What makes statistical distributions so unique?
$begingroup$
I am going to start this question with a definition.
Definition: If $Zsim mathcal{N}(0,1)$ and $U sim chi_{n}^2$, and $Z$ and $U$ are independent, then the distribution of $$frac{Z}{sqrt{frac{U}{n}}}$$
is called the $t$ distribution with $n$ degrees of freedom.
My question , which may sound strange, is, why is this so special? Why can't anyone just come up with a distribution which is some combination of other random variables and name it after themselves?
statistics random-variables
asked Jan 18 at 19:20
MathIsLife12MathIsLife12
589111
$endgroup$
add a comment |
$begingroup$
I am going to start this question with a definition.
Definition: If $Zsim mathcal{N}(0,1)$ and $U sim chi_{n}^2$, and $Z$ and $U$ are independent, then the distribution of $$frac{Z}{sqrt{frac{U}{n}}}$$
is called the $t$ distribution with $n$ degrees of freedom.
My question , which may sound strange, is, why is this so special? Why can't anyone just come up with a distribution which is some combination of other random variables and name it after themselves?
statistics random-variables
asked Jan 18 at 19:20
MathIsLife12MathIsLife12
589111
$endgroup$
1
$begingroup$
Of course you can just come up with a distribution and name it after yourself. But (1) that disitribution may not be interesting (in the sense of having important applications), and (2) it’s likely someone else has already come up with that distribution, so you better not expect everyone to call it by the name you've given it if people already call it something else.
$endgroup$
– symplectomorphic
Jan 18 at 19:23
1
$begingroup$
In this case, “Student’s T” distribution (which has an interesting history regarding its name, in fact) has important applications in the theory of statistical inference.
$endgroup$
– symplectomorphic
Jan 18 at 19:25
$begingroup$
The Student's $t$ distribution was in effect developed by "Student" whose real name was William Sealy Gosset who was hiding his name on his employer's instruction. It was named (including the "t") by R.A.Fisher. So it is difficult to say either named it after himself.
$endgroup$
– Henry
Jan 18 at 19:45
add a comment |
$begingroup$
I am going to start this question with a definition.
Definition: If $Zsim mathcal{N}(0,1)$ and $U sim chi_{n}^2$, and $Z$ and $U$ are independent, then the distribution of $$frac{Z}{sqrt{frac{U}{n}}}$$
is called the $t$ distribution with $n$ degrees of freedom.
My question , which may sound strange, is, why is this so special? Why can't anyone just come up with a distribution which is some combination of other random variables and name it after themselves?
statistics random-variables
asked Jan 18 at 19:20
MathIsLife12MathIsLife12
589111
$endgroup$
I am going to start this question with a definition.
Definition: If $Zsim mathcal{N}(0,1)$ and $U sim chi_{n}^2$, and $Z$ and $U$ are independent, then the distribution of $$frac{Z}{sqrt{frac{U}{n}}}$$
is called the $t$ distribution with $n$ degrees of freedom.
My question , which may sound strange, is, why is this so special? Why can't anyone just come up with a distribution which is some combination of other random variables and name it after themselves?
statistics random-variables
statistics random-variables
asked Jan 18 at 19:20
MathIsLife12MathIsLife12
589111
asked Jan 18 at 19:20
MathIsLife12MathIsLife12
589111
asked Jan 18 at 19:20
MathIsLife12MathIsLife12
589111
asked Jan 18 at 19:20
MathIsLife12MathIsLife12
589111
asked Jan 18 at 19:20
MathIsLife12MathIsLife12
589111
589111
1
$begingroup$
Of course you can just come up with a distribution and name it after yourself. But (1) that disitribution may not be interesting (in the sense of having important applications), and (2) it’s likely someone else has already come up with that distribution, so you better not expect everyone to call it by the name you've given it if people already call it something else.
$endgroup$
– symplectomorphic
Jan 18 at 19:23
1
$begingroup$
In this case, “Student’s T” distribution (which has an interesting history regarding its name, in fact) has important applications in the theory of statistical inference.
$endgroup$
– symplectomorphic
Jan 18 at 19:25
$begingroup$
The Student's $t$ distribution was in effect developed by "Student" whose real name was William Sealy Gosset who was hiding his name on his employer's instruction. It was named (including the "t") by R.A.Fisher. So it is difficult to say either named it after himself.
$endgroup$
– Henry
Jan 18 at 19:45
add a comment |
1
$begingroup$
Of course you can just come up with a distribution and name it after yourself. But (1) that disitribution may not be interesting (in the sense of having important applications), and (2) it’s likely someone else has already come up with that distribution, so you better not expect everyone to call it by the name you've given it if people already call it something else.
$endgroup$
– symplectomorphic
Jan 18 at 19:23
1
$begingroup$
In this case, “Student’s T” distribution (which has an interesting history regarding its name, in fact) has important applications in the theory of statistical inference.
$endgroup$
– symplectomorphic
Jan 18 at 19:25
$begingroup$
The Student's $t$ distribution was in effect developed by "Student" whose real name was William Sealy Gosset who was hiding his name on his employer's instruction. It was named (including the "t") by R.A.Fisher. So it is difficult to say either named it after himself.
