# Is there a probability distribution similar to Poisson, but with controlled variance?

Is there a probability distribution similar to Poisson, but with controlled variance?

Poisson distribution with a lambda has a fixed mean and fixed variance; both mean and variance are equal to the $$\lambda$$ parameter. I am looking for a distribution to generate samples that has properties similar to Poisson, but with smaller variance instead of a variance equal to $$\lambda$$.

Does Poisson have a family of distributions in which mean and variance can be controlled by two different parameters?

• Perhaps negative binomial is what you want.
– Dave
Mar 24, 2020 at 2:57
• That has larger variance, not smaller as OP requests in the post Mar 24, 2020 at 4:21