#### Power Series Distribution definition, formula with applications

### Power Series Distribution

### Properties of Power series distribution

- If θ=p/(1-p), f(θ)=(1+θ)^n and s={1,2,3,…,n), a set of (n+1) non-negative integers then the power series distribution is tends to binomial distribution
- If f(θ)=e^θ and s={0,1,2,3,…,∞} then the distribution tends to poisson distribution.
- If θ=p/(1-p), f(θ)=(1+θ)^-n and s={0,1,2,3,…,∞), then the power series distribution tends to negative binomial distribution.
- If f(θ)=-log(1-θ) and s={1,2,….}, then the power series distribution tends to logarthmic distribution.