The steady state intensity distribution function is derived from a single mode gain-noise laser model. The extrema of the steady state distribution function is investigated as the additive noise, multiplicative noise and injected signal are changing. It is shown that the multiplicative noise plays a key rule in the first-order-like phase transition in a laser system. The injected signal can reduce the phase transition. The additive noise causes the number and locations of the extrema in the steady state distribution function jumping back and forth.