Looking for a particular class of distributions The 2019 Stack Overflow Developer Survey Results Are InLooking for Anthony?Idempotence and the Rao–Blackwell theoremConditional distributions of (higher-order) autoregressive Markov processesLooking for a function R->[0,1) with particular propertiesListing the values of particular probability distributionsGenerating random numbers according to specific multivariate distributionIs the variance of a multivariate normal distribution restricted to a sphere smaller?derive the expectation of exponential function $e^-leftVert mathbfx - Vmathbfx+mathbfarightVert^2$ or its upper boundFinding a special class of distributionsSufficient statistic for class of distributions
What is the accessibility of a package's `Private` context variables?
Is flight data recorder erased after every flight?
FPGA - DIY Programming
How can I autofill dates in Excel excluding Sunday?
How are circuits which use complex ICs normally simulated?
Can we generate random numbers using irrational numbers like π and e?
Why didn't the Event Horizon Telescope team mention Sagittarius A*?
What do hard-Brexiteers want with respect to the Irish border?
Is three citations per paragraph excessive for undergraduate research paper?
Landlord wants to switch my lease to a "Land contract" to "get back at the city"
If I score a critical hit on an 18 or higher, what are my chances of getting a critical hit if I roll 3d20?
What are the motivations for publishing new editions of an existing textbook, beyond new discoveries in a field?
Shouldn't "much" here be used instead of "more"?
What to do when moving next to a bird sanctuary with a loosely-domesticated cat?
How to type this arrow in math mode?
Is this app Icon Browser Safe/Legit?
Protecting Dualbooting Windows from dangerous code (like rm -rf)
"as much details as you can remember"
Worn-tile Scrabble
Do these rules for Critical Successes and Critical Failures seem Fair?
What could be the right powersource for 15 seconds lifespan disposable giant chainsaw?
What is the meaning of Triage in Cybersec world?
Which Sci-Fi work first showed weapon of galactic-scale mass destruction?
What tool would a Roman-age civilization have for the breaking of silver and other metals into dust?
Looking for a particular class of distributions
The 2019 Stack Overflow Developer Survey Results Are InLooking for Anthony?Idempotence and the Rao–Blackwell theoremConditional distributions of (higher-order) autoregressive Markov processesLooking for a function R->[0,1) with particular propertiesListing the values of particular probability distributionsGenerating random numbers according to specific multivariate distributionIs the variance of a multivariate normal distribution restricted to a sphere smaller?derive the expectation of exponential function $e^-leftVert mathbfx - Vmathbfx+mathbfarightVert^2$ or its upper boundFinding a special class of distributionsSufficient statistic for class of distributions
$begingroup$
Choose some basis in $mathbbR^n$ and call one of its directions as "$z$". Let $x$ be a $n-$dimensional random variable s.t for all $3-$tuple of $n-$dimensional rotation matrices $R_1, R_2$ and $R_3$ I want the following expectation to be a constant (independent of $R_1, R_2$ and $R_3$),
$$mathbbE_x left[ (R_1 x)_z vert (R_2 x)_z vert vert (R_3 x)_z vert right]$$
- Are there non-trivial distributions with such properties? (...trivial cases are when the above is $0$ for the distribution being parity symmetric..)
Feel free to assume reasonable restrictions on the support of the distribution - like if say compact support on a sphere or such helps!
statistics probability-distributions
asked Mar 30 at 16:34
gradstudentgradstudent
19217
$endgroup$
add a comment |
$begingroup$
Choose some basis in $mathbbR^n$ and call one of its directions as "$z$". Let $x$ be a $n-$dimensional random variable s.t for all $3-$tuple of $n-$dimensional rotation matrices $R_1, R_2$ and $R_3$ I want the following expectation to be a constant (independent of $R_1, R_2$ and $R_3$),
$$mathbbE_x left[ (R_1 x)_z vert (R_2 x)_z vert vert (R_3 x)_z vert right]$$
- Are there non-trivial distributions with such properties? (...trivial cases are when the above is $0$ for the distribution being parity symmetric..)
Feel free to assume reasonable restrictions on the support of the distribution - like if say compact support on a sphere or such helps!
statistics probability-distributions
asked Mar 30 at 16:34
gradstudentgradstudent
19217
$endgroup$
$begingroup$
Does $(R_i x)_z$ mean the $z$-coordinate of $R_i x$?
$endgroup$
– kccu
Mar 30 at 16:39
$begingroup$
Yes! Thats exactly what I mean!
$endgroup$
– gradstudent
Mar 30 at 16:53
add a comment |
$begingroup$
Choose some basis in $mathbbR^n$ and call one of its directions as "$z$". Let $x$ be a $n-$dimensional random variable s.t for all $3-$tuple of $n-$dimensional rotation matrices $R_1, R_2$ and $R_3$ I want the following expectation to be a constant (independent of $R_1, R_2$ and $R_3$),
$$mathbbE_x left[ (R_1 x)_z vert (R_2 x)_z vert vert (R_3 x)_z vert right]$$
- Are there non-trivial distributions with such properties? (...trivial cases are when the above is $0$ for the distribution being parity symmetric..)
Feel free to assume reasonable restrictions on the support of the distribution - like if say compact support on a sphere or such helps!
statistics probability-distributions
asked Mar 30 at 16:34
gradstudentgradstudent
19217
$endgroup$
Choose some basis in $mathbbR^n$ and call one of its directions as "$z$". Let $x$ be a $n-$dimensional random variable s.t for all $3-$tuple of $n-$dimensional rotation matrices $R_1, R_2$ and $R_3$ I want the following expectation to be a constant (independent of $R_1, R_2$ and $R_3$),
$$mathbbE_x left[ (R_1 x)_z vert (R_2 x)_z vert vert (R_3 x)_z vert right]$$
- Are there non-trivial distributions with such properties? (...trivial cases are when the above is $0$ for the distribution being parity symmetric..)
