I am trying to plot poisson density fit to my data x. but it doesnt seem to give the right results

%y is seconds

y=[20 50 100 200];

%x1 counts after 20s,x2 couns after 50s, x3 counts after 100s, x4 counts after

%200s

x1=[47 59 56 56 61 54 72 64 53 73 59 62 43 61 63 70 55 59 70 52 62 76 64 68 63];

x2=[129 167 139 154 154 171 167 132 151 139];

x3=[317 297 301 312 329];

x4=[612 598];

%x is detections per second

x=[x1/y(1) x2/y(2) x3/y(3) x4/y(4)]';

% Set seed for reproducibility

rng default

% Fit a poisson distribution

pd = fitdist(x,'poisson');

% Calculate the theoretical PDF from the fit parameters

x_range = 2:3.8;

probability_predicted = pdf(pd,x_range);

% Plot histogram and fit

figure

histogram(x,9)

xlabel('Observation');

ylabel('Probability');

h = plot(x_range,probability_predicted,'-');

set(h,'MarkerSize',24)

[Jeff Miller]

The Poisson is not an appropriate model for your x variable of "detections per second". For example, in a Poisson distribution all the x's must be integers, but your x's are real numbers (e.g., 2.35).

I suspect there is no appropriate model that will allow you to treat the values from the different time intervals (eg 20s, 200s) as coming from the same distribution, but it is hard to say without knowing more about where your data came from and what you are trying to do with it.

[Judith Hershko]

waw yes thank you! If I only use x1 (20 s) which only has integers it works! Thank you for clarifying that!

[Judith Hershko]

But I also tried a normal destribution on x ( real numbers) using distribution filter and it does wok. Why would a normal destribution work on real numbers but poisson not?

[Jeff Miller]

Not sure if this will help, but...The normal distribution is a model for continuous numerical measurements that can take on any values. The Poisson is a model for counts, which have to be 0, 1, 2, 3, ...

[Judith Hershko]

Oh yes that helps a lot actually! Thank you so much!

Answer 1

[Shubham Khatri]

Hello,

It didnt work because Poisson distribution is a discrete probability distribution of the number of events occurring in a given time period, given the average number of times the event occurs over that time period. It would be good if you can share your data source to find a good fit of a model.

Hope it helps