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What is the formal definition of “probability distribution”
1
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Can someone please provide a useful reference on the definition of probabilistic distribution.
A very popular site (top of Google search) states:
A probability distribution is a table or an equation that links each outcome of a statistical experiment with its probability of occurrence.
https://stattrek.com/probability-distributions/probability-distribution.aspx
I feel that this definition is very unsatisfactory. I need a better one with a reference.
Thank you!
probability statistics probability-distributions reference-request
edited Feb 3 at 19:29
Pedro
10.9k23475
asked Feb 1 at 6:44
The man of your dreamThe man of your dream
23110
$endgroup$
add a comment |
1
$begingroup$
Can someone please provide a useful reference on the definition of probabilistic distribution.
A very popular site (top of Google search) states:
A probability distribution is a table or an equation that links each outcome of a statistical experiment with its probability of occurrence.
https://stattrek.com/probability-distributions/probability-distribution.aspx
I feel that this definition is very unsatisfactory. I need a better one with a reference.
Thank you!
probability statistics probability-distributions reference-request
edited Feb 3 at 19:29
Pedro
10.9k23475
asked Feb 1 at 6:44
The man of your dreamThe man of your dream
23110
$endgroup$
$begingroup$
I think the term "probability distribution" is more common than "probabilistic distribution" (which I haven't heard anyone use), so maybe for clarity the question should ask for a definition of "probability distribution". I too would like to know the consensus about what precisely this term means, because I have heard it used in different ways. Sometimes it seems to be used interchangeably with the term "probability measure". However, I think the term "distribution" refers specifically to the distribution of a random variable $X$, which is the probability measure on $mathbb R$ induced by $X$.
$endgroup$
– littleO
Feb 1 at 6:52
1
$begingroup$
Nonnegative measure of unit total mass.
$endgroup$
– Did
Feb 1 at 6:55
$begingroup$
@Did So just to confirm, that means the term "probability distribution" means exactly the same thing as "probability measure"?
$endgroup$
– littleO
Feb 1 at 6:59
1
$begingroup$
@littleO Yes, although the term "probability distribution" points at the possibility that one would introduce a random variable with this measure as distribution.
$endgroup$
– Did
Feb 1 at 7:03
add a comment |
1
1
1
$begingroup$
Can someone please provide a useful reference on the definition of probabilistic distribution.
A very popular site (top of Google search) states:
A probability distribution is a table or an equation that links each outcome of a statistical experiment with its probability of occurrence.
https://stattrek.com/probability-distributions/probability-distribution.aspx
I feel that this definition is very unsatisfactory. I need a better one with a reference.
Thank you!
probability statistics probability-distributions reference-request
edited Feb 3 at 19:29
Pedro
10.9k23475
asked Feb 1 at 6:44
The man of your dreamThe man of your dream
23110
$endgroup$
Can someone please provide a useful reference on the definition of probabilistic distribution.
A very popular site (top of Google search) states:
A probability distribution is a table or an equation that links each outcome of a statistical experiment with its probability of occurrence.
https://stattrek.com/probability-distributions/probability-distribution.aspx
I feel that this definition is very unsatisfactory. I need a better one with a reference.
Thank you!
probability statistics probability-distributions reference-request
probability statistics probability-distributions reference-request
edited Feb 3 at 19:29
Pedro
10.9k23475
asked Feb 1 at 6:44
The man of your dreamThe man of your dream
23110
edited Feb 3 at 19:29
Pedro
10.9k23475
asked Feb 1 at 6:44
The man of your dreamThe man of your dream
23110
edited Feb 3 at 19:29
Pedro
10.9k23475
edited Feb 3 at 19:29
Pedro
10.9k23475
edited Feb 3 at 19:29
Pedro
10.9k23475
10.9k23475
asked Feb 1 at 6:44
The man of your dreamThe man of your dream
23110
asked Feb 1 at 6:44
The man of your dreamThe man of your dream
23110
asked Feb 1 at 6:44
The man of your dreamThe man of your dream
23110
23110
$begingroup$
I think the term "probability distribution" is more common than "probabilistic distribution" (which I haven't heard anyone use), so maybe for clarity the question should ask for a definition of "probability distribution". I too would like to know the consensus about what precisely this term means, because I have heard it used in different ways. Sometimes it seems to be used interchangeably with the term "probability measure". However, I think the term "distribution" refers specifically to the distribution of a random variable $X$, which is the probability measure on $mathbb R$ induced by $X$.
