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I am a math student working with a group of field biologists. In multiple experiments of mark-recapture of the same population, they claimed that if the number of observations (recaptures) its large enough, it is possible to infer both population size ($N$) and proportion ($p=K/N$) based only on the sample, without prior knowledge of the number of individuals that were originally marked ($K$).

Considering a sample of size $n$ with $k$ marked individuals is drawn from the population, a histogram of the observed proportions its created using jackknifes subsamples. Then a hypergeometric distribution is fitted to the histogram using minimum squares. This leads to a pair of estimated parameters $\hat{p}$ and $\hat{N}$.

I am convinced that under the assumption of $K$ unknown this estimator converges to the sample size ($n$), i.e $\hat{N} \rightarrow n$ (or at least to a value different than $N$). However, I haven't proved it yet.

They tested this estimator with simulated data. My conclusion is that in the simulations the standard deviation of $\hat{N}$ its large enough so that the values of $N$ and $\hat{N}$ sometimes coincide.

I am creating this question to verify whether I am correct. Also, I am not very good explaining myself, and need to create an argument to convince non-specialists that $\hat{N} \rightarrow n$. Thank all of you for your help.

I am a math student working with a group of field biologists. In multiple experiments of mark-recapture of the same population, they claimed that if the number of observations (recaptures) is large enough, it is possible to infer both population size ($N$) and proportion ($p=K/N$) based only on the sample, without prior knowledge of the number of individuals that were originally marked ($K$).

Considering a sample of size $n$ with $k$ marked individuals is drawn from the population, a histogram of the observed proportions is created using jackknifes subsamples. Then a hypergeometric distribution is fitted to the histogram using minimum squares. This leads to a pair of estimated parameters $\hat{p}$ and $\hat{N}$.

I am convinced that under the assumption of $K$ unknown this estimator converges to the sample size ($n$), i.e $\hat{N} \rightarrow n$ (or at least to a value different than $N$). However, I haven't proved it yet.

They tested this estimator with simulated data. My conclusion is that in the simulations the standard deviation of $\hat{N}$ is large enough so that the values of $N$ and $\hat{N}$ sometimes coincide.

I am creating this question to verify whether I am correct. Also, I am not very good explaining myself, and need to create an argument to convince non-specialists that $\hat{N} \rightarrow n$. Thank all of you for your help.

I am a math student working with a group of field biologists. In multiple experiments of mark-recapture of the same population, they claimed that if the number of observations (recaptures) its large enough, it is possible to infer both population size ($N$) and proportion ($p=K/N$) based only on the sample, without prior knowledge of the number of individuals that were originally marked ($K$). I am convinced that this is not possible, and that any estimator based in this assumption converges to the sample size ($n$), i.e $\hat{N} \rightarrow n$.

They made an algorithm and they tested it with simulated data. My conclusion is that in the simulations the standard deviation of $\hat{N}$ its large enough so that the values of $N$ and $\hat{N}$ sometimes coincide.

I am creating this question to verify whether I am correct. Also, I am not very good explaining myself, and need to create an argument to convince non-specialists that $\hat{N} \rightarrow n$. Thank you for your help.

I am a math student working with a group of field biologists. In multiple experiments of mark-recapture of the same population, they claimed that if the number of observations (recaptures) its large enough, it is possible to infer both population size ($N$) and proportion ($p=K/N$) based only on the sample, without prior knowledge of the number of individuals that were originally marked ($K$).

Considering a sample of size $n$ with $k$ marked individuals is drawn from the population, a histogram of the observed proportions its created using jackknifes subsamples. Then a hypergeometric distribution is fitted to the histogram using minimum squares. This leads to a pair of estimated parameters $\hat{p}$ and $\hat{N}$.

I am convinced that under the assumption of $K$ unknown this estimator converges to the sample size ($n$), i.e $\hat{N} \rightarrow n$ (or at least to a value different than $N$). However, I haven't proved it yet.

They tested this estimator with simulated data. My conclusion is that in the simulations the standard deviation of $\hat{N}$ its large enough so that the values of $N$ and $\hat{N}$ sometimes coincide.

I am creating this question to verify whether I am correct. Also, I am not very good explaining myself, and need to create an argument to convince non-specialists that $\hat{N} \rightarrow n$. Thank all of you for your help.

I am a math student working with a group of field biologists. In experiments of mark-recapture, they claimed that if the number of observations (recaptures) its large enough, it is possible to infer both population size ($N$) and proportion ($p=K/N$) based only on the sample, without prior knowledge of the number of individuals that were originally marked ($K$). I am convinced that this is not possible, and that any estimator based in this assumption converges to the sample size ($s$), i.e $\hat{N} \rightarrow s$.

They made an algorithm and they tested it with simulated data. My conclusion is that in the simulations the standard deviation of $\hat{N}$ its large enough so that the values of $N$ and $\hat{N}$ sometimes coincide.

I am creating this question to verify whether I am correct. Also, I am not very good explaining myself, and need to create an argument to convince non-specialists that $\hat{N} \rightarrow s$. Thank you for your help.

I am a math student working with a group of field biologists. In multiple experiments of mark-recapture of the same population, they claimed that if the number of observations (recaptures) its large enough, it is possible to infer both population size ($N$) and proportion ($p=K/N$) based only on the sample, without prior knowledge of the number of individuals that were originally marked ($K$). I am convinced that this is not possible, and that any estimator based in this assumption converges to the sample size ($n$), i.e $\hat{N} \rightarrow n$.

They made an algorithm and they tested it with simulated data. My conclusion is that in the simulations the standard deviation of $\hat{N}$ its large enough so that the values of $N$ and $\hat{N}$ sometimes coincide.

I am creating this question to verify whether I am correct. Also, I am not very good explaining myself, and need to create an argument to convince non-specialists that $\hat{N} \rightarrow n$. Thank you for your help.