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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1answer
43 views

Test whether or not quantile values belong to a distribution

I have a list of 23 values for the following quantiles: ...
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What does 0.5sigma mean?

I want to ask about a term about "this data is within 0.5 sigma". If I understand correctly the person first calculates standart deviation(sigma) of his data and multiples his/her std ...
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The inverse cumulative distribution function evaluated at Halton draws [duplicate]

Sandor and Train (2004, Quasi-random simulation of discrete choice models) mention that "A randomized Halton sequence is a set of draws from the uniform distribution. To obtain draws from density ...
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54 views

Estimating quantiles for posterior predictive distribution

Let's say I have a parametrised distribution $X|\theta$ and a sample from the posterior distribution of $\theta$, $\hat{\theta}_1,...,\hat{\theta}_k$. If I was interested in the CDF of the predictive ...
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If I know all the parameters of a distribution (mean, deviation, skewness, kurtosis,...) how do I calculate what quantile a certain data is at?

I have a game with levels. I am tracking the time (in seconds) each of my users took to complete a certain level. What I want to accomplish is to show the user how their time compares to others (i.e. &...
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Creating an Index by summing percentiles

This is probably a basic concept but i want to understand if it makes sense mathematically. I want to create an index on how much somebody spends at grocery stores. So for each person I calculate the ...
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31 views

measuring distance between distributions by using distance between CDF estimate with CIs?

I'm working on an machine learning-related project that compares distributions of features and alerts user when a feature's distribution changed over time. I have been thinking about the best way to ...
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Confused about inverse function (quantile function)

I read a post that says: "Math definition is that the quantile function is the inverse of the distribution function at α. It specifies the value of the random variable such that the probability ...
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1answer
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Why type 8 quantile function is the best?

https://www.researchgate.net/publication/222105754_Sample_Quantiles_in_Statistical_Packages ...
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About the definition of quantile from empirical data? [duplicate]

R> quantile(c(1,2,3), 0.01) 1% 1.02 The above is an example output from the quantile() function in R. The problem with it ...
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How many points fall below quantile regression-line?

I am sorry for the relatively easy question regarding quantile regression. I am a little stuck, and reading these resources I can't resolve this problem right now: (1) http://www.econ.uiuc.edu/~roger/...
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Extract slopes for all fitted quantile regression models with different tau-values, R

I wonder how I can get the slopes of all the models that were fitted when I do the following: library(quantreq) z =rq(mpg ~ wt, data=mtcars, tau=-1) Putting the <...
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How to make conditional quantiles?

I have a dataset consisting two variables X and Y. Both of them are of length 250. Now, I want to make conditional quantiles of X and Y. I have been reading the papers of Koenker and Basset (1978) and ...
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Self-study: Comparing Uniform and Normal CDF/quantiles for a given range

Not sure if the title is perfect. Nevertheless, there are two persons drawing $\alpha$. ‘A’ draws from $N(0,1)$ and ‘B’ from $U(-2\sqrt{2\pi}, 2\sqrt{2\pi})$. For which person is it more likely that ...
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Proving convergence in distribution between order statistics and quantiles

The random variable of continuous type $X$ has CDF $F(x)$ $X_1, X_2, \cdots, X_n$ is a random sample of size $n$ from the distribution of $X$ Function $h(y)$ is defined as $h(y) = F^{-1}{(1-e^{-y})}I_{...
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Converting 2-D Quantiles to 2-D CDF

I've been given some data in a format I've not encountered before - quantiles and associated values in 2-D, e.g. height and weight as: For the 10th quantile in the height range, the 50th quantile in ...
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1answer
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Can you find a confidence interval from a set of percentile samples?

Let's say we run a simulation where thousands of measurements happen, each measurement has a numeric value. For each simulation we output a single aggregate value of all the measurements in the form ...
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Estimate population mean from "best of N" samples

If I have a data set for which I know all measurements represent the largest of N observations, is there a good method for estimating the mean of all observations? So for example if N=10 and I have 3 ...
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About the Normal distribution

I'm having troubles understanding the following problem Problem The volume of daily transactions (in millions of shares) in the New York Stock Exchange is a random variable that is distributed ...
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1answer
29 views

Regression with percentile independent variable

I am running a simple regression with average standardized exam scores at the school-level, and weekly household income at the neighborhood-level where the school is located. The two variables look as ...
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How does ordinal regression compare to quantile regression?

I am familiar with ordinal regression and quantile regression at a high level, but would like a deeper understanding of the two beginning on how they differ. Can someone compare and contrast the two, ...
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22 views

Understanding relationship between T-Score and percentile

Suppose I am told that a person's raw score on a certain test was 26, the T-Score is 45, and the percentile is 31. From what I know about T-Scores, I'm having trouble understanding whether such ...
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1answer
200 views

Inverse of cumulative density function for Multivariate Normal Distribution

How do I calculate the inverse of the cumulative distribution function (CDF) of a multivariate normal distribution? Does it even exist for the multivariate case? I know this is possible for a ...
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1answer
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How to best name the interval between two adjacent quantiles? Explained with the example of quartiles

Officially, there are three quartiles: They are the boundaries that divide any distribution into four equally populated intervals. Confusingly, people also refer to these 4 intervals as quartiles! Now,...
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1answer
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Distribution of percentile rank of largest value in sample

Let's imagine that I sample 100 values from some probability distribution $Distribution$ over the real numbers. Out of these samples, I pick the maximum value $m$. It seems intuitive (and apparently ...
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1answer
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Quantile regression on a constant: is this different from unconditional quantile?

