Question regarding MLEMaximum Likelihood Estimation (MLE) in layman termsAsymptotically unbiased estimator using MLEMLE estimate of $beta/sigma$ - Linear regressionFind MLE on custom density functionHow can I prove the maximum likelihood estimate of $mu$ is actually a maximum likelihood estimate?Stuck on rejection region for Likelihood ratio testProving that MLE is max(x1,…,xn)Reasons for different parameters via MoM and MLEIs MLE intrinsically connected to logs?Sufficient Statistic and MLEMLE for Beta distribution, with $beta$ = 3
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Question regarding MLE
Maximum Likelihood Estimation (MLE) in layman termsAsymptotically unbiased estimator using MLEMLE estimate of $beta/sigma$ - Linear regressionFind MLE on custom density functionHow can I prove the maximum likelihood estimate of $mu$ is actually a maximum likelihood estimate?Stuck on rejection region for Likelihood ratio testProving that MLE is max(x1,…,xn)Reasons for different parameters via MoM and MLEIs MLE intrinsically connected to logs?Sufficient Statistic and MLEMLE for Beta distribution, with $beta$ = 3
.everyoneloves__top-leaderboard:empty,.everyoneloves__mid-leaderboard:empty,.everyoneloves__bot-mid-leaderboard:empty margin-bottom:0;
$begingroup$
I have a question regarding maximum likelihood estimators/functions. I thought I understood the concept. But now i found an example of an Maximum likelihood function that i don’t get.
The question is to find the MLE for a hypergeometric distribution of M
I would have said that the Likelihood function is for $x_1,.....,x_k$
$$L(M)=prod_i=1^kfracbinomMx_ibinomN-Mn-x_ibinomNn$$
But now i found a solution just stating it to be
$$L(M)=fracbinomMxbinomN-Mn-xbinomNn$$
I don’t get why i can loose the Product sign...
Thanks for your help!
maximum-likelihood hypergeometric
edited Apr 23 at 7:59
StubbornAtom
3,3611537
asked Apr 23 at 7:44
AngAng
917
$endgroup$
add a comment |
$begingroup$
I have a question regarding maximum likelihood estimators/functions. I thought I understood the concept. But now i found an example of an Maximum likelihood function that i don’t get.
The question is to find the MLE for a hypergeometric distribution of M
I would have said that the Likelihood function is for $x_1,.....,x_k$
$$L(M)=prod_i=1^kfracbinomMx_ibinomN-Mn-x_ibinomNn$$
But now i found a solution just stating it to be
$$L(M)=fracbinomMxbinomN-Mn-xbinomNn$$
I don’t get why i can loose the Product sign...
Thanks for your help!
maximum-likelihood hypergeometric
edited Apr 23 at 7:59
StubbornAtom
3,3611537
asked Apr 23 at 7:44
AngAng
917
$endgroup$
1
$begingroup$
Maybe there is only one sample, i.e. $x_1=x$?
$endgroup$
– gunes
Apr 23 at 7:55
1
$begingroup$
Typically an exercise question would consider a single observation for MLE of hypergeometric distribution.
$endgroup$
– StubbornAtom
Apr 23 at 8:02
add a comment |
$begingroup$
I have a question regarding maximum likelihood estimators/functions. I thought I understood the concept. But now i found an example of an Maximum likelihood function that i don’t get.
The question is to find the MLE for a hypergeometric distribution of M
I would have said that the Likelihood function is for $x_1,.....,x_k$
$$L(M)=prod_i=1^kfracbinomMx_ibinomN-Mn-x_ibinomNn$$
But now i found a solution just stating it to be
$$L(M)=fracbinomMxbinomN-Mn-xbinomNn$$
I don’t get why i can loose the Product sign...
Thanks for your help!
maximum-likelihood hypergeometric
edited Apr 23 at 7:59
StubbornAtom
3,3611537
asked Apr 23 at 7:44
AngAng
917
$endgroup$
I have a question regarding maximum likelihood estimators/functions. I thought I understood the concept. But now i found an example of an Maximum likelihood function that i don’t get.
The question is to find the MLE for a hypergeometric distribution of M
I would have said that the Likelihood function is for $x_1,.....,x_k$
$$L(M)=prod_i=1^kfracbinomMx_ibinomN-Mn-x_ibinomNn$$
But now i found a solution just stating it to be
$$L(M)=fracbinomMxbinomN-Mn-xbinomNn$$
I don’t get why i can loose the Product sign...
