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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Can we write $P(A > B)$ in terms of their quantile functions?

Suppose $A$ and $B$ are two independent, continuous random variables with bounded supports $[min, max]$ and densities $f_A(a), f_B(b)$ and CDFs $F_A(a), F_B(b)$. Can we write $P(A > B)$ in terms of ...
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Prediction interval for continuous positive data including zeros

I am trying to figure out given a set of positive continuous numbers (including zeros) what would be the most appropriate way to calculate a prediction interval, or a normal range, i.e. a range in ...
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2 votes
2 answers
855 views

Should I treat these data points as outliers?

Currently, I am building my analytics portfolio as part of the Google Data Analytics course. I chose the option to analyze Divvy Bike Sharing data for the year 2021. But now I'm currently stuck in the ...
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Combining distribution stats of multiple populations

I have the following statistics of two independent populations: First population: ...
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Will taking mean of sample quantiles be an unbiased estimate the population quantile?

Say I have $N$ samples of 100 numbers all drawn IID from the same distribution $\mathcal{D}$. For each sample, I take the 95th quantile to get $N$ sample quantiles $\hat{q}_n$. Will taking the average ...
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qBCCGo function in GAMLSS package (quantile function)

I am working with GAMLSS technique and I use LMS (with three parameters of mean,variation and skewness) method. I found the follwoing formula to calculate the lower limit of normal as the link ...
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1 vote
2 answers
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Correcting for sample size in skewed data

Empirically I have noticed that when data is skewed, and when for example interested in the 99th percentile of latencies, that it is difficult to compare experiments with different sample sizes ...
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Estimates of the Quantile Regression

In the Quantile regresion model we assume that$$y_i=x_i^T\beta +\epsilon_i,\ i=1, 2, 3, ....,n$$ such that the conditional quantiles of the error terms are zero and for the OLS model we assume that ...
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Does the zeroth and 100-percentile exist and do the minimum and maximum of the data belong in those respective sets?

Does the zeroth and 100-percentile exist and do the minimum and maximum of a set of data belong in those respective sets?
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Understanding odds ratio in logistic regression for target variable

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Observation in Quantile Regression

i have 30 observations of yearly data and i try to do quantile but results is all of my variables is not significant. im wondering if we can use quantile regression on yearly data? or is there any ...
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27 views

Best practice for estimating values between 5% and 95% CIs for multimodal distribution

How can I improve my quantile estimation method for estimating values between the 5% and 95% confidence intervals for a multimodal distribution (as a mixture of gaussians) ? Where the CI are only for ...
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1 answer
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How to average multiple non-normal distributions?

I have the following statistics of two independent random variables: First random variable: ...
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The best way to determine what percentile a range of numbers closely aligns with?

I have a table of ~600 numbers and percentiles like below: Data 40th 50th 60th 70th 80th 90th 71 53 55 57 60 63 68 101 78 81 83 88 92 102 121 89 94 98 105 110 123 209 146 153 163 171 176 189 68 ...
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Asymmetries in the DKW bound

Suppose I have $n$ i.i.d. samples $X_1,...,X_n$ drawn from a distribution with CDF $F$. We use the samples to form the empirical CDF: $$F_n(x)=\frac{1}{n}\sum_{i=1}^{n} \mathbb{1}_{X_i\leq x}$$ The ...
2 votes
2 answers
50 views

Finding random number based on a specific discrete distribution using R

I have a discrete distribution with cumulative function: $$ F(x)=Pr(X \leq x) = \frac{1}{(x-1)!} \left( \Gamma(x,\lambda)-\frac{\lambda^{x-1} \exp(-\lambda)}{\lambda+1} \right) $$ for $x=1,2,3,\ldots ....
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1 vote
1 answer
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Quantile(X * k) = Quantile(X) * k?

I just wanted to verify that this is true. Say the .95th quantile of a random variable, $X$, is $q$. Then the .95th quantile of $\frac{X}{k}$ is $\frac{q}{k}$ where $k$ is a constant. I am assuming ...
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Robustness of Quantile Regression

Is the 99th Quantile Regression model a robust model? From my understanding, Quantile Regression is supposed to be robust in nature, but removing some outliers using IQR, the results obtained by 99th ...
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Estimate Conditonal Moments from Conditonal Quantiles

In Chang et al. "The Higher Moments of Future Earnings" (2014), the authors say say that based on (predicted) conditonal quantiles of a variable $y$, one can derive the (predicted) ...
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3 votes
1 answer
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Calculating expected value from quantiles

For probabilities $p_i=\frac{i}{10}$ where $i=1, \dots, 10$, the respective quantiles are $\tau_i$. How can I calculate an approximate expected value?
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2 answers
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Expected Shortfall vs VaR

I have a question about how to compute the Expected Shortfall practically. I know from the theory that the ES is the conditional Expectation of the Loss distribution (conditional on the VaR) and that ...
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1 vote
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Quantitatively determining a "baseline" value for a dataset

I'm wondering if there's a clean way to quantitatively find the "baseline" of a data set, or more specifically, a threshold below which the majority of samples are clustered. For the example ...
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1 answer
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Calculate value at risk from a given discrete distribution

How do I find the value at risk at 90% confidence interval i.e., VaR(10%) for a portfolio with the following profit/loss distribution? [-120 with prob = 0.0036, -55 with prob = 0.1128, and 10 with ...
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Understanding the computation of p-value and its v-test by catdes() of FactoMineR

One of the functions that helps to characterize clusters is the catdesc() function. The output of this function is very informative giving the following bits of information: ...
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Different Calculation Methods for Theoretical Quantiles of Q-Q Plot

There seem to be at least two different methods to calculate the theoretical quantiles in a Q-Q plot. In the following, the normal distribution is assumed to be the theoretical distribution. Split ...
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2 votes
1 answer
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Almost sure convergence of the difference of two quantiles

Let $X_1, ..., X_n$ be i.i.d. random variables with the same distribution as the random variable $X$. Let $F$ be the distribution function of $X$. We assume that $F$ and its quantile function $F^{-1}$ ...
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How to calculate VaR on DCC GARCH?

