sum of random variables
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2017 ◽  
Vol 11 (3) ◽  
Author(s):  
Subhabrata Samajder ◽  
Palash Sarkar

AbstractStatistical analysis of symmetric key attacks aims to obtain an expression for the data complexity which is the number of plaintext-ciphertext pairs needed to achieve the parameters of the attack. Existing statistical analyses invariably use some kind of approximation, the most common being the approximation of the distribution of a sum of random variables by a normal distribution. Such an approach leads to expressions for data complexities which are


2015 ◽  
Vol 15 (2) ◽  
pp. 42-52
Author(s):  
Eliza Anna Khemissi

Abstract In the article the author considers and analyzes operations and functions on risk variables. She takes into account the following variables: the sum of risk variables, its product, multiplication by a constant, division, maximum, minimum and median of a sum of random variables. She receives the formulas for probability distribution and basic distribution parameters. She conducts the analysis for dependent and independent random variables. She proposes the examples of the situations in the economy and production management of risk modelled by these operations. The analysis is conducted with the way of mathematical proving. Some of the formulas presented are taken from the literature but others are the permanent results of the author.


2011 ◽  
Vol 52 ◽  
pp. 369-374
Author(s):  
Aurelija Kasparavičiūtė ◽  
Leonas Saulis

In this paper, we consider a compound random variable Z = \sum^N_{j=1} vjXj , where 0 < v < 1, Z = 0, if N = 0. It is assumed that independent identically distributed random variables X1,X2, . . . with mean EX = μ and variance DX =σ2 > 0 are independent of a non-negative integer-valued random variable N. It should be noted that, in this scheme of summation, we must consider two cases: μ\neq 0 and μ = 0. The paper is designatedto the research of the upper estimates of normal approximation to the sum ˜ Z = (Z −EZ)(DZ)−1/2, theorems on large deviations in the Cramer and power Linnik zones and exponential inequalities for P( ˜ Z > x).    


2011 ◽  
Vol 48 (1) ◽  
pp. 56-63 ◽  
Author(s):  
Umberto Cherubini ◽  
Sabrina Mulinacci ◽  
Silvia Romagnoli

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