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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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?
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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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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 ...
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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 ...
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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 ...
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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. ...
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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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Percentile of the arithmetic mean of a lognormal distribution

The arithmetic mean of a lognormal distribution is greater than the geometric mean (which equals the median). So its percentile is greater than 50%. But how much greater? It depends on the geometric ...
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What Does the Beta Means in Quantile Regression?

I am trying to work out this formula here. However I am unsure what does the Beta stands for. Hope I get some help here. Thank you. This is part of the IMF Global Financial Stability Report October ...
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Calculation of quantiles with fitted parameters in Python

I am trying to make two-sample Q-Q plots in Python. A Python function that is used for calculating quantiles has the option of fitting parameters for the calculation of quantiles. These parameters are ...
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How to use auxiliary factors as weights in a Portfolio

(1) I am looking to form a Market Neutral Portfolio based off possibly 2 factors. Factor1 is the Primary factor, I rank all the stocks (say 1000 stocks) based off the Factor1 value, and pick top 100 ...
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Bootstrapped p-value of percentile

I have a scenario where a person presents an item to a panel of 10 experts, who then value the item. If at least 6 out of 10 experts say the value of the item is greater than zero, then it's ...
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Sampling from bivariate conditional distribution

I would like to sample from a bivariate conditional distribution $F(y_1, y_2 |X_1 = x_1, ..., X_p=x_p)$, where the distribution is determined non-parametrically. How can I sample from such a ...
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What's the -2σ quantile?

I'm researching about direct detection of Dark Matter and came across the -2σ quantile in this paper: https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.121.111302. (Page three at the bottom.) ...
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model to predict value of an observation vs its quantile in a population

I have 1 million customers, and I'm interested in predicting the revenue generated by each of the them in the following month. Consider two models: Model A: predict the actual revenue (e.g. in ...
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How to analyse a continuous data which is non-linear, heteroskedastic and is spatially autocorrelated?

I have data which is non-linear, heteroscedastic and is spatially autocorrelated. The predictor and response are continuous variables. Quantile regression accounts for the heteroscedasticity but I am ...
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How do measurement errors propagate into Percentiles?

I have a measurement systems that outputs $X_i + dX_i$ measurements. I'm trying to figure out the most correct way of estimating quality of measured device. The relative error $dX_i/X_i$ is normally ...
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Ranking by specific percentile

Is there a name for ranking categories by their value in a specific percentile (e.g., 33th percentile)? A fictitious example: Goethe published 9 books, Schiller published 7, and Herder published 3. We ...
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Quantile-quantile plot from scratch and comparing to multiple standard distributions

I want to do a QQ plot, where I compare a sample to multiple standard distributions, scaled, so that the points represented by the correct distribution are on the black line. I expect to do basically ...
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Doubt regarding inverse CDF/quantile function or qpois in R

Let's say I have a poisson with mean 9.29 (lambda). The probability of random variable being less than equal to 1 and 2 are "0.0009502101" and "0.004935002" respectively (i.e. P[X&...
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qrule mathematic interpolation in quantile estimation in R survey package

I've been having difficulty understanding the code for qrule_math in the survey package. This document here says this about it: ...
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Does the expectation of a quantile equal to the quantile of expectations?

Let $X$ be a random variable with finite expectation $E(X)$, and let's denote $X_{90}$ the 90% quantile of its distribution, meaning: $$P(X<X_{90})=0.9$$ Now, let Y be another random variable and ...
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Simulating a joint distribution with the inverse method

I have the following joint distribution: $$f(x, y) = 3x^2y^xe^{-x^3}(1 + x),\quad x \gt 0,\ y \in (0,1).$$ I want to simulate a sample of this distribution through the inverse method but I don't know ...
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Generate given percentile (or data) from n, mean, median, standard deviation, p1, p25, p50, p75, p99?

I apologize if this should be asked elsewhere. I have the following information: Where N=1808 I am trying to calculate a given percentile (in this case p99.723), or ideally, if possible, generate ...
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How to interpret a point in the qq plot? [duplicate]

I am trying to understand the Q–Q plot. Suppose I create a sample according a exponential distribution ...
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Quantile Variance and Mean

As I read articles related to quantile measurements of moments, I only found quantile skewness and kurtosis definitions. However, I couldn't find any quantile estimation of variance or mean. Is it ...
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Lower confidence interval for quantile function [duplicate]

I have a real-valued, unknown distribution $\mu$ and would like to find the largest threshold $t \in \mathbb{R}$ such that $\Pr_{X \sim \mu}\left[X \leq t\right] \leq q$ with high probability $1-\...
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Which is the correct solution to the hypothesis testing: $H_0 : \lambda =65, H_1 : \lambda >65$ , $X$ is a Poisson ($\lambda$) ,$\alpha=0.05$

