CDF-based nonparametric confidence interval
Okay kiddo, have you heard about confidence intervals? They are a way to tell how accurate our guess is about something.
Now, when we talk about nonparametric confidence intervals, it means we don't have to assume anything about the data we are studying, we just need to collect a bunch of numbers.
A CDF or cumulative distribution function is just a fancy way of saying how many of our numbers fall between certain values.
Here's an example, let's say we have a bunch of apples, and we want to figure out how many apples are bigger than a certain size. We can line up all the apples from smallest to biggest and count how many we have in total. Then, we can start at the smallest apple and count how many there are until we reach a certain size. This will give us the percentage of apples that are smaller than that size. As we move up in size, the percentage will increase until we reach 100%. This is called a cumulative distribution function.
Now, to make a confidence interval using this CDF, we take a certain percentage, let's say 95%, and find the corresponding values in the CDF. We draw lines at these values and the area between these lines represents our confidence interval. This means we are confident that the true value we are trying to estimate falls within this range.
So, to summarize, a cdf-based nonparametric confidence interval is a way to estimate a value with a certain degree of certainty using a cumulative distribution function of the data we collected without making any assumptions about the data.
Now, when we talk about nonparametric confidence intervals, it means we don't have to assume anything about the data we are studying, we just need to collect a bunch of numbers.
A CDF or cumulative distribution function is just a fancy way of saying how many of our numbers fall between certain values.
Here's an example, let's say we have a bunch of apples, and we want to figure out how many apples are bigger than a certain size. We can line up all the apples from smallest to biggest and count how many we have in total. Then, we can start at the smallest apple and count how many there are until we reach a certain size. This will give us the percentage of apples that are smaller than that size. As we move up in size, the percentage will increase until we reach 100%. This is called a cumulative distribution function.
Now, to make a confidence interval using this CDF, we take a certain percentage, let's say 95%, and find the corresponding values in the CDF. We draw lines at these values and the area between these lines represents our confidence interval. This means we are confident that the true value we are trying to estimate falls within this range.
So, to summarize, a cdf-based nonparametric confidence interval is a way to estimate a value with a certain degree of certainty using a cumulative distribution function of the data we collected without making any assumptions about the data.