List questions from quantile-function

Published on 11 Oct 2019 - 13:52

42

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Probabilistic quantile of an empiric distribution

Published on 25 Mar 2026 - 2:37

784

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Show that if the inverse cumulative distribution function is continuous, it is invertible

Published on 03 Jan 2020 - 20:21

180

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If $F$ is a distribution function and $t>0$, can we show that $F(F^{-1}(t))\ge t$?

Published on 06 Jan 2020 - 6:16

119

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If $F$ is a distribution function and $x_0\in F^{-1}([0,1])$, can we characterize $\left\{t\in[0,1]:F^{-1}(t)=x_0\right\}$?

Published on 06 Jan 2020 - 10:06

164

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Cumulative distribution function applied to random variable with a constant

Published on 23 Mar 2026 - 10:04

1.2k

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Questions about definition of Quantile function

Published on 23 Mar 2026 - 3:52

323

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Quantile given Characteristic function

Published on 25 Mar 2026 - 4:44

360

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List of closed form special cases and transformations of Wolfram language’s inverse beta regularized $\text I^{-1}_x(a,b)$.

Published on 25 Mar 2026 - 5:48

38

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Function of quantile function

Published on 02 Mar 2026 - 18:01

35

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Prove the equality: $\sup\{x\geq0 : F_X(x)\leq t\}=\int_0^{+\infty} 1_{\{ F_X(x)\leq t\}}\,dx$.

Published on 11 Apr 2023 - 8:08

40

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Controlling the distance between two quantile functions of discrete distributions

Published on 25 Mar 2026 - 4:43

47

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First Order stochastic dominance, but only for the upper-quantiles?

Published on 25 Mar 2026 - 6:01

106

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Pointwise convergence of generalized inverse function

Published on 25 Mar 2026 - 5:50

105

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Radon-Nikodym derivative of pushforwards: $\frac{d f_\# \mu}{d g_{\#} \mu}$

Published on 25 Mar 2026 - 4:06

List Question

The $L^1$ distance of two CDF is the $L^1$ distance of the quantile function coupling

Probabilistic quantile of an empiric distribution

Show that if the inverse cumulative distribution function is continuous, it is invertible

If $F$ is a distribution function and $t>0$, can we show that $F(F^{-1}(t))\ge t$?

If $F$ is a distribution function and $x_0\in F^{-1}([0,1])$, can we characterize $\left\{t\in[0,1]:F^{-1}(t)=x_0\right\}$?

Cumulative distribution function applied to random variable with a constant

Questions about definition of Quantile function

Quantile given Characteristic function

List of closed form special cases and transformations of Wolfram language’s inverse beta regularized $\text I^{-1}_x(a,b)$.

Function of quantile function

Prove the equality: $\sup\{x\geq0 : F_X(x)\leq t\}=\int_0^{+\infty} 1_{\{ F_X(x)\leq t\}}\,dx$.

Controlling the distance between two quantile functions of discrete distributions

First Order stochastic dominance, but only for the upper-quantiles?

Pointwise convergence of generalized inverse function

Radon-Nikodym derivative of pushforwards: $\frac{d f_\# \mu}{d g_{\#} \mu}$

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