Given the following hypothesis test: $H_0 : \lambda =65, H_1 : \lambda >65$ , where $\lambda$ is the parameter of an $X$ distributed as a Poisson $\alpha=0.05$ . We have n=10 samples. Using as ...
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n-th quantile for bivariate variable

I generate a 2000 bivariate random samples which are negative correlated. I used np.quantile to generate 10 quantile from this random samples. The related point is marked in the following figure. I am ...
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Computing Gini coefficient for a 2 parameters density function

I have a random variable $X$ defined by the following the density function, \begin{equation} f_{\theta_1, \theta_2}(x) = \begin{cases} \frac{\theta_1 \theta_2^{\theta_1}}{x^{\theta_1 + 1}}, &...
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Which type of quantiles are safest to report in R?

With this topic in mind: If there is no censoring, can be the naive 3rd quantile different from the one calculated with from the Kaplan-Meier? I'm wondering which one is the safest option. Of course I ...
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Is it possible to find the 99th percentile using other percentiles?

I have the 10th, 20th, 25th, 30th, 40th, 50th (I assume this is the same as the mean), 60th, 70th, 75th, 80th and 90th percentile values of a data set. This is for the distribution of salaries in the ...
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Grouping using percentiles

I did visual binning process in spss and made three cutpoints like in this image: I did check off included I want to know the percentage range or value for each group. If I describe it in this way is ...
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Is percentile a good method?

Hello I'm an undergraduate student doing research about prevalence of carpal tunnel syndrome among college students I want to follow the method of this research (prevalence of carpal tunnel syndrome ...
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How to compare equality of the distribution at different quantiles

I have a dataset from which I am taking a set of descriptive statistics as follows: The value measured is productivity of a firm for each of the group at different quantile (I use Stata command: table ...
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Non parametric Monte Carlo estimation in R

Let's say that we have a dataset of a single vector : ...
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Bootstrap BCa Quantiles of the quantile function

Let's say I have a vector $x$ on $n=250,$ (in R) x = rnorm(250) The quantile of $\alpha=0.01$ is : ...
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conditional quantile and conditional expectation

I was reading some papers and I found some parts are tricky to understand. Assume I have price data , what does it mean to calculate the conditional mean of the price data given yesterday price ? ...
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Estimator for quantile of kernel of mixture distribution

I have a mixture distribution such as $$ X_t = \sum_{i} w^i_t X^i_t , \quad \text{with } w^i_t \in \{0, 1\}$$ and $\sum_{i} w^i_t = 1$. where $X^i_t$ are i.i.d , $\forall t$. I call the $X^i$ the ...
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Quantile of joint distribution

Give iid random vectors $(x_1,y_1),\dots, (x_n,y_n)$ from the two dimensional cumulative distribution function $J(x,y)$. The marginal CDF of $x$ (rep. $y$) is $F(x)$ (reps. same $F(y)$). They have ...
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Quantifying the bias of a quantile estimator based on order statistics, and its relation to asymptotic unbiasedness

From what I understand, the quantile estimator based on order statistics is asymptotically unbiased (and follows a Normal distribution). I have been looking for a quantification of the non-asymptotic ...
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Identifying the appropriate model for determining the dimension with the most impact on poverty

I am working on a research to determine the dimension (health, unemployment, education and standard of living) with the most impact on poverty. The response variable is the decile score obtained for ...
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Convergence of Percentile in Power Law

I have a probability distribution, that in its tail follows a power law. I've noticed, while I was simulating samples, and determining parameters experimentally, that as I increase the value of a ...
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Weighting the calculation of sample quantiles

Is there a general method for determining what the weights are when calculating sample quantiles? Specifically, how do you do this in the case of repeat measurements -- can (should) you take the ...
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Quantile estimation for discrete data

For quantile estimation for data coming from a discrete distribution, do you have to use one of the quantile estimators R-1, R-2, or R-3? For example, R-3 uses the nearest even order statistic after ...
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How do you do a qq plot in R for a discrete Weibull distribution?

To do this, I think I need to calculate the inverse CDF, but I have learned here that the discrete Weibull (type I) as given by: $$F_{I}(x)=1-\exp\left[-\left(\frac{x+1}{\alpha}\right)^\beta \right]$$ ...
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What is $\mathbb{E}\left( \Phi^{-1}(U)\right)$, $U \sim \mathcal{U}(0,1)$?

Let $\Phi(\cdot)$ denote the CDF of a standard normal random variable and let $U \sim \mathcal{U}(0,1)$. What can we say about $$\mathbb{E}\left( \Phi^{-1}(U)\right)?$$
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