scholarly journals Distribution of Geometrically Weighted Sum of Bernoulli Random Variables

2011 ◽  
Vol 02 (11) ◽  
pp. 1382-1386 ◽  
Author(s):  
Deepesh Bhati ◽  
Phazamile Kgosi ◽  
Ranganath Narayanacharya Rattihalli
Keyword(s):  
Random Variables ◽  
Weighted Sum ◽  
Bernoulli Random Variables

On improvements of the order of approximation in the Poisson limit theorem

1996 ◽  
Vol 33 (01) ◽  
pp. 146-155 ◽  
Author(s):  
K. Borovkov ◽  
D. Pfeifer
Keyword(s):  
Limit Theorem ◽  
Random Variables ◽  
Poisson Approximation ◽  
Order Of Approximation ◽  
Operator Semigroups ◽  
Bernoulli Random Variables ◽  
Usual Rate ◽  
Poisson Limit ◽  
Poisson Measures ◽  
Special Case

In this paper we consider improvements in the rate of approximation for the distribution of sums of independent Bernoulli random variables via convolutions of Poisson measures with signed measures of specific type. As a special case, the distribution of the number of records in an i.i.d. sequence of length n is investigated. For this particular example, it is shown that the usual rate of Poisson approximation of O(1/log n) can be lowered to O(1/n 2). The general case is discussed in terms of operator semigroups.

Modelling Catchment Rainfall Using Sum of Correlated Gamma Variables

2013 ◽  
Vol 63 (2) ◽  
Author(s):  
Zakaria, R. ◽  
Howlett, P. G. ◽  
Piantadosi, J. ◽  
Boland, J. W. ◽  
Moslim, N. H.
Keyword(s):  
Spatial Analysis ◽  
Random Variables ◽  
Monthly Rainfall ◽  
Rainfall Data ◽  
Weighted Sum ◽  
Statistical Parameters ◽  
Dependent Random Variables ◽  
Rainfall Model

One of the major difficulties in simulating rainfall is the need to accurately represent rainfall accumulations. An accurate simulation of monthly rainfall should also provide an accurate simulation of yearly rainfall by summing the monthly totals. A major problem in this regard is that rainfall distributions for successive months may not be independent. Thus the rainfall accumulation problem must be represented as the summation of dependent random variables. This study is aimed to show if the statistical parameters for several stations within a particular catchment is known, then a weighted sum is used to determine a rainfall model for the entire local catchment. A spatial analysis for the sum of rainfall volumes from four selected meteorological stations within the same region using the monthly rainfall data is conducted. The sum of n correlated gamma variables is used to model the sum of monthly rainfall totals from four stations when there is significant correlation between the stations.

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