An estimate of the rate of convergence to a limit distribution in the minimum scheme of a random number of identically distributed random variables

1991 ◽  
Vol 57 (4) ◽  
pp. 3306-3310
Author(s):  
S. T. Rachev ◽  
L. B. Klebanov ◽  
A. Yu. Yakovlev
Keyword(s):  
Rate Of Convergence ◽  
Limit Distribution ◽  
Random Number ◽  
Random Variables

scholarly journals Theorems on large deviations for the sum of random number of summands

2010 ◽  
Vol 51 ◽  
Author(s):  
Aurelija Kasparavičiūtė ◽  
Leonas Saulis
Keyword(s):  
Large Deviations ◽  
Rate Of Convergence ◽  
Random Number ◽  
Normal Approximation ◽  
Random Variables ◽  
Random Variable ◽  
Compound Process ◽  
Independent Identically Distributed

In this paper, we present the rate of convergence of normal approximation and the theorem on large deviations for a compound process Zt = \sumNt i=1 t aiXi, where Z0 = 0 and ai > 0, of weighted independent identically distributed random variables Xi, i = 1, 2, . . . with  mean EXi = µ and variance DXi = σ2 > 0. It is assumed that Nt is a non-negative integervalued random variable, which depends on t > 0 and is independent of Xi, i = 1, 2, . . . .

An expansion for the distribution function of a random sum

1973 ◽  
Vol 10 (4) ◽  
pp. 869-874 ◽  
Author(s):  
L. M. Marsh
Keyword(s):  
Distribution Function ◽  
Normal Distribution ◽  
Rate Of Convergence ◽  
Special Form ◽  
Edgeworth Expansion ◽  
Random Number ◽  
Probability Generating Function ◽  
Random Variables ◽  
Fixed Number ◽  
Random Sum

The Edgeworth expansion gives an indication of the rate of convergence of the distribution function of the sum of a fixed number of random variables to the normal distribution. A similar expansion is given here for the distribution function of the sum of a random number N of random variables, when the probability generating function of N takes a special form.

An expansion for the distribution function of a random sum

1973 ◽  
Vol 10 (04) ◽  
pp. 869-874 ◽  
Author(s):  
L. M. Marsh
Keyword(s):  
Distribution Function ◽  
Normal Distribution ◽  
Rate Of Convergence ◽  
Special Form ◽  
Edgeworth Expansion ◽  
Random Number ◽  
Probability Generating Function ◽  
Random Variables ◽  
Fixed Number ◽  
Random Sum

The Edgeworth expansion gives an indication of the rate of convergence of the distribution function of the sum of a fixed number of random variables to the normal distribution. A similar expansion is given here for the distribution function of the sum of a random number N of random variables, when the probability generating function of N takes a special form.

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