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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26 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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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
48 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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3answers
55 views

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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39 views

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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33 views

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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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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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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Estimating user percentile given avg, min, max, occasional true percentile for multiple tests

I have data that given me both a user's score for a test, along with the high, average, and low across the class for every test. Every so often (ex. every 3 tests), I am able to query the user's true ...
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Is a differentiable quantile function a sufficient condition for performing the reparametrization trick with respect to a distribution?

The goal with the "reparametrization trick" is to to sample a noise variable $\epsilon$ from a simple distribution of our choice (like a standard Gaussian). We want to apply a deterministic ...
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Is there an r function for generating the standard error of mean or percentiles for fitted values from 'nlme' based models?

I have created a model using 'nlme' from my dataset in r, and have added the '.fixed fitted values' to my dataset using 'broom.mixed': ...
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How to find out conditional probability distribution of dependent variable given the independent variable in quantile regression?

Suppose I'm given a problem of estimating future values of a particular entity, treating it as a linear regression problem, assumptions of linear regression model like heteroscedasticity are violated. ...
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1answer
166 views

Uncertainty propagation for the solution of an integral equation

I have a dataset and I use Maximum Likelihood Estimation to estimate the values of the parameters of a weibull distribution. The MLE theory provides with theoretical Confidence Intervals (asymptotical,...
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3answers
583 views

Inverse transform sampling - CDF is not invertible

Suppose the cumulative distribution function $F$ is given but not invertible to use the inverse transform sampling technique (to compute $X=F^{-1}(Y)$). Do we have other alternative methods? I would ...
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Should we use the absolute value of errors in quantile regression loss function?

I am trying to use quantile regression loss function. Most of the implementations I see here, here, and here are using the error directly: ...
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Is there one universally agreed-upon definition of a quantile? If not what definitions exist? [duplicate]

I just realized that in R, the quantile function offers different types of quantiles. In my first statistics class, I learned the definition of a quantile being that value below which a given ...
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Quantile Matching using the skewed t-distribution from Azzalini & Capitanio (2003)

I try to replicate some findings from a paper (page 11/12 of https://www.newyorkfed.org/medialibrary/media/research/staff_reports/sr914.pdf). In this paper they estimated some quantiles using quantile ...
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How to estimate cut off percentiles to classify cost per metric?

I work at an ad agency and one of our key performance metrics is what we call "cost per outcome". Right now I have advertisements grouped by type of advertisement, lets say type "A"...
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What graphs / plots are best suited to visualise percentiles?

I have Year 12 final exam rank of students which is a percentile and information on if they graduated or not. For these 2 classes I want to visualise Year 12 PERCENTILES. Is a histogram suited for ...
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How to represent dependencies between horizons and uncertainty when forecasting multiple horizons?

Suppose the following case of univariate time series forecasting. We forecast sales of a product 1 till 7 days ahead. The true distribution of the actual sales is the following: there is a 100% chance ...
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Defining quantiles for complex survey samples

I am looking to accumulate a comprehensive list of definitions for quantiles under complex sampling that have been published or implemented in software. I'm not worrying about the separate problem of ...
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20 views

quantile-quantile plots theoretical z-scores

I looked on stackexchange and didn't not find any answers, hopefully someone can explain this intuitively. In quantile-quantile plots to see if my data is normally distributed, I understand that we ...
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1answer
61 views

Summing Differently-Distributed, Correlated Random Variables

I have four mutually correlated time series. Each contains 40 observations but is fundamentally and decisively differently distributed from its peers. The first series follows a Laplace distribution, ...
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1answer
35 views

What percentile is the following mark?

$24$ students took a test and they each scored a mark from $0$ to $100$. Gillian scored $71$. $18$ students scored lower than her and $5$ students scored higher than her. Gillian is the $19$th mark. ...
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48 views

Sampling from a continuous 2 dimensional probability distribution function for importance sampling

I just want to clarify a few points with regarding to sampling from a continuous 2-dimensional probability density function. If I want to sample from this pdf, I could sample from a 1D pdf, $P(x)$, ...
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Deriving Inverse of Cumulative Distribution function [closed]

let $f(x)$ be a probability distribution, and $g(x)$ be the cumulative distribution of that probability distribution (CDF) By definition, CDF is: $ g(x)=\int_{-\infty}^{x} f(x) dx $ Given $g(x)$, I ...
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1answer
36 views

Understanding notation in proof of probability integral transform

I'm attempting to understand one line of the proof for the probability integral transform as found on wikipedia: Suppose that a random variable $X$ has a continuous distribution for which the cdf is $...
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R's survey package interpolation handling for median estimates

This is a question concerning Lumley's survey package for R. Specifically, its handling of interpolation for median estimation, after several hours of looking into ...
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1answer
48 views

Pinball loss as a synonym for quantile loss: misleading?

