Mixing
Are all continuous random variables normally distributed?
Clash Royale CLAN TAG#URR8PPP
.everyoneloves__top-leaderboard:empty,.everyoneloves__mid-leaderboard:empty margin-bottom:0;
up vote
3
down vote
favorite
All the time I see examples of the normal/Gaussian distribution with continuous random variables. So my question is do all continuous random variables have a Gaussian distribution?
mathematical-statistics normal-distribution
edited Aug 13 at 16:16
Alexis
15.2k34492
asked Aug 13 at 16:01
Manikantha Nekkalapudi
275
 |Â
show 3 more comments
up vote
3
down vote
favorite
All the time I see examples of the normal/Gaussian distribution with continuous random variables. So my question is do all continuous random variables have a Gaussian distribution?
mathematical-statistics normal-distribution
edited Aug 13 at 16:16
Alexis
15.2k34492
asked Aug 13 at 16:01
Manikantha Nekkalapudi
275
2
For some examples there a triangle, gamma and beta distributions and others?
– Michael Chernick
Aug 13 at 16:24
2
@MichaelChernick Links help: triangle distribution, gamma distribution, beta distribution. :)
– Alexis
Aug 13 at 16:28
7
It's easy to construct a non-normally distributed continuous random variable: Draw any PDF-looking function with finite area underneath it, and normalize it so the area underneath it is 1. You can image a PDF that isn't bell-shaped.
– Nuclear Wang
Aug 13 at 16:35
3
Note that even if a distribution looks "normally distributed, it may not actually be normally distributed
– Silverfish
Aug 13 at 19:13
3
Imagine listening for the next peal of thunder in a thunderstorm. You'll usually wait only a few seconds, but might wait much longer. Clearly this cannot be symmetric, so cannot be normally distributed. Or consider the distribution of annual incomes -- in western countries, median income will be in the tens of thousands of dollars (a bit under $60K in the US). But many incomes are well over ten times that average. Again, it won't be symmetric so cannot possibly be normally distributed.
– Glen_b♦
Aug 14 at 4:46
 |Â
show 3 more comments
up vote
3
down vote
favorite
up vote
3
down vote
favorite
All the time I see examples of the normal/Gaussian distribution with continuous random variables. So my question is do all continuous random variables have a Gaussian distribution?
mathematical-statistics normal-distribution
edited Aug 13 at 16:16
Alexis
15.2k34492
asked Aug 13 at 16:01
Manikantha Nekkalapudi
275
All the time I see examples of the normal/Gaussian distribution with continuous random variables. So my question is do all continuous random variables have a Gaussian distribution?
mathematical-statistics normal-distribution
edited Aug 13 at 16:16
Alexis
15.2k34492
asked Aug 13 at 16:01
Manikantha Nekkalapudi
275
edited Aug 13 at 16:16
Alexis
15.2k34492
edited Aug 13 at 16:16
Alexis
15.2k34492
edited Aug 13 at 16:16
Alexis
15.2k34492
15.2k34492
asked Aug 13 at 16:01
Manikantha Nekkalapudi
275
asked Aug 13 at 16:01
Manikantha Nekkalapudi
275
asked Aug 13 at 16:01
Manikantha Nekkalapudi
275
275
2
For some examples there a triangle, gamma and beta distributions and others?
– Michael Chernick
Aug 13 at 16:24
2
@MichaelChernick Links help: triangle distribution, gamma distribution, beta distribution. :)
– Alexis
Aug 13 at 16:28
7
It's easy to construct a non-normally distributed continuous random variable: Draw any PDF-looking function with finite area underneath it, and normalize it so the area underneath it is 1. You can image a PDF that isn't bell-shaped.
– Nuclear Wang
Aug 13 at 16:35
3
Note that even if a distribution looks "normally distributed, it may not actually be normally distributed
– Silverfish
Aug 13 at 19:13
3
Imagine listening for the next peal of thunder in a thunderstorm. You'll usually wait only a few seconds, but might wait much longer. Clearly this cannot be symmetric, so cannot be normally distributed. Or consider the distribution of annual incomes -- in western countries, median income will be in the tens of thousands of dollars (a bit under $60K in the US). But many incomes are well over ten times that average. Again, it won't be symmetric so cannot possibly be normally distributed.
– Glen_b♦
Aug 14 at 4:46
 |Â
show 3 more comments
2
For some examples there a triangle, gamma and beta distributions and others?
– Michael Chernick
Aug 13 at 16:24
2
@MichaelChernick Links help: triangle distribution, gamma distribution, beta distribution. :)
– Alexis
Aug 13 at 16:28
7
It's easy to construct a non-normally distributed continuous random variable: Draw any PDF-looking function with finite area underneath it, and normalize it so the area underneath it is 1. You can image a PDF that isn't bell-shaped.
