List questions from quantile-function

Published on 03 May 2026 - 12:39

63

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Probabilistic quantile of an empiric distribution

Published on 04 May 2026 - 4:37

790

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

Published on 04 May 2026 - 12:36

188

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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 May 2026 - 6:57

125

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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 04 May 2026 - 12:44

179

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Cumulative distribution function applied to random variable with a constant

Published on 04 May 2026 - 10:29

1.2k

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Questions about definition of Quantile function

Published on 07 May 2026 - 12:50

330

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Quantile given Characteristic function

Published on 07 May 2026 - 9:26

381

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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 04 May 2026 - 11:43

46

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Function of quantile function

Published on 05 May 2026 - 16:06

43

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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 05 May 2026 - 13:42

46

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Controlling the distance between two quantile functions of discrete distributions

Published on 05 May 2026 - 15:56

52

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

Published on 10 May 2026 - 13:29

111

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Pointwise convergence of generalized inverse function

Published on 06 May 2026 - 14:27

110

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

Published on 05 May 2026 - 14:16

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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