$endgroup$
– littleO
Feb 1 at 6:52
1
$begingroup$
Nonnegative measure of unit total mass.
$endgroup$
– Did
Feb 1 at 6:55
$begingroup$
@Did So just to confirm, that means the term "probability distribution" means exactly the same thing as "probability measure"?
$endgroup$
– littleO
Feb 1 at 6:59
1
$begingroup$
@littleO Yes, although the term "probability distribution" points at the possibility that one would introduce a random variable with this measure as distribution.
$endgroup$
– Did
Feb 1 at 7:03
add a comment |
$begingroup$
I think the term "probability distribution" is more common than "probabilistic distribution" (which I haven't heard anyone use), so maybe for clarity the question should ask for a definition of "probability distribution". I too would like to know the consensus about what precisely this term means, because I have heard it used in different ways. Sometimes it seems to be used interchangeably with the term "probability measure". However, I think the term "distribution" refers specifically to the distribution of a random variable $X$, which is the probability measure on $mathbb R$ induced by $X$.
$endgroup$
– littleO
Feb 1 at 6:52
1
$begingroup$
Nonnegative measure of unit total mass.
$endgroup$
– Did
Feb 1 at 6:55
$begingroup$
@Did So just to confirm, that means the term "probability distribution" means exactly the same thing as "probability measure"?
$endgroup$
– littleO
Feb 1 at 6:59
1
$begingroup$
@littleO Yes, although the term "probability distribution" points at the possibility that one would introduce a random variable with this measure as distribution.
$endgroup$
– Did
Feb 1 at 7:03
$begingroup$
I think the term "probability distribution" is more common than "probabilistic distribution" (which I haven't heard anyone use), so maybe for clarity the question should ask for a definition of "probability distribution". I too would like to know the consensus about what precisely this term means, because I have heard it used in different ways. Sometimes it seems to be used interchangeably with the term "probability measure". However, I think the term "distribution" refers specifically to the distribution of a random variable $X$, which is the probability measure on $mathbb R$ induced by $X$.
$endgroup$
– littleO
Feb 1 at 6:52
$begingroup$
I think the term "probability distribution" is more common than "probabilistic distribution" (which I haven't heard anyone use), so maybe for clarity the question should ask for a definition of "probability distribution". I too would like to know the consensus about what precisely this term means, because I have heard it used in different ways. Sometimes it seems to be used interchangeably with the term "probability measure". However, I think the term "distribution" refers specifically to the distribution of a random variable $X$, which is the probability measure on $mathbb R$ induced by $X$.
$endgroup$
– littleO
Feb 1 at 6:52
1
1
$begingroup$
Nonnegative measure of unit total mass.
$endgroup$
– Did
Feb 1 at 6:55
$begingroup$
Nonnegative measure of unit total mass.
$endgroup$
– Did
Feb 1 at 6:55
$begingroup$
@Did So just to confirm, that means the term "probability distribution" means exactly the same thing as "probability measure"?
$endgroup$
– littleO
Feb 1 at 6:59
$begingroup$
@Did So just to confirm, that means the term "probability distribution" means exactly the same thing as "probability measure"?
$endgroup$
– littleO
Feb 1 at 6:59
1
1
$begingroup$
@littleO Yes, although the term "probability distribution" points at the possibility that one would introduce a random variable with this measure as distribution.
$endgroup$
– Did
Feb 1 at 7:03
$begingroup$
@littleO Yes, although the term "probability distribution" points at the possibility that one would introduce a random variable with this measure as distribution.
$endgroup$
– Did
Feb 1 at 7:03
add a comment |
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$begingroup$
I think the term "probability distribution" is more common than "probabilistic distribution" (which I haven't heard anyone use), so maybe for clarity the question should ask for a definition of "probability distribution". I too would like to know the consensus about what precisely this term means, because I have heard it used in different ways. Sometimes it seems to be used interchangeably with the term "probability measure". However, I think the term "distribution" refers specifically to the distribution of a random variable $X$, which is the probability measure on $mathbb R$ induced by $X$.
$endgroup$
– littleO
Feb 1 at 6:52
1
$begingroup$
Nonnegative measure of unit total mass.
$endgroup$
– Did
Feb 1 at 6:55
$begingroup$
@Did So just to confirm, that means the term "probability distribution" means exactly the same thing as "probability measure"?
$endgroup$
– littleO
Feb 1 at 6:59
1
$begingroup$
@littleO Yes, although the term "probability distribution" points at the possibility that one would introduce a random variable with this measure as distribution.
$endgroup$
– Did
Feb 1 at 7:03