# Questions tagged [quantile]

one of several equally-frequent subranges of a data set or random distribution; for example, a percentile or quartile

43 questions
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### Bootstrap method & Confidence Interval

I'm trying to figure out how this method works. My data: 1000 samples from unknown distribution. I need to create 40 vectors from those 1000 samples (each vector with 20 samples) For every one of the ...
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### basic Quantile proves

Let this be my definition of a quantile funktion. X is a real-valued random variable. And let F be it's distribution function. then \begin{align*} F^{-1}(a):=\inf\{x\in \mathbb{R}: F(x) \ge a\}. \end{...
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### Quantile function for binomial distribution?

A test will succeed with a certain percentage. Now this test is repeated X number of times. I want to be able to get an estimate of the total number of succeeded test. Given that I know both the ...
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### Sample quantile of order p

My book says the following : "Let $X_{(1)}, X_{(2)}, ..., X_{(n)}$ be a set of values ordered in ascending order ($X_{(1)} \leq X_{(2)} \leq ... \leq X_{(n)})$. For a given $p$ ($0 \le p \le 1$), ...
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### Bootstrap estimation of the 95% confidence intervals for the 95% quantile for gamma distribution

I cant find any where information or algorithm how to apply in steps the bootstrap procedure to estimate the 95% confidence intervals for the 95% quantile from a random sample. Does anyone knows how ...
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### Sample median of Cauchy distribution is consistent. How?

When we use chebyshev's inequality to show whether an estimator is consistent or not, we require the mean square error of the estimator and I do not know sample median's probability distribution. So ...
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### If $(Q_3-Q_2)=\frac34(Q_2-Q_1)$, then

If $(Q_3-Q_2)=\frac34(Q_2-Q_1)$, then There are more data which are less than the median value There are more data which are less than the modal value There are less data greater than the mean value ...
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### What is the lower quartile of the set of data?

I came across this problem asking the lower quartile of the ungrouped data. My answer is 3, but other references say it should be 2.5. Here's the data: 1, 1, 2, 2, 3, 3, 4, 4, 6, 7, 8, 10, 11, 14, 15,...
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### A question about quantile function of normal distribution

Suppose that I know a normal distribution of randome varible $X$ satisfies the property that $P(20<X<30) = 0.9$, is that true that the lower quartile of $X$ must be between $20$ and $25$? I ...
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### Calculation of quantiles of a uniform distribution over a sphere

How do we calculate quantiles of a uniform distribution over a sphere ? Can anyone provide me with a tutorial ?
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### Is there any probability distribution that can fit based on 3 quantiles?

Assuming that we know quantiles 0.25, 0.5 and 0.75, is it possible to fit a distribution from these values ? What distribution ? How ? Thank you Edit : I forgot to mention that I would like the ...
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### how binary quantile regression divides the dependent variable into quantiles

I am not very clear with binary quantile regression. As if it was ordinary quantile regression, it would divide the dependent variable's value by its ascending value into quantiles. But I cannot ...
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### Upper bound for distance between actual and sample quantiles

Let $\xi_p$ be pth quantile of the distribution $F(x)$ with derivative at $\xi_p$, $f(\xi_p) >0$. Then, $$|\hat\xi_{p,n} - \xi_p| \leq \frac{2}{f(\xi_p)}\sqrt{\frac{\log n}{n}}$$ almost surely ...
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### For cdf $F(x)$ ad empirical cdf $F_n(x)$, show that $|F^{-1}\big(F_n(\xi_p)\big)-\hat\xi_p|\overset{a.s}\to0$

Suppose $X_1,\cdots,X_n$ are i.i.d. continuous random variables from distribution with cdf $F(x)$.Let $F_n(x)$ be a random variable defined by $$F_n(x)=\frac{1}n\sum_{i=1}^nI\{X_i\le x\}.$$ Define the ...
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### How to prove that sample of size $O(\epsilon^{-2} log \delta^{-1})$ is enough to predict quantiles?

There is a known problem: You are given a stream of numbers and you need to find it's $q$-th quantile ($0 \le q \le 1$). You may get wrong answer but you need to return answer between $q-\epsilon$-th ...
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### Quantiles when the population contains only one unique value

My apologies for the mixing of the terms quartile and quantile below. I am interested in the general case of quantiles, but I'm using a quartile as a specific example. Also feel free to clarify any ...
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I’ve been dealing with an issue about change-of-variable formula. Let $\mu$ be a probability measure on $\mathbf R_+$. Let $F(x) = μ([0,p])$ and $Q$ its quantile function, ie $Q(p) = \inf \{q \in \... 0answers 30 views ### Asymptotic behaviour of the process$U_n=U_{n-1}+s(U_{n-1})X_n$, where$X_n$is iid Let$s, s^*:\mathbb{R}^+ \to \mathbb{R}^+$($0\in\mathbb{R}^+$) such that$0 \le s(x), s^*(x) \le x$for every$x \in \mathbb{R}^+$and$X, X_1, \ldots$is iid with$\mathbb{E}X>0$. Let$U_{0,s}=1$... 0answers 27 views ### Evaluation of$p$th Quantile? Let$X$be a random variable having PDF$f(x) = \frac{1}{\lambda} e^{-\frac{\lambda}{x}} , x > 0 , \lambda > 0$. And I was trying to find out the$p$th Quantile, for which we have to set$\int_{...
Let $\{X_i\}_{i=1}^n$ be a random sample, $Y_i=\delta(X_i)$ for some function $\delta(\cdot)$, and $Q(\tau)$ be the population quantile function of $Y_i$. We can estimate $Q(\cdot)$ by the empirical ...