Histogram normalisation: a question about terminology

Let's consider the histogram and histcounts functions, as in these two cases:

num_bins = 30; % <-- note: I specify the "number of bins" and not the "bin width", which can be different from 1

% Case 1
histcounts(X,num_bins,'Normalization','probability'); 
histogram(X,'NumBins',num_bins,'Normalization','probability');

% Case 2
histcounts(X,num_bins,'Normalization','pdf'); 
histogram(X,'NumBins',num_bins,'Normalization','pdf');

Do I understand correctly that

1. For Case 1, I get the "Relative Frequency Histogram" or an "empirical estimate of the Probability Mass Function"?
2. For Case 2, - where I divide by the bin widths as well -, I get the an "empirical estimate of the Probability Density Function"?

[Sim]

@MathWorks Support Team...?

Answer 1

[Satwik Samayamantry]

Hi Sim,

Yeah you got it right. Your understanding for both cases is correct.

[Sim]

Thanks for your comment @Satwik Samayamantry! Before accepting your answer, do you know/have some reference supporting your answer?

[Steven Lord]

See the description of the Normalization name-value argument on either of the histogram or histcounts documentation pages. It describes exactly what the Values property of the histogram or the first output of the histcounts function represent.

[Sim]

thanks @Steven Lord :-)