$endgroup$
– Henry
Jan 18 at 19:45
1
1
$begingroup$
Of course you can just come up with a distribution and name it after yourself. But (1) that disitribution may not be interesting (in the sense of having important applications), and (2) it’s likely someone else has already come up with that distribution, so you better not expect everyone to call it by the name you've given it if people already call it something else.
$endgroup$
– symplectomorphic
Jan 18 at 19:23
$begingroup$
Of course you can just come up with a distribution and name it after yourself. But (1) that disitribution may not be interesting (in the sense of having important applications), and (2) it’s likely someone else has already come up with that distribution, so you better not expect everyone to call it by the name you've given it if people already call it something else.
$endgroup$
– symplectomorphic
Jan 18 at 19:23
1
1
$begingroup$
In this case, “Student’s T” distribution (which has an interesting history regarding its name, in fact) has important applications in the theory of statistical inference.
$endgroup$
– symplectomorphic
Jan 18 at 19:25
$begingroup$
In this case, “Student’s T” distribution (which has an interesting history regarding its name, in fact) has important applications in the theory of statistical inference.
$endgroup$
– symplectomorphic
Jan 18 at 19:25
$begingroup$
The Student's $t$ distribution was in effect developed by "Student" whose real name was William Sealy Gosset who was hiding his name on his employer's instruction. It was named (including the "t") by R.A.Fisher. So it is difficult to say either named it after himself.
$endgroup$
– Henry
Jan 18 at 19:45
$begingroup$
The Student's $t$ distribution was in effect developed by "Student" whose real name was William Sealy Gosset who was hiding his name on his employer's instruction. It was named (including the "t") by R.A.Fisher. So it is difficult to say either named it after himself.
$endgroup$
– Henry
Jan 18 at 19:45
add a comment |
1 Answer
1
active
oldest
votes
$begingroup$
Naming something after yourself maybe considered inappropriate. If the distribution that you discovered is important and useful enough then probably other researchers will already name if after you. Regarding the first question -
"Why can't anyone just come up with a distribution which is some combination of other random variables?"
You can, but the question is $(1)$ why is your distribution important and $(2)$ what it can be used for?
The fact that there are around $20$ (or so) "important" distribution is because they are very useful. For example, the normal distribution comes up almost everywhere due to the Central Limit Theorem, Student's $t$ distribution is the bread and butter of basic statistical hypothesis testing (and probably the most used and abused distribution in the medical research), Poisson distribution is the basic counting process that happens to be super useful and versatile in modelling real-world applications, and so on. That is, coming up with a new distribution shouldn't be that hard, coming up with a new analytically convenient distribution will be much harder and coming up with a new analytically convenient and useful distribution is very hard. Therefore, it is unlikely that new distributions, that I'm sure being invented and discovered pretty often, will become popular and widely used.
answered Jan 18 at 19:37
V. VancakV. Vancak
11.1k2926
$endgroup$
$begingroup$
Thanks for the answer. Just to clear things up, I am in no way interested in naming anything after me. It was just to emphasize the point.
$endgroup$
– MathIsLife12
Jan 18 at 19:38
add a comment |
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%2f3078643%2fwhat-makes-statistical-distributions-so-unique%23new-answer', 'question_page');
}
);
Post as a guest
Required, but never shown
1 Answer
1
active
oldest
votes
1 Answer
1
active
oldest
votes
active
oldest
votes
active
oldest
votes
$begingroup$
Naming something after yourself maybe considered inappropriate. If the distribution that you discovered is important and useful enough then probably other researchers will already name if after you. Regarding the first question -
"Why can't anyone just come up with a distribution which is some combination of other random variables?"
You can, but the question is $(1)$ why is your distribution important and $(2)$ what it can be used for?
The fact that there are around $20$ (or so) "important" distribution is because they are very useful. For example, the normal distribution comes up almost everywhere due to the Central Limit Theorem, Student's $t$ distribution is the bread and butter of basic statistical hypothesis testing (and probably the most used and abused distribution in the medical research), Poisson distribution is the basic counting process that happens to be super useful and versatile in modelling real-world applications, and so on. That is, coming up with a new distribution shouldn't be that hard, coming up with a new analytically convenient distribution will be much harder and coming up with a new analytically convenient and useful distribution is very hard. Therefore, it is unlikely that new distributions, that I'm sure being invented and discovered pretty often, will become popular and widely used.
answered Jan 18 at 19:37
V. VancakV. Vancak
11.1k2926
$endgroup$
$begingroup$
Thanks for the answer. Just to clear things up, I am in no way interested in naming anything after me. It was just to emphasize the point.
$endgroup$
– MathIsLife12
Jan 18 at 19:38
add a comment |
$begingroup$
Naming something after yourself maybe considered inappropriate. If the distribution that you discovered is important and useful enough then probably other researchers will already name if after you. Regarding the first question -
"Why can't anyone just come up with a distribution which is some combination of other random variables?"
You can, but the question is $(1)$ why is your distribution important and $(2)$ what it can be used for?