Feel free to assume reasonable restrictions on the support of the distribution - like if say compact support on a sphere or such helps!
statistics probability-distributions
statistics probability-distributions
asked Mar 30 at 16:34
gradstudentgradstudent
19217
asked Mar 30 at 16:34
gradstudentgradstudent
19217
edited Mar 30 at 16:54
gradstudent
asked Mar 30 at 16:34
gradstudentgradstudent
19217
asked Mar 30 at 16:34
gradstudentgradstudent
19217
asked Mar 30 at 16:34
gradstudentgradstudent
19217
19217
$begingroup$
Does $(R_i x)_z$ mean the $z$-coordinate of $R_i x$?
$endgroup$
– kccu
Mar 30 at 16:39
$begingroup$
Yes! Thats exactly what I mean!
$endgroup$
– gradstudent
Mar 30 at 16:53
add a comment |
$begingroup$
Does $(R_i x)_z$ mean the $z$-coordinate of $R_i x$?
$endgroup$
– kccu
Mar 30 at 16:39
$begingroup$
Yes! Thats exactly what I mean!
$endgroup$
– gradstudent
Mar 30 at 16:53
$begingroup$
Does $(R_i x)_z$ mean the $z$-coordinate of $R_i x$?
$endgroup$
– kccu
Mar 30 at 16:39
$begingroup$
Does $(R_i x)_z$ mean the $z$-coordinate of $R_i x$?
$endgroup$
– kccu
Mar 30 at 16:39
$begingroup$
Yes! Thats exactly what I mean!
$endgroup$
– gradstudent
Mar 30 at 16:53
$begingroup$
Yes! Thats exactly what I mean!
$endgroup$
– gradstudent
Mar 30 at 16:53
add a comment |
0
active
oldest
votes
Your Answer
StackExchange.ifUsing("editor", function ()
return StackExchange.using("mathjaxEditing", function ()
StackExchange.MarkdownEditor.creationCallbacks.add(function (editor, postfix)
StackExchange.mathjaxEditing.prepareWmdForMathJax(editor, postfix, [["$", "$"], ["\\(","\\)"]]);
);
);
, "mathjax-editing");
StackExchange.ready(function()
var channelOptions =
tags: "".split(" "),
id: "69"
;
initTagRenderer("".split(" "), "".split(" "), channelOptions);
StackExchange.using("externalEditor", function()
// Have to fire editor after snippets, if snippets enabled
if (StackExchange.settings.snippets.snippetsEnabled)
StackExchange.using("snippets", function()
createEditor();
);
else
createEditor();
);
function createEditor()
StackExchange.prepareEditor(
heartbeatType: 'answer',
autoActivateHeartbeat: false,
convertImagesToLinks: true,
noModals: true,
showLowRepImageUploadWarning: true,
reputationToPostImages: 10,
bindNavPrevention: true,
postfix: "",
imageUploader:
brandingHtml: "Powered by u003ca class="icon-imgur-white" href="https://imgur.com/"u003eu003c/au003e",
contentPolicyHtml: "User contributions licensed under u003ca href="https://creativecommons.org/licenses/by-sa/3.0/"u003ecc by-sa 3.0 with attribution requiredu003c/au003e u003ca href="https://stackoverflow.com/legal/content-policy"u003e(content policy)u003c/au003e",
allowUrls: true
,
noCode: true, onDemand: true,
discardSelector: ".discard-answer"
,immediatelyShowMarkdownHelp:true
);
);
Sign up or log in
StackExchange.ready(function ()
StackExchange.helpers.onClickDraftSave('#login-link');
);
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
StackExchange.ready(
function ()
StackExchange.openid.initPostLogin('.new-post-login', 'https%3a%2f%2fmath.stackexchange.com%2fquestions%2f3168489%2flooking-for-a-particular-class-of-distributions%23new-answer', 'question_page');
);
Post as a guest
Required, but never shown
0
active
oldest
votes
0
active
oldest
votes
active
oldest
votes
active
oldest
votes
Thanks for contributing an answer to Mathematics Stack Exchange!
- Please be sure to answer the question. Provide details and share your research!
But avoid …
- Asking for help, clarification, or responding to other answers.
- Making statements based on opinion; back them up with references or personal experience.
Use MathJax to format equations. MathJax reference.
To learn more, see our tips on writing great answers.
Sign up or log in
StackExchange.ready(function ()
StackExchange.helpers.onClickDraftSave('#login-link');
);
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
StackExchange.ready(
function ()
StackExchange.openid.initPostLogin('.new-post-login', 'https%3a%2f%2fmath.stackexchange.com%2fquestions%2f3168489%2flooking-for-a-particular-class-of-distributions%23new-answer', 'question_page');
);
Post as a guest
Required, but never shown
Sign up or log in
StackExchange.ready(function ()
StackExchange.helpers.onClickDraftSave('#login-link');
);
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
Sign up or log in
StackExchange.ready(function ()
StackExchange.helpers.onClickDraftSave('#login-link');
);
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
Sign up or log in
StackExchange.ready(function ()
StackExchange.helpers.onClickDraftSave('#login-link');
);
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
$begingroup$
Does $(R_i x)_z$ mean the $z$-coordinate of $R_i x$?
$endgroup$
– kccu
Mar 30 at 16:39
$begingroup$
Yes! Thats exactly what I mean!
$endgroup$
– gradstudent
Mar 30 at 16:53