– Nuclear Wang
Aug 13 at 16:35
3
Note that even if a distribution looks "normally distributed, it may not actually be normally distributed
– Silverfish
Aug 13 at 19:13
3
Imagine listening for the next peal of thunder in a thunderstorm. You'll usually wait only a few seconds, but might wait much longer. Clearly this cannot be symmetric, so cannot be normally distributed. Or consider the distribution of annual incomes -- in western countries, median income will be in the tens of thousands of dollars (a bit under $60K in the US). But many incomes are well over ten times that average. Again, it won't be symmetric so cannot possibly be normally distributed.
– Glen_b♦
Aug 14 at 4:46
2
2
For some examples there a triangle, gamma and beta distributions and others?
– Michael Chernick
Aug 13 at 16:24
For some examples there a triangle, gamma and beta distributions and others?
– Michael Chernick
Aug 13 at 16:24
2
2
@MichaelChernick Links help: triangle distribution, gamma distribution, beta distribution. :)
– Alexis
Aug 13 at 16:28
@MichaelChernick Links help: triangle distribution, gamma distribution, beta distribution. :)
– Alexis
Aug 13 at 16:28
7
7
It's easy to construct a non-normally distributed continuous random variable: Draw any PDF-looking function with finite area underneath it, and normalize it so the area underneath it is 1. You can image a PDF that isn't bell-shaped.
– Nuclear Wang
Aug 13 at 16:35
It's easy to construct a non-normally distributed continuous random variable: Draw any PDF-looking function with finite area underneath it, and normalize it so the area underneath it is 1. You can image a PDF that isn't bell-shaped.
– Nuclear Wang
Aug 13 at 16:35
3
3
Note that even if a distribution looks "normally distributed, it may not actually be normally distributed
– Silverfish
Aug 13 at 19:13
Note that even if a distribution looks "normally distributed, it may not actually be normally distributed
– Silverfish
Aug 13 at 19:13
3
3
Imagine listening for the next peal of thunder in a thunderstorm. You'll usually wait only a few seconds, but might wait much longer. Clearly this cannot be symmetric, so cannot be normally distributed. Or consider the distribution of annual incomes -- in western countries, median income will be in the tens of thousands of dollars (a bit under $60K in the US). But many incomes are well over ten times that average. Again, it won't be symmetric so cannot possibly be normally distributed.
– Glen_b♦
Aug 14 at 4:46
Imagine listening for the next peal of thunder in a thunderstorm. You'll usually wait only a few seconds, but might wait much longer. Clearly this cannot be symmetric, so cannot be normally distributed. Or consider the distribution of annual incomes -- in western countries, median income will be in the tens of thousands of dollars (a bit under $60K in the US). But many incomes are well over ten times that average. Again, it won't be symmetric so cannot possibly be normally distributed.
– Glen_b♦
Aug 14 at 4:46
 |Â
show 3 more comments
3 Answers
3
active
oldest
votes
up vote
9
down vote
accepted
No.
Lots of real life variables have distributions which are better described as other distributions. t-distributions (heavier tails) are common, as are various skewed distributions, for example, many real measurements must be positive, so greater than or equal to zero, but can have a long tail of high values. Quite a lot of real world data is counts, or similar integer data, which is often better described by a Poisson distribution.
In my personal experience, in epidemiology, bio-medicine, and sociology, genuinely 'normal' distributions, that is real data which can best described as a normal distribution, are uncommon, but it does depend on the filed you work in, and exactly what data you are looking at.
answered Aug 13 at 16:14
astaines
30625
add a comment |Â
up vote
19
down vote
No.
There are many continuous probability distributions out of all the probability distributions. There are whole books containing nothing but such things.
Some of the non-normal continuous distributions introduced to new students of statistics include:
- The continuous uniform distribution
Student's T distribution- The exponential distribution
The normal/Gaussian distribution is important because of the Central Limit Theorem (CLT), which shows that for very many situations the sum of randomly distributed independent variables will tend to have a normal distribution, regardless of the constituent variables' original distributions. This can be useful for performing certain kinds of commonly-used statistical inference, which probably contributes to the frequency with which one encounters the normal/Gaussian distribution. Student's T distribution mentioned above gives some formalism to the "tend" in the CLT's "...will tend to have a normal distribution...", and is therefore also useful in these commonly used forms of statistical inference.
answered Aug 13 at 16:12
Alexis
15.2k34492
add a comment |Â
up vote
2
down vote
Not necessarily. The shape of the distribution is contingent on the continuous random variable's PDF - which isn't expressly Gaussian. Some counterexamples include the student-t distribution and the Laplace distribution.
answered Aug 13 at 21:28
Pranav Vempati
214
add a comment |Â
3 Answers
3
active
oldest
votes
3 Answers
3
active
oldest
votes
active
oldest
votes
active
oldest
votes
up vote
9
down vote
accepted
No.
Lots of real life variables have distributions which are better described as other distributions. t-distributions (heavier tails) are common, as are various skewed distributions, for example, many real measurements must be positive, so greater than or equal to zero, but can have a long tail of high values. Quite a lot of real world data is counts, or similar integer data, which is often better described by a Poisson distribution.
In my personal experience, in epidemiology, bio-medicine, and sociology, genuinely 'normal' distributions, that is real data which can best described as a normal distribution, are uncommon, but it does depend on the filed you work in, and exactly what data you are looking at.
answered Aug 13 at 16:14
astaines
30625
add a comment |Â
up vote
9
down vote
accepted
No.
Lots of real life variables have distributions which are better described as other distributions. t-distributions (heavier tails) are common, as are various skewed distributions, for example, many real measurements must be positive, so greater than or equal to zero, but can have a long tail of high values. Quite a lot of real world data is counts, or similar integer data, which is often better described by a Poisson distribution.
In my personal experience, in epidemiology, bio-medicine, and sociology, genuinely 'normal' distributions, that is real data which can best described as a normal distribution, are uncommon, but it does depend on the filed you work in, and exactly what data you are looking at.
answered Aug 13 at 16:14
astaines
30625
add a comment |Â
up vote
9
down vote
accepted
up vote
9
down vote
accepted
No.
Lots of real life variables have distributions which are better described as other distributions. t-distributions (heavier tails) are common, as are various skewed distributions, for example, many real measurements must be positive, so greater than or equal to zero, but can have a long tail of high values. Quite a lot of real world data is counts, or similar integer data, which is often better described by a Poisson distribution.
In my personal experience, in epidemiology, bio-medicine, and sociology, genuinely 'normal' distributions, that is real data which can best described as a normal distribution, are uncommon, but it does depend on the filed you work in, and exactly what data you are looking at.
answered Aug 13 at 16:14
astaines
30625
No.
Lots of real life variables have distributions which are better described as other distributions. t-distributions (heavier tails) are common, as are various skewed distributions, for example, many real measurements must be positive, so greater than or equal to zero, but can have a long tail of high values. Quite a lot of real world data is counts, or similar integer data, which is often better described by a Poisson distribution.
In my personal experience, in epidemiology, bio-medicine, and sociology, genuinely 'normal' distributions, that is real data which can best described as a normal distribution, are uncommon, but it does depend on the filed you work in, and exactly what data you are looking at.
answered Aug 13 at 16:14
astaines
30625
answered Aug 13 at 16:14
astaines
30625
answered Aug 13 at 16:14
astaines
30625
answered Aug 13 at 16:14
astaines
30625
30625
add a comment |Â
add a comment |Â
up vote
19
down vote
No.
There are many continuous probability distributions out of all the probability distributions. There are whole books containing nothing but such things.
Some of the non-normal continuous distributions introduced to new students of statistics include:
- The continuous uniform distribution
Student's T distribution- The exponential distribution
The normal/Gaussian distribution is important because of the Central Limit Theorem (CLT), which shows that for very many situations the sum of randomly distributed independent variables will tend to have a normal distribution, regardless of the constituent variables' original distributions. This can be useful for performing certain kinds of commonly-used statistical inference, which probably contributes to the frequency with which one encounters the normal/Gaussian distribution. Student's T distribution mentioned above gives some formalism to the "tend" in the CLT's "...will tend to have a normal distribution...", and is therefore also useful in these commonly used forms of statistical inference.
answered Aug 13 at 16:12
Alexis
15.2k34492
add a comment |Â
up vote
19
down vote
No.
There are many continuous probability distributions out of all the probability distributions. There are whole books containing nothing but such things.
Some of the non-normal continuous distributions introduced to new students of statistics include:
- The continuous uniform distribution
Student's T distribution- The exponential distribution
The normal/Gaussian distribution is important because of the Central Limit Theorem (CLT), which shows that for very many situations the sum of randomly distributed independent variables will tend to have a normal distribution, regardless of the constituent variables' original distributions. This can be useful for performing certain kinds of commonly-used statistical inference, which probably contributes to the frequency with which one encounters the normal/Gaussian distribution. Student's T distribution mentioned above gives some formalism to the "tend" in the CLT's "...will tend to have a normal distribution...", and is therefore also useful in these commonly used forms of statistical inference.
answered Aug 13 at 16:12
Alexis
15.2k34492
add a comment |Â
up vote
19
down vote
up vote
19
down vote
No.