Thanks for your help!
maximum-likelihood hypergeometric
maximum-likelihood hypergeometric
edited Apr 23 at 7:59
StubbornAtom
3,3611537
asked Apr 23 at 7:44
AngAng
917
edited Apr 23 at 7:59
StubbornAtom
3,3611537
asked Apr 23 at 7:44
AngAng
917
edited Apr 23 at 7:59
StubbornAtom
3,3611537
edited Apr 23 at 7:59
StubbornAtom
3,3611537
edited Apr 23 at 7:59
StubbornAtom
3,3611537
3,3611537
asked Apr 23 at 7:44
AngAng
917
asked Apr 23 at 7:44
AngAng
917
asked Apr 23 at 7:44
AngAng
917
917
1
$begingroup$
Maybe there is only one sample, i.e. $x_1=x$?
$endgroup$
– gunes
Apr 23 at 7:55
1
$begingroup$
Typically an exercise question would consider a single observation for MLE of hypergeometric distribution.
$endgroup$
– StubbornAtom
Apr 23 at 8:02
add a comment |
1
$begingroup$
Maybe there is only one sample, i.e. $x_1=x$?
$endgroup$
– gunes
Apr 23 at 7:55
1
$begingroup$
Typically an exercise question would consider a single observation for MLE of hypergeometric distribution.
$endgroup$
– StubbornAtom
Apr 23 at 8:02
1
1
$begingroup$
Maybe there is only one sample, i.e. $x_1=x$?
$endgroup$
– gunes
Apr 23 at 7:55
$begingroup$
Maybe there is only one sample, i.e. $x_1=x$?
$endgroup$
– gunes
Apr 23 at 7:55
1
1
$begingroup$
Typically an exercise question would consider a single observation for MLE of hypergeometric distribution.
$endgroup$
– StubbornAtom
Apr 23 at 8:02
$begingroup$
Typically an exercise question would consider a single observation for MLE of hypergeometric distribution.
$endgroup$
– StubbornAtom
Apr 23 at 8:02
add a comment |
1 Answer
1
active
oldest
votes
$begingroup$
Your second formula is the probability mass function of hypergeometric distribution. Likelihood function $mathcalL$ is defined as probability mass (or density) function $f$ evaluated on some point $x$ that is maximized in terms of parameter $theta$
$$
mathcalL(theta|X) = f(X, theta)
$$
if you have more then one such point, you usually assume that they are independent and identically distributed (all come from the same distribution), what leads to likelihood defined in terms of all your data
$$
mathcalL(theta|X_1,X_2,dots,X_n) = prod_i=1^n f(X_i, theta)
$$
This is what the first formula is.
answered Apr 23 at 8:00
Tim♦Tim
61k9135230
$endgroup$
$begingroup$
The problem question, does state neither. that is why i would try to solve for any k. (X1....Xk)... my problem is that i have no idea how to solve it with the product sign.... i know i have to look at L(M)/L(M+1) and i can do that for the second formula without a problem. But i cant seem to get anywhere with the general form. (My math knowledge is not that great though....)
$endgroup$
– Ang
Apr 23 at 8:47
1
$begingroup$
@Ang sorry but I don't understand your comment. What exactly is the problem? Your question was asking about meaning of the $prod$ symbol, so I explained it.
$endgroup$
– Tim♦
Apr 23 at 8:50
$begingroup$
many thanks for that. i am sorry if i sounded rude, this was not my intent. how would one solve for the estimator with the product sign? i am getting nowhere when trying to solve....
$endgroup$
– Ang
Apr 23 at 8:56
$begingroup$
@Ang this seems to be separate question. Maybe post it as a separate question, with describing in greater detail how did you try solving it and where are you stuck.
$endgroup$
– Tim♦
Apr 23 at 9:01
$begingroup$
thanks! i will attempt a few more times and then post :) maybe i get lucky!
$endgroup$
– Ang
Apr 23 at 9:02
add a comment |
Your Answer
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1 Answer
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active
oldest
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1 Answer
1
active
oldest
votes
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votes
$begingroup$
Your second formula is the probability mass function of hypergeometric distribution. Likelihood function $mathcalL$ is defined as probability mass (or density) function $f$ evaluated on some point $x$ that is maximized in terms of parameter $theta$
$$
mathcalL(theta|X) = f(X, theta)
$$
if you have more then one such point, you usually assume that they are independent and identically distributed (all come from the same distribution), what leads to likelihood defined in terms of all your data
$$
mathcalL(theta|X_1,X_2,dots,X_n) = prod_i=1^n f(X_i, theta)
$$
This is what the first formula is.
answered Apr 23 at 8:00
Tim♦Tim
61k9135230
$endgroup$
$begingroup$
The problem question, does state neither. that is why i would try to solve for any k. (X1....Xk)... my problem is that i have no idea how to solve it with the product sign.... i know i have to look at L(M)/L(M+1) and i can do that for the second formula without a problem. But i cant seem to get anywhere with the general form. (My math knowledge is not that great though....)
