# How to calculate the probability of a datapoint fitting in a known distribution

I have a set of samples, each with a concentration for element A which is shown on a log scale on X-axis on the histogram below. The number of samples with the same concentration is shown on Y-axis. As you can see in the histogram, the distribution resembles a multimodal distribution. Based on the experiment I am using, the left modal, I know for a fact, that is only instrumental noise (this is how I defined noise: those data points larger than mean of data+3*standard deviation) but the right modal is the real data. so basically for those samples with concentrations shown on the left modal, the real concentration value is zero.

My questions are;

1- I need a measurement (p-value) that gives me the probability value that each of the data points from the right modal belong (or doesn't) to the left modal (fits or doesn't fit).

2- If, instead of another distribution on the right (the right modal), I only had one data point on the right, how would I measure the probability that this data point fits or it doesn't fit to the right modal (aka. noise).

Thank you very much in advance.

PS:
1- Any hint which I can implement in R will be preferable.
2-The red lines are the mean values for the each of the two modals.

## 1 Answer

0 down vote accept

Update:

I used single sample t-test for comparing each of the data points on the right side with the distribution on the left. Then I calculated the p-value of the t-test. T-test for single sample can be done by the regualr t-test function in R except instead of the second distribution we need to define the value of "mu" which is the value of the data point we are comparing to the distribution. This is basically as if we want to compare the p-value of comparing the mean of the distribution on the left to a limit (e.g. how likely it is that the mean of the distribution on the left is smaller than value x [mu=x]).