There are many continuous probability distributions out of all the probability distributions. There are whole books containing nothing but such things.
Some of the non-normal continuous distributions introduced to new students of statistics include:
- The continuous uniform distribution
Student's T distribution- The exponential distribution
The normal/Gaussian distribution is important because of the Central Limit Theorem (CLT), which shows that for very many situations the sum of randomly distributed independent variables will tend to have a normal distribution, regardless of the constituent variables' original distributions. This can be useful for performing certain kinds of commonly-used statistical inference, which probably contributes to the frequency with which one encounters the normal/Gaussian distribution. Student's T distribution mentioned above gives some formalism to the "tend" in the CLT's "...will tend to have a normal distribution...", and is therefore also useful in these commonly used forms of statistical inference.
answered Aug 13 at 16:12
Alexis
15.2k34492
No.
There are many continuous probability distributions out of all the probability distributions. There are whole books containing nothing but such things.
Some of the non-normal continuous distributions introduced to new students of statistics include:
- The continuous uniform distribution
Student's T distribution- The exponential distribution
The normal/Gaussian distribution is important because of the Central Limit Theorem (CLT), which shows that for very many situations the sum of randomly distributed independent variables will tend to have a normal distribution, regardless of the constituent variables' original distributions. This can be useful for performing certain kinds of commonly-used statistical inference, which probably contributes to the frequency with which one encounters the normal/Gaussian distribution. Student's T distribution mentioned above gives some formalism to the "tend" in the CLT's "...will tend to have a normal distribution...", and is therefore also useful in these commonly used forms of statistical inference.
answered Aug 13 at 16:12
Alexis
15.2k34492
edited Aug 13 at 16:25
answered Aug 13 at 16:12
Alexis
15.2k34492
answered Aug 13 at 16:12
Alexis
15.2k34492
answered Aug 13 at 16:12
Alexis
15.2k34492
15.2k34492
add a comment |Â
add a comment |Â
up vote
2
down vote
Not necessarily. The shape of the distribution is contingent on the continuous random variable's PDF - which isn't expressly Gaussian. Some counterexamples include the student-t distribution and the Laplace distribution.
answered Aug 13 at 21:28
Pranav Vempati
214
add a comment |Â
up vote
2
down vote
Not necessarily. The shape of the distribution is contingent on the continuous random variable's PDF - which isn't expressly Gaussian. Some counterexamples include the student-t distribution and the Laplace distribution.
answered Aug 13 at 21:28
Pranav Vempati
214
add a comment |Â
up vote
2
down vote
up vote
2
down vote
Not necessarily. The shape of the distribution is contingent on the continuous random variable's PDF - which isn't expressly Gaussian. Some counterexamples include the student-t distribution and the Laplace distribution.
answered Aug 13 at 21:28
Pranav Vempati
214
Not necessarily. The shape of the distribution is contingent on the continuous random variable's PDF - which isn't expressly Gaussian. Some counterexamples include the student-t distribution and the Laplace distribution.
answered Aug 13 at 21:28
Pranav Vempati
214
answered Aug 13 at 21:28
Pranav Vempati
214
answered Aug 13 at 21:28
Pranav Vempati
214
answered Aug 13 at 21:28
Pranav Vempati
214
214
add a comment |Â
add a comment |Â
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
StackExchange.ready(
function ()
StackExchange.openid.initPostLogin('.new-post-login', 'https%3a%2f%2fstats.stackexchange.com%2fquestions%2f362013%2fare-all-continuous-random-variables-normally-distributed%23new-answer', 'question_page');
);
Post as a guest
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
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
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
2
For some examples there a triangle, gamma and beta distributions and others?
– Michael Chernick
Aug 13 at 16:24
2
@MichaelChernick Links help: triangle distribution, gamma distribution, beta distribution. :)
– Alexis
Aug 13 at 16:28
7
It's easy to construct a non-normally distributed continuous random variable: Draw any PDF-looking function with finite area underneath it, and normalize it so the area underneath it is 1. You can image a PDF that isn't bell-shaped.
– Nuclear Wang
Aug 13 at 16:35
3
Note that even if a distribution looks "normally distributed, it may not actually be normally distributed
– Silverfish
Aug 13 at 19:13
3
Imagine listening for the next peal of thunder in a thunderstorm. You'll usually wait only a few seconds, but might wait much longer. Clearly this cannot be symmetric, so cannot be normally distributed. Or consider the distribution of annual incomes -- in western countries, median income will be in the tens of thousands of dollars (a bit under $60K in the US). But many incomes are well over ten times that average. Again, it won't be symmetric so cannot possibly be normally distributed.
– Glen_b♦
Aug 14 at 4:46