$endgroup$
– Ang
Apr 23 at 8:47
1
$begingroup$
@Ang sorry but I don't understand your comment. What exactly is the problem? Your question was asking about meaning of the $prod$ symbol, so I explained it.
$endgroup$
– Tim♦
Apr 23 at 8:50
$begingroup$
many thanks for that. i am sorry if i sounded rude, this was not my intent. how would one solve for the estimator with the product sign? i am getting nowhere when trying to solve....
$endgroup$
– Ang
Apr 23 at 8:56
$begingroup$
@Ang this seems to be separate question. Maybe post it as a separate question, with describing in greater detail how did you try solving it and where are you stuck.
$endgroup$
– Tim♦
Apr 23 at 9:01
$begingroup$
thanks! i will attempt a few more times and then post :) maybe i get lucky!
$endgroup$
– Ang
Apr 23 at 9:02
add a comment |
$begingroup$
Your second formula is the probability mass function of hypergeometric distribution. Likelihood function $mathcalL$ is defined as probability mass (or density) function $f$ evaluated on some point $x$ that is maximized in terms of parameter $theta$
$$
mathcalL(theta|X) = f(X, theta)
$$
if you have more then one such point, you usually assume that they are independent and identically distributed (all come from the same distribution), what leads to likelihood defined in terms of all your data
$$
mathcalL(theta|X_1,X_2,dots,X_n) = prod_i=1^n f(X_i, theta)
$$
This is what the first formula is.
answered Apr 23 at 8:00
Tim♦Tim
61k9135230
$endgroup$
$begingroup$
The problem question, does state neither. that is why i would try to solve for any k. (X1....Xk)... my problem is that i have no idea how to solve it with the product sign.... i know i have to look at L(M)/L(M+1) and i can do that for the second formula without a problem. But i cant seem to get anywhere with the general form. (My math knowledge is not that great though....)
$endgroup$
– Ang
Apr 23 at 8:47
1
$begingroup$
@Ang sorry but I don't understand your comment. What exactly is the problem? Your question was asking about meaning of the $prod$ symbol, so I explained it.
$endgroup$
– Tim♦
Apr 23 at 8:50
$begingroup$
many thanks for that. i am sorry if i sounded rude, this was not my intent. how would one solve for the estimator with the product sign? i am getting nowhere when trying to solve....
$endgroup$
– Ang
Apr 23 at 8:56
$begingroup$
@Ang this seems to be separate question. Maybe post it as a separate question, with describing in greater detail how did you try solving it and where are you stuck.
$endgroup$
– Tim♦
Apr 23 at 9:01
$begingroup$
thanks! i will attempt a few more times and then post :) maybe i get lucky!
$endgroup$
– Ang
Apr 23 at 9:02
add a comment |
$begingroup$
Your second formula is the probability mass function of hypergeometric distribution. Likelihood function $mathcalL$ is defined as probability mass (or density) function $f$ evaluated on some point $x$ that is maximized in terms of parameter $theta$
$$
mathcalL(theta|X) = f(X, theta)
$$
if you have more then one such point, you usually assume that they are independent and identically distributed (all come from the same distribution), what leads to likelihood defined in terms of all your data
$$
mathcalL(theta|X_1,X_2,dots,X_n) = prod_i=1^n f(X_i, theta)
$$
This is what the first formula is.
answered Apr 23 at 8:00
Tim♦Tim
61k9135230
$endgroup$
Your second formula is the probability mass function of hypergeometric distribution. Likelihood function $mathcalL$ is defined as probability mass (or density) function $f$ evaluated on some point $x$ that is maximized in terms of parameter $theta$
$$
mathcalL(theta|X) = f(X, theta)
$$
if you have more then one such point, you usually assume that they are independent and identically distributed (all come from the same distribution), what leads to likelihood defined in terms of all your data
$$
mathcalL(theta|X_1,X_2,dots,X_n) = prod_i=1^n f(X_i, theta)
$$
This is what the first formula is.
answered Apr 23 at 8:00
Tim♦Tim
61k9135230
answered Apr 23 at 8:00
Tim♦Tim
61k9135230
answered Apr 23 at 8:00
Tim♦Tim
61k9135230
answered Apr 23 at 8:00
Tim♦Tim
61k9135230
61k9135230
$begingroup$
The problem question, does state neither. that is why i would try to solve for any k. (X1....Xk)... my problem is that i have no idea how to solve it with the product sign.... i know i have to look at L(M)/L(M+1) and i can do that for the second formula without a problem. But i cant seem to get anywhere with the general form. (My math knowledge is not that great though....)
