# Confidence interval of density distribution

#### junishigohoka

##### New Member
Hi, I am a university student and I have a trouble with the following example.
This is not what I am actually confronting, but I think it will make you understand my point easily.

What I want to know is the true distribution of the hair length of a man.
So I randomly chose 10 men, and I took random 100 hairs from each of them.
Now, I have 10 probability density plots.

How should I estimate the distribution of the hair length and the 95 confidence interval of the distribution?

Thank you.

Jun

#### mmercker

##### Member
Hi, first you have to check which type of distribution you have. E.g. you can check via QQ-plot if your data (for each man) are normally distributed. If your data are normally distributed, you can calculate the mean value of the hairs of each man, leading to 10 values M1,..,M10. Now you can calculate their Mean M and variance V, the squareroot of the variance sqrt(V) is the standard error SE of the average hair length M. 95%-CIs are now computed via: [M-1.96*SE,M+1.96*SE]. Ist this what you want? However, these calculations assume that data are normally distributed, as mentioned above, this has to be proven. Best, mmercker

#### junishigohoka

##### New Member

I think what you provided is "average of ten means of hair length with 95% CIs".
But what I want to do is like this:
I plotted 10 curves each of which represents one man, on the same plot area.
I want to summarise these 10 curves into one curve with certain width which represents CIs of the probability density of each hair length.

For example, when the probability density of hair length of 20 cm is 0.07, how much is the CI for that? When the probability density of hair length of 25 cm is 0.04, how much is the CI for that?
I want to visualise the CIs of all the point along the density distribution curve .

Thank you.

Jun

#### mmercker

##### Member
when the probability density of hair length of 20 cm is 0.07, how much is the CI for that?
Sorry, what I don't understand: the probability density is not a single value buth rather a curve with a certain shape, so how to calculate a CI for a curve, what do you mean by that? Maybe you can attach a drawing/scetch of what you mean?

Last edited: