How to generate an array of poisson distributed (without any built-in function) 0 and 1 of a known lambda value?

I want an array of 0 and 1 where the occurrences of the event are limited to '1' for a certain time of observation(bin). The values should be Poisson distributed, where I can input the lambda value. How can I code this on MATLAB without use any Poisson's built-in function?

[Ameer Hamza]

How do you know if it is Poisson distributed if the array only contains 0 and 1. Poisson distribution is defined for all discrete values. Or do you want some sort of truncated Poisson distribution?

[Jeff Miller]

Putting Ameer's point a little differently, if you only want to generate 0's and 1's, why not just figure out what probability p you want for the 1 and use binornd(1,p)?

[John D'Errico]

Do you have such a low Poisson rate that you KNOW there will never be anything larger than a 1? If you can never have more than 1 arrival, then it is not a true Poisson. So are you really sure this is a Poisson process? As Jeff points out, you can reduce this to a simple binomial sampling based on your statement. Just decide the rate you want to see.

[Yun-Hui Chen]

Oh, I'm so sorry that I did't describe the problem clearly.

I want the figure's x-axis sample size's range is in [0,1], and the y-axis is mean the occuttences of the event(like the customer come) are limited to '1'.

My problem is like generate a Poisson random variable. I have read ABUL HASNAT's ask whose ask is similar my problem for reference. But ABUL HASNAT's code will run the event like two customers arrival in the same time(like below's picture). I want change the code's Poisson random variables to if it has the Poisson random then only show '1' mean the event happen.

Answer 1

[Ameer Hamza]

Read about inverse transform sampling() https://en.wikipedia.org/wiki/Inverse_transform_sampling . You will at least need to use rand().

[Yun-Hui Chen]

Thank you so much, this information is very helpful to me. I have sloved my problem.