Pearson distribution
Okay kiddo, so let me tell you about something called the Pearson distribution. It's a way to look at lots and lots of numbers and find patterns in them.
Imagine you have a bunch of marbles of different sizes, and you want to sort them into groups. You might put all the really big ones in one group, and all the tiny ones in another group. That's kind of what a Pearson distribution does, but with numbers instead of marbles.
Now, the thing about Pearson distributions is that they are based on three numbers: the mean, the standard deviation, and the skewness. Those are big words, but let me explain what they mean.
The mean is just the average of all the numbers. So if you had a bunch of numbers like 1, 3, and 5, the mean would be (1 + 3 + 5) / 3, which is 3.
The standard deviation is a little trickier. It tells you how spread out the numbers are. Imagine you have a bunch of marbles that are all the same size, and you add a few bigger ones. The standard deviation would go up, because now the marbles are more spread out in size. But if you add a lot of marbles that are all the same size, the standard deviation would go down, because now they're more tightly clustered together.
Finally, the skewness tells you if the numbers are all bunched up on one side or the other. Imagine you have a bunch of marbles on a see-saw. If there are a lot of marbles on one side, the see-saw will be tipped. That's kind of like skewness - it tells you if the numbers are all bunched up on one side or the other.
So a Pearson distribution takes all of these things - the mean, the standard deviation, and the skewness - and uses them to sort the numbers into groups. This helps us understand patterns in the data and make predictions about what might happen next.
Imagine you have a bunch of marbles of different sizes, and you want to sort them into groups. You might put all the really big ones in one group, and all the tiny ones in another group. That's kind of what a Pearson distribution does, but with numbers instead of marbles.
Now, the thing about Pearson distributions is that they are based on three numbers: the mean, the standard deviation, and the skewness. Those are big words, but let me explain what they mean.
The mean is just the average of all the numbers. So if you had a bunch of numbers like 1, 3, and 5, the mean would be (1 + 3 + 5) / 3, which is 3.
The standard deviation is a little trickier. It tells you how spread out the numbers are. Imagine you have a bunch of marbles that are all the same size, and you add a few bigger ones. The standard deviation would go up, because now the marbles are more spread out in size. But if you add a lot of marbles that are all the same size, the standard deviation would go down, because now they're more tightly clustered together.
Finally, the skewness tells you if the numbers are all bunched up on one side or the other. Imagine you have a bunch of marbles on a see-saw. If there are a lot of marbles on one side, the see-saw will be tipped. That's kind of like skewness - it tells you if the numbers are all bunched up on one side or the other.
So a Pearson distribution takes all of these things - the mean, the standard deviation, and the skewness - and uses them to sort the numbers into groups. This helps us understand patterns in the data and make predictions about what might happen next.