journal6 ›› 2000, Vol. 21 ›› Issue (2): 24-27.

• Mathematics • Previous Articles     Next Articles

A Characteristics of A Class of Poisson Type Distribution


  1. ( Deparment of Mathematics, Tianjin Normal University, Tianjin 300073, China)
  • Online:2000-06-15 Published:2013-01-16

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- 1ni= 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

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