Normal approximation for sum of random number of summands

Abstract

Normal aproximationof sum Zt =ΣNti=1Xi of i.i.d. random variables (r.v.) Xi , i = 1, 2, . . . with mean EXi = μ and variance DXi = σ2 > 0 is analyzed taking into consideration large deviations. Here Nt is non-negative integer-valued random variable, which depends on t , but not depends at Xi , i = 1, 2, . . ..

Keywords

• distribution function
• characteristic function
• cumulant
• large deviations
• exponential inequality