I am using a DCC (and CCC) GARCH model to model volatility of electricity price returns (using spot and futures) i.e. I have more variables in my model. I need to calculate VaR using these models but ...
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1 answer
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Compute value at risk from DCC GARCH (in R)

I am struggling to obtain the Value at Risk from my DCC GARCH analysis. I have done the following code: ...
3 votes
1 answer
177 views

Estimating a quantile from an unknown distribution

I have a variable $x \sim N(0,1)$, of dimension $p$, with each $x_i$ independent. I want to find the quantile, $q$, such that $$\mathbb{P}\left(\frac{\sum_{i=1}^p (|x_i| - b_i) }{c} \geq q \right) = a,...
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Quantile Regression Pseudo R-Squared

When computing the Pseudo R-squared value in quantreg in R or statsmodel in Python, what is an acceptable range to justify goodness of fit? Also, what is the functional form of Pseudo R-Squared ...
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1 answer
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90th percentile growth rate distribution

It's been a while since I dealt with statistics, I guess I need to brush upon my knowledge about it but as I was reading an article for my class I had a hard time understanding the author's main point ...
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35 views

How do I measure goodness of fit of data transformations that standardize for variables?

I am modeling a dependent variable which has significantly different distributions when grouped by various independent variables. Consequently, it is difficult to compare previous values of the ...
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Should I remove/cap "Extreme Values" from Variables and at which percentile should capping be done?

In my dataset, I have a variable corresponding to the monthly average playtime hours of the players. The dataset has 200K records. I estimated various percentiles of the variable - from 0 to 1 for ...
3 votes
1 answer
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Compute the quantile function of this distribution

I want to compute the quantile function of a Bin(4, 1/3) random variable and plot it with R, but I don't know where to start from. Any help or hint is highly ...
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Issues with transforming the response using quantile mapping?

I am in a modeling setup where having a normal (or T; unskewed) response distribution is important. I have chosen to use quantile mapping to transform my response. My process is to use GAMLSS in R to ...
1 vote
1 answer
100 views

Quantile Regression proof

I'm interested in understanding the formal proof of why Quantile Regression works. That is, show me in which conditions the pinball/quantile loss provides asymptotic consistent estimations of the ...
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25 views

How to best categorize a continuous variable that has many observations with the same value?

I have an air pollution variable (PM2.5 measurements) for a dataset of 9,506 participants based on geographical location. Because many of the participants live in the same general area, there is a ...
1 vote
1 answer
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How to compute 90-th percentile of data with Inf values? [closed]

I need to compute an effective diameter is 90-th percentile of the distribution of shortest path lengths of a graph. My attempt is: ...
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1 answer
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Percentile(s) - logical explanation

What EXACTLY do percentiles (/does which) mean, how are they distributed exactly (equally/weighed)?
1 vote
2 answers
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How to estimate correlations between the standard errors on empirical quantile estimates from two correlated series?

I have two very long series of samples from a pair of correlated random variables, $x$ and $y$. (they are fat tailed distributions, roughly Pareto, if that helps). (if you're curious...$x$ and $y$ are ...
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1 answer
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Does this plot indicate the data is normal distributed?

I use qqnorm to plot my data as the photo attached. Does this plot indicate the data is normal distributed?
3 votes
1 answer
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Jacobian of function returning $m$ evenly-spaced order statistics of an $n$-dimensional vector

Let $y\in\mathbb{R}^n$, and let $f:\mathbb{R}^n\to\mathbb{R}^m$ be the transformation that outputs $m$ evenly-spaced order statistics (including the extremes) of $y$. What is the Jacobian of this ...
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2 votes
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Predicting percentiles with percentile data [closed]

I have a few independent variables and 5 dependent(target) variables. The target variables are percentiles (10th, 25th, 50th, 75th, 90th) and I want to predict the same in that order. What approach ...
0 votes
2 answers
249 views

How to correctly bucket data into quantiles: by index or by value?

I've been recently involved in a discussion surrounding the assignment of individual values to n-tiles. One way of doing it would be to rank all of the data in ascending order, dividing it into $n$ ...
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Is there any way to adjust a percentile for number of observations per person?

I've got a program that I'm trying to measure the latency of at the 95th percentile. The data has a long tail, so I'd expect the 95th percentile to be relatively high. To give a contrived example, let'...
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What's a good rule of thumb for choosing a sufficient number of quantiles in quantile transformation?

I'm a currently developing a regression model based on the Choquet Integral. To tackle outliers I am using the Quantile Transformer, provided by scikit-learn. I was wondering how the quantile number ...
1 vote
1 answer
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Quantiles of the response variable in generalised linear model with binary outcome (survival analysis)

I have a dataset that looks more or less like this (interval-censored outcome, multiple screening events per patient, not synchronised): ...
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Getting normal distribution from spike distribution through data transformation

I'm trying to preprocess my data before feeding it to neural network. The goal is to get a normal distribution. I have 3 different features distributed as follows: One can see bimodal, skewed and ...
1 vote
0 answers
25 views

Bounds on percentile given z-score

Suppose we have a random variable $X$ that can take real values from 0 to 100, according to a distribution $f$, for which the expectation $E(X)$ and the variance $SD(X)^2$ are well defined and finite. ...
1 vote
1 answer
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How to decide cut off?

I will try my best to explain this simple doubt that I have. I have three responses (Increased, decreased and no change) and I have calculated the percentage for each. For instance, for X case- 46% ...

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