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# Questions tagged [quantile]

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

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### Are there 3 or 4 quartiles? 99 or 100 percentiles?

So I understand that a quartile is a quantile where the data is divided into four groups. 1 2 3 ---|---|---|--- And 1, 2, and 3 are the quartiles. The ...
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### Construct a random variable with a given distribution

Suppose that ($\Omega$, $\mathcal{F}$,$P$) where $\mathcal{F}$ is the $\sigma$-algebra of Lebesgue measurable subsets of $\Omega\equiv[0,1]$ and $P$ is the Lebesgue measure. Let $G:\mathbb{R}\to[0,1]$ ...
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### what i am doing wrong in calculating quartiles

can somebody please help me to understand? Why 1st quartile in this data is equal 4.5 and 3rd quartile is equal 6.5. I am getting 4.25 and 6.25 , but not 4.5 and not 6.5. I use formula (n+1)/4 for ...
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### Empirical quantile definition?

Suppose we have an order set of data $\mathcal X=\{x^{(1)},x^{(2)},...,x^{(n)}\}$ such that $x^{(1)}\le x^{(2)}\le ...\le x^{(n)}$. For some reason in my course's definition of empirical quantile, we ...
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### Uniqueness of solution to quantile minimization problem

I read here: http://librarum.org/book/11685/31 (p. 51, Ex. 3) that quantiles are solutions to certain minimization problem. Here is the proof: http://www.math.ucla.edu/~tom/MathematicalStatistics/...
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### How to show that $\Phi^{-1}(1-x) =O(\sqrt{\log{x^{-1}}})$

In the middle of some proof, I have faced an expression $\Phi^{-1}(1-x) =O(\sqrt{\log{x^{-1}}})$, where $\Phi(\cdot)^{-1}$ is a quantile function of the standard normal distribution and $x \in (0,1)$. ...
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### Implications on the cdf of $\epsilon_1-\epsilon_2$ of conditions on the cdf's of $\epsilon_1, \epsilon_2$

Consider three random variables $\epsilon_1, \epsilon_2, X$. Let $F_{\epsilon_i}(\cdot| x)$ denote the cumulative distribution function (cdf) of $\epsilon_i$ conditional on $X=x$ for any $i\in \{1,2\}$...
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### How is this statistical index called?

I need to calculate an index that is to be derived like this: If we have some data: 850 700 500 480 300 100 50, we first sort it from the large to small: ...
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### Calculating Quantile for a specific problem

so I understand how to calculate the 0.5 quantile of the given question. I calculate the CDF of x and then I multiply it to 0.5 But what if there's more than one function for multiple intervals? How ...
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### Quantile based Shannon entropy

I'm reading two papers "Quantile based entropy function" and "Quantile based entropy of order statistics". I'm a bit confused whether the quantile based entropy function (Eq 7 in the first paper and ...
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### Loss of uniqueness of quantiles

We know that, if $X$ is a continuous random variable with a strictly increasing distribution function or DF $F(x)$ then, its $p$th quantile is unique. But if the distribution function is non-...
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### Tail difference of quantiles of (symmetric) distribution functions

Assume, for example, $z_\alpha$ are $\Phi^{-1}(\alpha)$ quantiles from standard normal distribution, $\alpha > 0$. If we are interested in the sum$$z_\alpha + z_{1 - \alpha}$$ for standard normal ...
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### Prove that $\min_{\mu}\sum_{i=1}^n|y_i-\mu|=\text{median}\{y_1,\cdots,y_n\}$ [duplicate]

How to prove the equation below in a simple way? $$\min_{\mu}\sum_{i=1}^n|y_i-\mu|=\text{median}\{y_1,\cdots,y_n\}$$
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### Quantile function of the r th order statistics of i.n.n.i.d. random variables

I am repeatedly drawing $n$ random samples where the first sample is drawn from $f(x, \theta_1)$ the second from $f(x, \theta_2)$, $\enspace \dots$ , and the $n^{\text{th}}$ from $f(x, \theta_n)$. ...
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 $p$ ($0 \le p \le 1$), ...
The biweight midvariance $\zeta^2$ is a measure of scale that is more robust to non-normal distributions. It is defined as follows by [1] in three steps. For observations $X_i$, $i = 1,2,\cdots,n$, ...