Return to Question

Given $X, Y$ independent and non-normal, I'm recording histograms of $X$ and of $Z = X + Y$. I'm trying to figure out $Var(Y)$ and its sampling error.

I thought I could just calculate $Var(Y) = Var(Z) - Var(X)$ and use the sum of the sampling variances to produce the variance related to the final error, but the process breaks down when $Y$ is small or might not exist, occasionally resulting in a negative difference that has no meaning to me as a variance. That is, $Var(Z) - Var(X) < 0$ possibly due to sampling error.

When this difference is negative, it seems either the proposition that $Z = X + Y$ is false, or simply that the real value is close to zero and not enough samples have been taken to get the measured result close enough to zero yet.

Is there a way to determine the likelihood that the proposition is false or true when the measured value is very negative?

Given $X, Y$ independent and non-normal, I'm recording histograms of $X$ and of $Z = X + Y$, sampled when $Y$ is not present and when it is, respectfully. I'm trying to figure out $Var(Y)$ and its sampling error.

I thought I could just calculate $Var(Y) = Var(Z) - Var(X)$ and use the sum of the sampling variances to produce the variance related to the final error, but the process breaks down when $Y$ is small or might not exist, occasionally resulting in a negative difference that has no meaning to me as a variance. That is, $Var(Z) - Var(X) < 0$ possibly due to sampling error.

When this difference is negative, it seems either the proposition that $Z = X + Y$ is false, or simply that the real value is close to zero and not enough samples have been taken to get the measured result close enough to zero yet.

Is there a way to determine the likelihood that the proposition is false or true when the measured value is very negative?

Given $X, Y$ independent and non-normal, I'm recording histograms of $X$ and of $Z = X + Y$. I'm trying to figure out $Var(Y)$ and its sampling error.

I thought I could just calculate $Var(Y) = Var(Z) - Var(X)$ and use the sum of the sampling variances to produce the variance related to the final error, but the process breaks down when B is small or might not exist, occasionally resulting in a negative difference that has no meaning to me as a variance. That is, $Var(Z) - Var(X) < 0$ possibly due to sampling error.

When this difference is negative, it seems either the proposition that B is a sum with A is false, or simply that the real value is close to zero and not enough samples have been taken to get the measured result close enough to zero yet.

Is there a way to determine the likelihood that the proposition is false or true when the measured value is very negative?

Given $X, Y$ independent and non-normal, I'm recording histograms of $X$ and of $Z = X + Y$. I'm trying to figure out $Var(Y)$ and its sampling error.

I thought I could just calculate $Var(Y) = Var(Z) - Var(X)$ and use the sum of the sampling variances to produce the variance related to the final error, but the process breaks down when $Y$ is small or might not exist, occasionally resulting in a negative difference that has no meaning to me as a variance. That is, $Var(Z) - Var(X) < 0$ possibly due to sampling error.

When this difference is negative, it seems either the proposition that $Z = X + Y$ is false, or simply that the real value is close to zero and not enough samples have been taken to get the measured result close enough to zero yet.

Is there a way to determine the likelihood that the proposition is false or true when the measured value is very negative?

I am producing pairs of histograms, where A is the "background", and B is separately sampled theoretically from the same source as A but possibly summed with values of unknown distribution C. I'm interested in the variance of the unknown distribution, if it exists, with error. The distributions are often non-normal.

I thought I could just subtract the variances of A and B and use the sum of sampling variances to produce some idea of error, but the process breaks down when B is small or might not exist, occasionally resulting in a negative difference that has no meaning to me as a variance.

When this difference is negative, it seems either the proposition that B is a sum with A is false, or simply that the real value is close to zero and not enough samples have been taken to get the measured result close enough to zero yet.

Is there a way to determine the likelihood that the proposition is false or true when the measured value is very negative?

Given $X, Y$ independent and non-normal, I'm recording histograms of $X$ and of $Z = X + Y$. I'm trying to figure out $Var(Y)$ and its sampling error.

I thought I could just calculate $Var(Y) = Var(Z) - Var(X)$ and use the sum of the sampling variances to produce the variance related to the final error, but the process breaks down when B is small or might not exist, occasionally resulting in a negative difference that has no meaning to me as a variance. That is, $Var(Z) - Var(X) < 0$ possibly due to sampling error.

When this difference is negative, it seems either the proposition that B is a sum with A is false, or simply that the real value is close to zero and not enough samples have been taken to get the measured result close enough to zero yet.

Is there a way to determine the likelihood that the proposition is false or true when the measured value is very negative?