I have the impression that the term pinball loss refers to the same as quantile loss (a.k.a. tick function); e.g. see the thread "How to calculate pinball loss for quantiles and for point forecasts?". ...
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2answers
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Value-at-Risk formula with GARCH-model

I'm totally aware of that if we look at some loss process $L_t$, then $\text{VaR}(\alpha)$ is a quantile of the loss distribution. If we assume that $L_t=-X_t$ is the negative returns and they follow ...
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Estimating tail deviation from Q-Q plots

I am running experiments and for certain cases am able to find a suitable distribution for the data. However, in most cases, depending on a certain parameter, the observed vs fitted distributions have ...
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49 views

The quantile of prob=0.05 and mean

What is the meaning of the difference between the quantile of prob=0.05 and mean for a sample form a specific distribution? In other words, I would like to understand the relationship between ...
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Calculating probability with multiple conditions

I am trying to understand something. Let's say we have 2000 samples and two different conitions. If we use condition #1, we get a result but if we use condition #2, we get different result. Is there a ...
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1answer
106 views

representing quantile like quartile in form of normal distribution curve

I learned in statistics the first quartile, 2nd quartile, and 3rd quartile can be represented in the figure1 below I came across this part of the article Step 4 - Feature Engineering.In this portion ...
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1answer
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Can the t-test be used to test the difference between percentiles of 2 samples? [duplicate]

For example, instead of testing the difference in mean, I want to test the difference in the 75th percentile of the 2 groups. Does the central limit theorem hold? and what would be the equation for ...
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1answer
33 views

Percentiles boundaries [duplicate]

When a distribution is cut into percentiles, is there any rule whether it should be included the lower or the upper bound inside the percentile? Example: 1,2,3,4,5,6,7 The median is obviously 4. If ...
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1answer
76 views

How to find the upper outlier threshold in a right skewed distribution?

Say we have a right skewed distribution (tail on the right side) like income. Above what value can I consider data points to be outliers? One way could be Q3 (75th percentile) + 1.5 * Interquartile ...
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1answer
67 views

Rejection Sampling when the proposal is a mixture of two distributions

Given a density $f(x; \alpha, 1) = x^{\alpha-1}\exp(-x)/\Gamma(\alpha)$ and a proposal density $q(x) = \alpha_1.q_1(x) + \alpha_2.q_2(x)$ I want to generate random samples using Rejection Sampling ...
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5answers
102 views

Calculating the 50th percentile in a small data set

I'm trying to learn the concept of percentile. Question: Given these numbers: {1, 2, 3, 900}, I'm trying to calculate the 50th percentile. My answer: 3. But different websites are saying: 2.5 My ...
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1answer
61 views

XGBoost question on weighted quantile sketch described in paper

The right-hand-side of Equation (3) in the XGBoost paper is $$\sum_{i=1}^n [g_i f_t(\mathbf{x}_i)+\frac{1}{2}h_if_t^2(\mathbf{x}_i)]+\Omega(f_t) \tag{3}$$ In the Section 3.3 "Weighted Quantile ...
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1answer
111 views

Estimating user percentile given avg, min, max for multiple tests

I have data that given me both a user's score for a test, along with the high, average, and low across the class for every test. How would I estimate the user's percentile with this data? We know ...
0
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1answer
19 views

Optimizing PDF using CDF deltas

In the paper introducing PixelCNN++ they optimize the PDF of a logistic function by minimizing the difference between the CDF around the sample points (x ± epsilon). I am trying to understand when it ...
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1answer
75 views

Understanding of quantile plot versus remove outliers plot

I have sample height for some people sample with a quantile plot like this: I need to check that the sample belongs to normal distribution. I remove outliers <...

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