What is the name of the function $G(z)=E[X|Xgeq z] P(Xgeq z)$?
$begingroup$
Take some real valued continuous random variable $X$ with CDF $F$. Take a function $G:mathbb{R}to mathbb{R}$ defined as
$$G(z)=int^infty_z xdF(x)=mathbb{E}[X|Xgeq z]
mathbb{P}(Xgeq z).$$
Does $G$ have a name?
Apologies if this is not an appropriate question for this site but I don't want to make up a name for it if there is a known nomenclature for it.
probability-theory probability-distributions soft-question
asked Dec 20 '18 at 21:08
tsmtsm
31919
$endgroup$
add a comment |
$begingroup$
Take some real valued continuous random variable $X$ with CDF $F$. Take a function $G:mathbb{R}to mathbb{R}$ defined as
$$G(z)=int^infty_z xdF(x)=mathbb{E}[X|Xgeq z]
mathbb{P}(Xgeq z).$$
Does $G$ have a name?
Apologies if this is not an appropriate question for this site but I don't want to make up a name for it if there is a known nomenclature for it.
probability-theory probability-distributions soft-question
asked Dec 20 '18 at 21:08
tsmtsm
31919
$endgroup$
1
$begingroup$
It has been called "life expectancy" in some contexts, but I don't know if this term is widely used by mathematicians.
$endgroup$
– kimchi lover
Dec 20 '18 at 21:13
$begingroup$
Isn't it just the conditional expectation as you identified, $E[X|X>z]$?
$endgroup$
– eSurfsnake
Dec 20 '18 at 22:53
add a comment |
$begingroup$
Take some real valued continuous random variable $X$ with CDF $F$. Take a function $G:mathbb{R}to mathbb{R}$ defined as
$$G(z)=int^infty_z xdF(x)=mathbb{E}[X|Xgeq z]
mathbb{P}(Xgeq z).$$
Does $G$ have a name?
Apologies if this is not an appropriate question for this site but I don't want to make up a name for it if there is a known nomenclature for it.
probability-theory probability-distributions soft-question
asked Dec 20 '18 at 21:08
tsmtsm
31919
$endgroup$
Take some real valued continuous random variable $X$ with CDF $F$. Take a function $G:mathbb{R}to mathbb{R}$ defined as
$$G(z)=int^infty_z xdF(x)=mathbb{E}[X|Xgeq z]
mathbb{P}(Xgeq z).$$
Does $G$ have a name?
Apologies if this is not an appropriate question for this site but I don't want to make up a name for it if there is a known nomenclature for it.
probability-theory probability-distributions soft-question
probability-theory probability-distributions soft-question
asked Dec 20 '18 at 21:08
tsmtsm
31919
asked Dec 20 '18 at 21:08
tsmtsm
31919
edited Dec 23 '18 at 1:16
tsm
asked Dec 20 '18 at 21:08
tsmtsm
31919
asked Dec 20 '18 at 21:08
tsmtsm
31919
asked Dec 20 '18 at 21:08
tsmtsm
31919
31919
1
$begingroup$
It has been called "life expectancy" in some contexts, but I don't know if this term is widely used by mathematicians.
$endgroup$
– kimchi lover
Dec 20 '18 at 21:13
$begingroup$
Isn't it just the conditional expectation as you identified, $E[X|X>z]$?
$endgroup$
– eSurfsnake
Dec 20 '18 at 22:53
add a comment |
1
$begingroup$
It has been called "life expectancy" in some contexts, but I don't know if this term is widely used by mathematicians.
$endgroup$
– kimchi lover
Dec 20 '18 at 21:13
$begingroup$
Isn't it just the conditional expectation as you identified, $E[X|X>z]$?
$endgroup$
– eSurfsnake
Dec 20 '18 at 22:53
1
1
$begingroup$
It has been called "life expectancy" in some contexts, but I don't know if this term is widely used by mathematicians.
$endgroup$
– kimchi lover
Dec 20 '18 at 21:13
$begingroup$
It has been called "life expectancy" in some contexts, but I don't know if this term is widely used by mathematicians.
$endgroup$
– kimchi lover
Dec 20 '18 at 21:13
$begingroup$
Isn't it just the conditional expectation as you identified, $E[X|X>z]$?
$endgroup$
– eSurfsnake
Dec 20 '18 at 22:53
$begingroup$
Isn't it just the conditional expectation as you identified, $E[X|X>z]$?
$endgroup$
– eSurfsnake
Dec 20 '18 at 22:53
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%2f3047964%2fwhat-is-the-name-of-the-function-gz-exx-geq-z-px-geq-z%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%2f3047964%2fwhat-is-the-name-of-the-function-gz-exx-geq-z-px-geq-z%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
1
$begingroup$
It has been called "life expectancy" in some contexts, but I don't know if this term is widely used by mathematicians.
$endgroup$
– kimchi lover
Dec 20 '18 at 21:13
$begingroup$
Isn't it just the conditional expectation as you identified, $E[X|X>z]$?
$endgroup$
– eSurfsnake
Dec 20 '18 at 22:53