Mixing
Domain of Central Limit Theorem
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The central limit theorem says that if you take infinite number of samples ( > 30) from a population, compute their mean values, and collect them, you will reach normal distribution. Is this valid for other parameters?
What I mean in this question is if we take infinite number of samples, compute their variances or any other parameter, and collect them, do we construct a normal distribution ?
Answer:
I made some researches to check if we can expand Central Limit Theorem for all parameters, and we could not find an academic or experimental document. However, I wrote its code. By using random number generator, I generated samples of numbers between 1 and 6, which means I imitated rolling dice problem. I created 100 000 samples and each of them consists of 300 observations(numbers). I drew its distribution plot with the help of Seaborn. As a result, Sampling distributions of sample variance and sample standard deviation are also like normal distribution.
normal-distribution central-limit-theorem parameter-estimation
asked Jan 6 at 14:14
GoktugGoktug
1356
$endgroup$
add a comment |
$begingroup$
The central limit theorem says that if you take infinite number of samples ( > 30) from a population, compute their mean values, and collect them, you will reach normal distribution. Is this valid for other parameters?
What I mean in this question is if we take infinite number of samples, compute their variances or any other parameter, and collect them, do we construct a normal distribution ?
Answer:
I made some researches to check if we can expand Central Limit Theorem for all parameters, and we could not find an academic or experimental document. However, I wrote its code. By using random number generator, I generated samples of numbers between 1 and 6, which means I imitated rolling dice problem. I created 100 000 samples and each of them consists of 300 observations(numbers). I drew its distribution plot with the help of Seaborn. As a result, Sampling distributions of sample variance and sample standard deviation are also like normal distribution.
normal-distribution central-limit-theorem parameter-estimation
asked Jan 6 at 14:14
GoktugGoktug
1356
$endgroup$
$begingroup$
en.wikipedia.org/wiki/Central_limit_theorem
$endgroup$
– Math_QED
Jan 6 at 14:24
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This is a good question. You can easily find the answer if you search for something like “distribution of the sample variance” which I assume is what you mean. Also note that “too many” and “accumulate” don’t make much sense.
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– lcv
Jan 6 at 14:38
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Okey, I edited it with the wordsinfiniteandcollect.
$endgroup$
– Goktug
Jan 6 at 14:51
add a comment |
$begingroup$
The central limit theorem says that if you take infinite number of samples ( > 30) from a population, compute their mean values, and collect them, you will reach normal distribution. Is this valid for other parameters?
What I mean in this question is if we take infinite number of samples, compute their variances or any other parameter, and collect them, do we construct a normal distribution ?
Answer:
I made some researches to check if we can expand Central Limit Theorem for all parameters, and we could not find an academic or experimental document. However, I wrote its code. By using random number generator, I generated samples of numbers between 1 and 6, which means I imitated rolling dice problem. I created 100 000 samples and each of them consists of 300 observations(numbers). I drew its distribution plot with the help of Seaborn. As a result, Sampling distributions of sample variance and sample standard deviation are also like normal distribution.
normal-distribution central-limit-theorem parameter-estimation
asked Jan 6 at 14:14
GoktugGoktug
1356
$endgroup$
The central limit theorem says that if you take infinite number of samples ( > 30) from a population, compute their mean values, and collect them, you will reach normal distribution. Is this valid for other parameters?
What I mean in this question is if we take infinite number of samples, compute their variances or any other parameter, and collect them, do we construct a normal distribution ?
Answer:
I made some researches to check if we can expand Central Limit Theorem for all parameters, and we could not find an academic or experimental document. However, I wrote its code. By using random number generator, I generated samples of numbers between 1 and 6, which means I imitated rolling dice problem. I created 100 000 samples and each of them consists of 300 observations(numbers). I drew its distribution plot with the help of Seaborn. As a result, Sampling distributions of sample variance and sample standard deviation are also like normal distribution.
normal-distribution central-limit-theorem parameter-estimation
normal-distribution central-limit-theorem parameter-estimation
asked Jan 6 at 14:14
GoktugGoktug
1356
asked Jan 6 at 14:14
GoktugGoktug
1356
edited Jan 6 at 16:17
Goktug
asked Jan 6 at 14:14
GoktugGoktug
1356
asked Jan 6 at 14:14
GoktugGoktug
1356
asked Jan 6 at 14:14
GoktugGoktug
1356
1356
$begingroup$
en.wikipedia.org/wiki/Central_limit_theorem
$endgroup$
– Math_QED
Jan 6 at 14:24
$begingroup$
This is a good question. You can easily find the answer if you search for something like “distribution of the sample variance” which I assume is what you mean. Also note that “too many” and “accumulate” don’t make much sense.
$endgroup$
– lcv
Jan 6 at 14:38
$begingroup$
Okey, I edited it with the wordsinfiniteandcollect.
$endgroup$
– Goktug
Jan 6 at 14:51
add a comment |
$begingroup$
en.wikipedia.org/wiki/Central_limit_theorem
$endgroup$
– Math_QED
Jan 6 at 14:24
$begingroup$
This is a good question. You can easily find the answer if you search for something like “distribution of the sample variance” which I assume is what you mean. Also note that “too many” and “accumulate” don’t make much sense.
$endgroup$
– lcv
Jan 6 at 14:38
$begingroup$
Okey, I edited it with the wordsinfiniteandcollect.
$endgroup$
– Goktug
Jan 6 at 14:51
$begingroup$
en.wikipedia.org/wiki/Central_limit_theorem
$endgroup$
– Math_QED
Jan 6 at 14:24
$begingroup$
en.wikipedia.org/wiki/Central_limit_theorem
$endgroup$
– Math_QED
Jan 6 at 14:24
$begingroup$
This is a good question. You can easily find the answer if you search for something like “distribution of the sample variance” which I assume is what you mean. Also note that “too many” and “accumulate” don’t make much sense.
$endgroup$
– lcv
Jan 6 at 14:38
$begingroup$
This is a good question. You can easily find the answer if you search for something like “distribution of the sample variance” which I assume is what you mean. Also note that “too many” and “accumulate” don’t make much sense.
$endgroup$
– lcv
Jan 6 at 14:38
$begingroup$
Okey, I edited it with the words
infinite and collect.$endgroup$
– Goktug
Jan 6 at 14:51
$begingroup$
Okey, I edited it with the words
infinite and collect.$endgroup$
– Goktug
Jan 6 at 14:51
add a comment |
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$begingroup$
en.wikipedia.org/wiki/Central_limit_theorem
$endgroup$
– Math_QED
Jan 6 at 14:24
$begingroup$
This is a good question. You can easily find the answer if you search for something like “distribution of the sample variance” which I assume is what you mean. Also note that “too many” and “accumulate” don’t make much sense.
$endgroup$
– lcv
Jan 6 at 14:38
$begingroup$
Okey, I edited it with the words
infiniteandcollect.$endgroup$
– Goktug
Jan 6 at 14:51