NormalDistribution: The Z-Score formula is actually the probability density function

[PeterKneale]

@s-andrews @ewels

Expected: The function below named getZScoreForValue should calculate the Z-Score.
Actual: The implementation is actually the probability density function (PDF) of the normal distribution at a given value

Looking at the code calling the function (and chatting with a colleague who knows more about FastQC's intention here) we came to the conclusion that the function is just misnamed and the behaviour of the code is correct but cant be sure.

If you can let me know either way i'll ensure that the function has the correct name and add unit tests demonstrating its behaviour.

https://github.com/s-andrews/FastQC/blob/master/uk/ac/babraham/FastQC/Statistics/NormalDistribution.java

public class NormalDistribution {

	private double mean;
	private double stdev;
	
	public NormalDistribution (double mean, double stdev) {
		this.mean = mean;
		this.stdev = stdev;
	}
	
	public double getZScoreForValue (double value) {
		double lhs = 1d/(Math.sqrt(2*Math.PI*stdev*stdev));
		double rhs = Math.pow(Math.E, 0 - (Math.pow(value-mean,2)/(2*stdev*stdev)));		
		return lhs*rhs;
	}
}

ChatGPT helped to decipher the issue.

[s-andrews]

The naming is misleading - it's supposed to be the probability density so the code is correct. It's just the code which calculates the expected distribution of GC values given a mean and sd, so it calculates the probability for a given zscore.

[PeterKneale]

Understood, shall i rename and add tests?

[s-andrews]

Sure, that would be great, thanks!

[PeterKneale]

Interestingly there is already an implementation of the probability density function in NormalDistribution.java the apache math3 codebase that has been vendored in to the repository.

They look to be mathematically equivalent but I can verify that with some tests, also the vendored version is reportedly faster.