$endgroup$
– Ang
Apr 23 at 8:47
1
$begingroup$
@Ang sorry but I don't understand your comment. What exactly is the problem? Your question was asking about meaning of the $prod$ symbol, so I explained it.
$endgroup$
– Tim♦
Apr 23 at 8:50
$begingroup$
many thanks for that. i am sorry if i sounded rude, this was not my intent. how would one solve for the estimator with the product sign? i am getting nowhere when trying to solve....
$endgroup$
– Ang
Apr 23 at 8:56
$begingroup$
@Ang this seems to be separate question. Maybe post it as a separate question, with describing in greater detail how did you try solving it and where are you stuck.
$endgroup$
– Tim♦
Apr 23 at 9:01
$begingroup$
thanks! i will attempt a few more times and then post :) maybe i get lucky!
$endgroup$
– Ang
Apr 23 at 9:02
add a comment |
$begingroup$
The problem question, does state neither. that is why i would try to solve for any k. (X1....Xk)... my problem is that i have no idea how to solve it with the product sign.... i know i have to look at L(M)/L(M+1) and i can do that for the second formula without a problem. But i cant seem to get anywhere with the general form. (My math knowledge is not that great though....)
$endgroup$
– Ang
Apr 23 at 8:47
1
$begingroup$
@Ang sorry but I don't understand your comment. What exactly is the problem? Your question was asking about meaning of the $prod$ symbol, so I explained it.
$endgroup$
– Tim♦
Apr 23 at 8:50
$begingroup$
many thanks for that. i am sorry if i sounded rude, this was not my intent. how would one solve for the estimator with the product sign? i am getting nowhere when trying to solve....
$endgroup$
– Ang
Apr 23 at 8:56
$begingroup$
@Ang this seems to be separate question. Maybe post it as a separate question, with describing in greater detail how did you try solving it and where are you stuck.
$endgroup$
– Tim♦
Apr 23 at 9:01
$begingroup$
thanks! i will attempt a few more times and then post :) maybe i get lucky!
$endgroup$
– Ang
Apr 23 at 9:02
$begingroup$
The problem question, does state neither. that is why i would try to solve for any k. (X1....Xk)... my problem is that i have no idea how to solve it with the product sign.... i know i have to look at L(M)/L(M+1) and i can do that for the second formula without a problem. But i cant seem to get anywhere with the general form. (My math knowledge is not that great though....)
$endgroup$
– Ang
Apr 23 at 8:47
$begingroup$
The problem question, does state neither. that is why i would try to solve for any k. (X1....Xk)... my problem is that i have no idea how to solve it with the product sign.... i know i have to look at L(M)/L(M+1) and i can do that for the second formula without a problem. But i cant seem to get anywhere with the general form. (My math knowledge is not that great though....)
$endgroup$
– Ang
Apr 23 at 8:47
1
1
$begingroup$
@Ang sorry but I don't understand your comment. What exactly is the problem? Your question was asking about meaning of the $prod$ symbol, so I explained it.
$endgroup$
– Tim♦
Apr 23 at 8:50
$begingroup$
@Ang sorry but I don't understand your comment. What exactly is the problem? Your question was asking about meaning of the $prod$ symbol, so I explained it.
$endgroup$
– Tim♦
Apr 23 at 8:50
$begingroup$
many thanks for that. i am sorry if i sounded rude, this was not my intent. how would one solve for the estimator with the product sign? i am getting nowhere when trying to solve....
$endgroup$
– Ang
Apr 23 at 8:56
$begingroup$
many thanks for that. i am sorry if i sounded rude, this was not my intent. how would one solve for the estimator with the product sign? i am getting nowhere when trying to solve....
$endgroup$
– Ang
Apr 23 at 8:56
$begingroup$
@Ang this seems to be separate question. Maybe post it as a separate question, with describing in greater detail how did you try solving it and where are you stuck.
$endgroup$
– Tim♦
Apr 23 at 9:01
$begingroup$
@Ang this seems to be separate question. Maybe post it as a separate question, with describing in greater detail how did you try solving it and where are you stuck.
$endgroup$
– Tim♦
Apr 23 at 9:01
$begingroup$
thanks! i will attempt a few more times and then post :) maybe i get lucky!
$endgroup$
– Ang
Apr 23 at 9:02
$begingroup$
thanks! i will attempt a few more times and then post :) maybe i get lucky!
$endgroup$
– Ang
Apr 23 at 9:02
add a comment |
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1
$begingroup$
Maybe there is only one sample, i.e. $x_1=x$?
$endgroup$
– gunes
Apr 23 at 7:55
1
$begingroup$
Typically an exercise question would consider a single observation for MLE of hypergeometric distribution.
$endgroup$
– StubbornAtom
Apr 23 at 8:02