab or Python to perform smooth non-parametric fitting of empirical CDF data? [closed]

I have numerical process that generates percentiles values of a certain random variable $X$, meaning that I have $x_i$ values and their corresponding probability values $\hat{F}(x_i)$. I want to fit a ...
Xavier Romão's user avatar
1 vote
1 answer
47 views

How to calculate the width of violin at given value

I have been searching for this, but I couldn't find a salutation. I know we could calculate at what values the quantiles are of a violin plot. But I was wondering how we could calculate the width of a ...
Quinten's user avatar
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0 answers
23 views

Subadditivity of quantile function of Irwin-Hall distribution over n

I am struggling to prove that the quantile function of Irwin-Hall distribution is subadditve over n (the number of uniform distributed random variables that the Irwin-Hall distribution is created of). ...
user387130's user avatar

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