Questions tagged [quantile]

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

87 questions
23 views

Calculate theoretical quantiles with calculator (qq-plot)

Let's say we have the following data: $-1.8, -0.82, 0.3, 1.2, 1.6$ Now I want to make a qq-plot out of it by hand, just with a calculator (Casio fc 991). I start by sorting the values in ranks j ...
18 views

19 views

Convexity of a function of generalized inverse CDF.

How can I prove (or disprove) that the following function is convex on $X$. $$\rho(X,Z) = Max \{ F^{-1}_Z(t)-F^{-1}_X(t),0 \},$$ where $F^{-1}_X(t)= inf \{ x : F_X(x) \geq t \}$ with $0 \le t \le 1$....
133 views

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 ...
29 views

2k views

Basic Quantile Calculation

I have a slight confusion with the current method of calculation of a quantile for a give ungrouped distribution. To give you an example, i shall refer to calculation of a Quartile, but this doubt ...
108 views

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 $f(x, \theta_n)$. ...
38 views

consistency of inverse cdf

If $\hat{F}(x)$ is a consistent estimator of $F(x)$ where $F(x)$ is a cdf, can we state that $\hat{F}^{-1}(x)$ is also a consistent estimator of $F^{-1}(x)$? Is that straightforward? Why? You can make ...
566 views

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 $G:\mathbb{R}\to[0,1]$ ...
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 $p$ ($0 \le p \le 1$), ...
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 ...