With a linear model, estimating an OLS regression of y on a constant only will give us the mean of y. I was wondering whether ...
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How to estimate with confidence the quantiles of an unknown random variable using sample mean and variance?

Let $X$ be a uniform distribution of inputs to be used for sampling. Let $f(x)$ be an expensive function. If we take samples from $X$ and give them as input to $f$ we get outputs $y_1, y_2, \ldots, ...
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What caused change in percentile?

We report 95th percentile and 50th percentile of the time series data for every week. The data is time-series data in the following format date. sensor_id. sensor_location. hardware_version. ...
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1answer
183 views

Best way to construct a QQ-plot

I want to assess the normality of a dataset (which is log-normally distributed data transformed back to normal) using a Q-Q plot. I stumbled on the fact that there are many ways to build such a plot, ...
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Inverse 4-parameters Cumulative Weibull Distribution

May someone write the inverse of the FOUR-parameters Weibull cumulative distribution (percent point function), please? I am referring to the 4-parameters formula appearing in Sigmaplot.
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Generating random variables from a given distribution function using inversion sampling

Given this distribution function $f(x)$ : $$ f\left(x\right)=\left\{\begin{matrix}x+1,-1\le x\le0\\1-x,0<x\le1\\\end{matrix}\right. $$ Generate random variables using Inverse sampling method in R: ...
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Is this statement about the sum of quantiles correct?

Let $X$ and $Y$ be continuous random variables both having some density, not identically distributed but independent. Imagine I'm interested in the quantile $q_{X+Y}(\alpha)$ for some $\alpha \in (0,1)...
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What is an intuitive explanation for Q90 (X+Y) > Q90(X) + Q90(Y) in fat-tailed variables. Non Subadditivity

In a business situation, management keeps a reserve of money for a 'rainy day' just in case costs are more than expected. The 90th percentile ($Q_{90}$ in the following) might be an indicator of how ...
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1answer
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quantiles and cut by value range differences

Let's assume we have 6 companies with these returns: 10%, 8%, 7%, 7%, 1%, -5% If I want to cut them by terciles, the grouping will be: ...
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Median ranks and percentile ranks

In Statistics by Freedman et al. there's this example Suppose the percentile rank of one student on the SAT is $90\%$, among the first-year students. Predict his percentile rank on first-year GPA. ...
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1answer
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How to compute quantile of a mixed distribution? [duplicate]

A mixed distribution where cumulative probability distribution function (CDF) is given by G(x)= (1-p)H(x)+pF(x) where, p=0.2 (assumed in this case as it ranges ...
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Why don't Beta-Binomial Confidence Intervals Asymptotically Converge?

I've been using the beta-binomial for modelling overdispersed proportions, and I've become a bit confused by the behaviour of the quantiles. I would expect that as $N$ increases, the result of $\text{...
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1answer
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Can Value at Risk and Expected Shortfall be equal?

I am struggling with the study of value at risk (VaR) and expected shortfall (ES). In particular, I am looking for some cases in which these two measures can be equal. I know that, given a loss cdf $...
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If I have 25th, 50th and 75th percentile, can I estimate 99th percentile?

Supposing I have only: 25th percentile: 0.56 50th percentile: 0.70 75th percentile: 1.10 I don’t know other data (sample size, mean etc. ). Only those three value. And assuming data is normal ...
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How to detect endogeinity, in a quantile regression?

I ran a quantile regression on Stata. I strongly suspect that endogeneity is present. As one of my variables signs is inverted, in a result that makes absolutely no sense. But how do I move from ...
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What does it mean if VaR is equal to CVaR (Expected Shortfall)?

I've been running some VaR and CVaR tests for some stocks at 95% and 99% confidence limits. for some reason, when applying a 99% limit I seem to receive the exact same values for CVaR and VaR when ...
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What learnings can I take from my regression plots to improve model performance?

I am trying to predict ecommerce conversion utilizing a simple multivariate regression. In the process I am using a log transformation of conversion as my dependent variable and log transformed ...
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Correlated coefficients in quantile regression model

I have a question in understanding the quantile regression model. Because the regression at different quantiles always uses all the samples. Would this lead to the correlation in different quantiles ...
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Quantile interpretation

If I have have the score for $q=0.9$, say $Y=y_{0.9}$. Does this mean that the probability of measuring a score $<y_{0.9}$ is 0.9? Edit: Basically I have one dependent variable, $y$ (a type of ...
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Possibilities for rolling two dice: one is six-sided and the other one is four-sided

I have seen a question from someone's old exam. Two dice, one has 6 sides and the other 4 sides. Question: a) What is the probability that the possible outcome(sum of two dice) would be at least 9? ...
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1answer
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Bootstrap for probability of observing certain data

I am working with years data and I want to see how likely it is for something to have happened for the first time in, say, 1997 given other dates as well. Let me explain. I have something (a lab ...
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good quotation on the control part of statistical quality control?

I'm writing a paper making use of techniques from statistical quality control, and would like to include a quotation that expresses a sentiment something like this: Statistical quality control is not ...
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3answers
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What information is required to aggregate percentiles

I have several thousand large datasets that are too big to fit into memory at once, so I need to keep them separate. It is easy enough to get the count, mean, std dev, min and max for the whole ...
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how to generate data from a distribution whose cdf is not in closed form? [duplicate]

I am working on a distribution whose pdf and cdf is $$f(x,\alpha,\beta)=\frac{(\frac{\beta}{\alpha})(\frac{x}{\alpha})^{\beta}}{(1+(\frac{x}{\alpha})^{\beta})^{2}}\frac{\sin(\frac{\pi}{\beta})}{(\frac{...

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