Asymetrical Distribution

[SimpsonAye]

Hi all,

I have almost finished a lengthy study on Domestic Abuse and the associated risks etc. My organisation uses a risk score split into Standard Risk (0-23), Medium Risk (24-44) and High Risk (45+) relationships. This scoring system is used within several agencies. More resources can be provided as the risk increases.

I pulled 29,794 scores from the database, ranging from 0-100 and noticed that the percentages of distribution were as follows:

Standard - 74.84%
Medium - 19.29%
High - 5.87%

I have a column graph that shows an asymetrical distribution (naturally given the data set is one sided).

I have the capacity to alter the scoring system for the standard and medium risks to be 0-20, 21-44.

This shifted distribution to 67.77% Standard, 26.36% Medium and High 5.87%.

I guess my question is, should normal distribution percentages (68-95-99.7) be used for asymetrical curves if the data set is one sided (especially when I can change the risk brackets to spread the data more evenly)? I can provide the relevant stats and graphs if requested.

 

[SimpsonAye]

Current Distribution of Risk Scores:


Recommended Modified Risk Scores:

 

[Deleted member 4993]

View attachment 19916

View attachment 19917

Current Distribution of Risk Scores:
View attachment 19918

Recommended Modified Risk Scores:
View attachment 19919

This looks more like a log-normal distribution.

Have you studied that distribution and its characteristics?

You may want to review:

Log Normal Distribution -- from Wolfram MathWorld

A continuous distribution in which the logarithm of a variable has a normal distribution. It is a general case of Gibrat's distribution, to which the log normal distribution reduces with S=1 and M=0. A log normal distribution results if the variable is the product of a large number of...

mathworld.wolfram.com

 

[SimpsonAye]

Thanks, will have a read. Has been a number of years since I've looked at data sets.