MATLAB: Does the log-normal distribution not fit the data

Question

Hello,

I am fitting some realively simple data with a log normal distribution.

I am then generating a probability distribution from that fit.

Shouldn't this roughly match the intial data?

when I plot it on top of normalized histogram of the data, the shape is appropriate but the scale is about ten-fold lower.

Example below.

parmat = lognfit(data)
pdf    = lognpdf(0:1:1000,parmat(1),parmat(2))
figure;hold on
histogram(data,[0:1:1000],'normalization','probability')
plot(0:1:1000,pdf)

In this case shouldn't the probability density function approximate the histrogam, rather than being one tenth or less the values of the histogram probability?

Thanks.

Answer 1

Consider thisexample:

X = lognrnd(0,1,[1,1000]);
histogram(X,100,'normalization','probability')
hold on
ezplot(@(x) lognpdf(x,0,1))

So the two plots seems scaled wrong.

But the histogram normlization chosen was one such that the sum of the bars is 1. Consider the choices given though.

ezplot(@(x) lognpdf(x,0,1))
hold on
histogram(X,100,'normalization','pdf')

You made what may have seemed a reasonable choice in your normailzation, but the wrong one in hindsight. Remember that a PDF does not contain actual probabilities, something that is a source of frequent consternation for some people when someone sees a PDF that returns numbers greater than 1.