Abstract
The main aim of this note is to establish some bounds in Poisson approximation for row-wise arrays of independent integer-valued random variables via the Trotter-Renyi distance. Some results related to random sums of independent integer-valued random variables are also investigated.MSC:60F05, 60G50, 41A36.
Highlights
Let {Xn,j, j =, . . . , n; n =, . . .} be a row-wise triangular array of independent integervalued random variables with success probabilities P(Xn,j = ) = pn,j; P(Xn,j = ) = – pn,j – qn,j; pn,j, qn,j ∈ (, ); pn,j + qn,j ∈ (, ); j =, . . . , n; n =, . . . . Set Sn = n j= Xn,j and λn = E(Sn) = pn,jSuppose that limn→∞ λn λ ( < +∞).We will denote by
The main aim of this paper is to establish the bounds of the Le Cam-style inequalities for independent discrete integer-valued random variables using the Trotter-Renyi distance based on Trotter-Renyi operator
Suppose that AX, AY are operators associated with two independent random variables X and Y
Summary
The main aim of this paper is to establish the bounds of the Le Cam-style inequalities for independent discrete integer-valued random variables using the Trotter-Renyi distance based on Trotter-Renyi operator (see [ , ], for more details). Section gives some results on Le Cam’s inequalities, based on the Trotter-Renyi distance, for independent integer-valued distributed random variables. . Suppose that AX , AY are operators associated with two independent random variables X and Y .
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