Converting 1 Distribution to Another

zeloc

New Member
#1
I have a set of values ranging from .01 to 918 with n = 7368. About 3000 values are below 1 and about 150 values are greater than 100. The mean and standard deviation are 9.85 and 47.91.

I would like to convert these numbers to a ranking so that the lowest one is assigned the number 1 and the highest 7368. Unfortunately I cannot just sort them and I need an equation that would take a number in the first group and give the number in the second group.

I have tried converting the initial raw scores into z scores and then converting them to a new scale with a mean of 3684 and SD of 2126.81 (which would be the mean and SD of a set of numbers going from 1 to 7368) but the results are nothing close to the linear relationship I want. The numbers start around 3200 and go up to 44,000.

Does anyone know how I can do something like this, even if it is not perfect? More generally, how I convert other distributions into a ranking using mathematical formulas? I am willing to read and study what I need to if someone can point me in the right direction.

Thanks!
 

Dragan

Super Moderator
#2
I would like to convert these numbers to a ranking so that the lowest one is assigned the number 1 and the highest 7368. ... More generally, how I convert other distributions into a ranking using mathematical formulas? I am willing to read and study what I need to if someone can point me in the right direction.

Thanks!
Here's an algorithm that will rank data. You will first have to sort the data.

N=SAMPLE SIZE
INPUT: XO=ORIGINAL DATA; XS=SORTED DATA.
OUTPUT: IRX=RANKED DATA

DO 5 I=1,N
DO 10 I2=1,N
IF (XO(I) .EQ. XS(I2)) GOTO 8
10 CONTINUE
8 IRX(I)=I2
5 CONTINUE
END
 

zeloc

New Member
#3
Thanks for the post.

In the application I am running I am not able to enter any programs, I can only enter a mathematical formula that would take 1 value and display another. That looks like a computer program, do you know if there is any way to do this mathematically even if it means using 2 or 3 separate equations to convert each portion of the initial set to the distribution I am looking for?
 

zeloc

New Member
#4
Have done some more thinking on this, the easiest way might be to divide all numbers by 918 and then multiply every number by 7000. This wouldn't give me a ranking, but would produce values between 1 and 7000 which I would then do for each set and have a way to compare these numbers to each other. Is there any way to get closer than this approximation?
 

Outlier

TS Contributor
#5
I have a set of values ranging from .01 to 918 with n = 7368.

I would like to convert these numbers to a ranking so that the lowest one is assigned the number 1 and the highest 7368.
Unless I'm missing something, I used the Excel functions SLOPE and INTERCEPT to solve the equation for this straight line, which is of the form Y = aX +b, where a is the slope and b is the Y intercept.

Y, which ranges from 1 to 7368, is 8.025141886 [= a] times X, which ranges from 0.01 to 918, plus 0.919748581 [= b].
 
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