Question

$\phi(t)=\sqrt{1-t^2} \ $ if $|t|<1$ and $\phi(t)=0$ if $|t| \geq 1.$ Prove that $\phi(t)$ is not a characteristic function

score 126 · Answer 1 · 2023-12-19 08:49:50

126

Views

$\phi(t)=\sqrt{1-t^2} \ $ if $|t|<1$ and $\phi(t)=0$ if $|t| \geq 1.$ Prove that $\phi(t)$ is not a characteristic function

Published on 19 Dec 2023 - 8:49

score 237 · Answer 2 · 2023-12-28 22:50:33

237

Views

Characteristic function of product of two random variables with arbitrary normal distributions

Published on 28 Dec 2023 - 22:50

score 58 · Answer 3 · 2023-12-29 16:56:46

58

Views

Monotone characteristic function

Published on 29 Dec 2023 - 16:56

score 184 · Answer 4 · 2026-03-25 18:51:13

184

Views

Gil-Pelaez Formula consistently ends up being equal to 0

Published on 25 Mar 2026 - 18:51

score 78 · Answer 5 · 2026-03-25 20:08:12

78

Views

Compute standard normal CDF from CDF using Gil-Pelaez inversion formula

Published on 25 Mar 2026 - 20:08

score 125 · Answer 6 · 2024-01-08 15:01:49

125

Views

Prove that if characteristic function is absolutely integrable then corresponding density function will be uniformly continuous.

Published on 08 Jan 2024 - 15:01

score 286 · Answer 7 · 2024-01-11 03:06:07

286

Views

Show that two random vectors have the same distribution

Published on 11 Jan 2024 - 3:06

score 88 · Answer 8 · 2024-01-21 07:35:23

88

Views

An interesting property of characteristic function

Published on 21 Jan 2024 - 7:35

score 60 · Answer 9 · 2026-03-28 23:16:36

60

Views

Suppose $(X_{n})_{n}$ is series of i.i.d. random variables and $E(X_{1})=2$. Compute $\lim_{n\to\infty} (n \ln (\varphi_{X_{1}}(\frac{2}{n})))$

Published on 28 Mar 2026 - 23:16

score 46 · Answer 10 · 2024-01-21 19:33:28

46

Views

Get PDF from Taylor series of characteristic function

Published on 21 Jan 2024 - 19:33

score 42 · Answer 11 · 2024-01-22 07:17:46

42

Views

Is there a way to calculate $E\left[\mathrm{sgn}(X)X^n\right]$ if I don't know the pdf for $X$ but I do know the characteristic function?

Published on 22 Jan 2024 - 7:17

score 34 · Answer 12 · 2026-03-29 02:28:38

34

Views

Probability Density Function of Compound Poisson Process

Published on 29 Mar 2026 - 2:28

score 58 · Answer 13 · 2024-01-26 22:30:51

58

Views

Characteristic functions to evaluate integral

Published on 26 Jan 2024 - 22:30

score 50 · Answer 14 · 2024-01-27 16:58:50

50

Views

Decay of the Fourier transform of the indicator of the unit $\ell^p$ ball when $p < 1$.

Published on 27 Jan 2024 - 16:58

score 33 · Answer 15 · 2024-02-04 09:17:12

33

Views

Characteristic Function of Multivariate Distribution

Published on 04 Feb 2024 - 9:17

List Question

$\phi(t)=\sqrt{1-t^2} \ $ if $|t|<1$ and $\phi(t)=0$ if $|t| \geq 1.$ Prove that $\phi(t)$ is not a characteristic function

Characteristic function of product of two random variables with arbitrary normal distributions

Monotone characteristic function

Gil-Pelaez Formula consistently ends up being equal to 0

Compute standard normal CDF from CDF using Gil-Pelaez inversion formula

Prove that if characteristic function is absolutely integrable then corresponding density function will be uniformly continuous.

Show that two random vectors have the same distribution

An interesting property of characteristic function

Suppose $(X_{n})_{n}$ is series of i.i.d. random variables and $E(X_{1})=2$. Compute $\lim_{n\to\infty} (n \ln (\varphi_{X_{1}}(\frac{2}{n})))$

Get PDF from Taylor series of characteristic function

Is there a way to calculate $E\left[\mathrm{sgn}(X)X^n\right]$ if I don't know the pdf for $X$ but I do know the characteristic function?

Probability Density Function of Compound Poisson Process

Characteristic functions to evaluate integral

Decay of the Fourier transform of the indicator of the unit $\ell^p$ ball when $p < 1$.

Characteristic Function of Multivariate Distribution

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