The fact that there are around $20$ (or so) "important" distribution is because they are very useful. For example, the normal distribution comes up almost everywhere due to the Central Limit Theorem, Student's $t$ distribution is the bread and butter of basic statistical hypothesis testing (and probably the most used and abused distribution in the medical research), Poisson distribution is the basic counting process that happens to be super useful and versatile in modelling real-world applications, and so on. That is, coming up with a new distribution shouldn't be that hard, coming up with a new analytically convenient distribution will be much harder and coming up with a new analytically convenient and useful distribution is very hard. Therefore, it is unlikely that new distributions, that I'm sure being invented and discovered pretty often, will become popular and widely used.
answered Jan 18 at 19:37
V. VancakV. Vancak
11.1k2926
$endgroup$
$begingroup$
Thanks for the answer. Just to clear things up, I am in no way interested in naming anything after me. It was just to emphasize the point.
$endgroup$
– MathIsLife12
Jan 18 at 19:38
add a comment |
$begingroup$
Naming something after yourself maybe considered inappropriate. If the distribution that you discovered is important and useful enough then probably other researchers will already name if after you. Regarding the first question -
"Why can't anyone just come up with a distribution which is some combination of other random variables?"
You can, but the question is $(1)$ why is your distribution important and $(2)$ what it can be used for?
The fact that there are around $20$ (or so) "important" distribution is because they are very useful. For example, the normal distribution comes up almost everywhere due to the Central Limit Theorem, Student's $t$ distribution is the bread and butter of basic statistical hypothesis testing (and probably the most used and abused distribution in the medical research), Poisson distribution is the basic counting process that happens to be super useful and versatile in modelling real-world applications, and so on. That is, coming up with a new distribution shouldn't be that hard, coming up with a new analytically convenient distribution will be much harder and coming up with a new analytically convenient and useful distribution is very hard. Therefore, it is unlikely that new distributions, that I'm sure being invented and discovered pretty often, will become popular and widely used.
answered Jan 18 at 19:37
V. VancakV. Vancak
11.1k2926
$endgroup$
Naming something after yourself maybe considered inappropriate. If the distribution that you discovered is important and useful enough then probably other researchers will already name if after you. Regarding the first question -
"Why can't anyone just come up with a distribution which is some combination of other random variables?"
You can, but the question is $(1)$ why is your distribution important and $(2)$ what it can be used for?
The fact that there are around $20$ (or so) "important" distribution is because they are very useful. For example, the normal distribution comes up almost everywhere due to the Central Limit Theorem, Student's $t$ distribution is the bread and butter of basic statistical hypothesis testing (and probably the most used and abused distribution in the medical research), Poisson distribution is the basic counting process that happens to be super useful and versatile in modelling real-world applications, and so on. That is, coming up with a new distribution shouldn't be that hard, coming up with a new analytically convenient distribution will be much harder and coming up with a new analytically convenient and useful distribution is very hard. Therefore, it is unlikely that new distributions, that I'm sure being invented and discovered pretty often, will become popular and widely used.
answered Jan 18 at 19:37
V. VancakV. Vancak
11.1k2926
answered Jan 18 at 19:37
V. VancakV. Vancak
11.1k2926
answered Jan 18 at 19:37
V. VancakV. Vancak
11.1k2926
answered Jan 18 at 19:37
V. VancakV. Vancak
11.1k2926
11.1k2926
$begingroup$
Thanks for the answer. Just to clear things up, I am in no way interested in naming anything after me. It was just to emphasize the point.
$endgroup$
– MathIsLife12
Jan 18 at 19:38
add a comment |
$begingroup$
Thanks for the answer. Just to clear things up, I am in no way interested in naming anything after me. It was just to emphasize the point.
$endgroup$
– MathIsLife12
Jan 18 at 19:38
$begingroup$
Thanks for the answer. Just to clear things up, I am in no way interested in naming anything after me. It was just to emphasize the point.
$endgroup$
– MathIsLife12
Jan 18 at 19:38
$begingroup$
Thanks for the answer. Just to clear things up, I am in no way interested in naming anything after me. It was just to emphasize the point.
$endgroup$
– MathIsLife12
Jan 18 at 19:38
add a comment |
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%2f3078643%2fwhat-makes-statistical-distributions-so-unique%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
$begingroup$
Of course you can just come up with a distribution and name it after yourself. But (1) that disitribution may not be interesting (in the sense of having important applications), and (2) it’s likely someone else has already come up with that distribution, so you better not expect everyone to call it by the name you've given it if people already call it something else.
$endgroup$
– symplectomorphic
Jan 18 at 19:23
1
$begingroup$
In this case, “Student’s T” distribution (which has an interesting history regarding its name, in fact) has important applications in the theory of statistical inference.
$endgroup$
– symplectomorphic
Jan 18 at 19:25
$begingroup$
The Student's $t$ distribution was in effect developed by "Student" whose real name was William Sealy Gosset who was hiding his name on his employer's instruction. It was named (including the "t") by R.A.Fisher. So it is difficult to say either named it after himself.
$endgroup$
– Henry
Jan 18 at 19:45