Abstract: It is proved in this parper that population X of nonsingula distribut ion with EX²<∞ is of Poisson type dis-tribution P ( λ, α , 1) if and only i f the statistic T₂- T ₁ has constantre gression on T _1, where T₁=
X =1n
ni= 1Xi  is sample mean and T₂=1n- 1
ni= 1(Xi -
X )² is sample variance.

Key words: constant regression, conditional mathematical expectation, analytic characteristic function, cumulant, cumulant generat ing function, Poisson type distribution