Algorithm AS 204: The Distribution of a Positive Linear Combination of χ 2 Random Variables

1984 ◽  
Vol 33 (3) ◽  
pp. 332 ◽  
Author(s):  
R. W. Farebrother
Keyword(s):  
Linear Combination ◽  
Random Variables ◽  
Positive Linear Combination

Estimating the cumulative distribution function for the linear combination of gamma random variables

2017 ◽  
Vol 20 (5) ◽  
pp. 939-951
Author(s):  
Amal Almarwani ◽  
Bashair Aljohani ◽  
Rasha Almutairi ◽  
Nada Albalawi ◽  
Alya O. Al Mutairi
Keyword(s):  
Distribution Function ◽  
Linear Combination ◽  
Cumulative Distribution Function ◽  
Random Variables ◽  
Cumulative Distribution

Continuity for multi-type branching processes with varying environments

1999 ◽  
Vol 36 (01) ◽  
pp. 139-145 ◽  
Author(s):  
Owen Dafydd Jones
Keyword(s):  
Linear Combination ◽  
Branching Process ◽  
Branching Processes ◽  
Random Variables ◽  
Main Tool ◽  
Concentration Function ◽  
Independent Random Variables ◽  
Varying Environments

Conditions are derived for the components of the normed limit of a multi-type branching process with varying environments, to be continuous on (0, ∞). The main tool is an inequality for the concentration function of sums of independent random variables, due originally to Petrov. Using this, we show that if there is a discontinuity present, then a particular linear combination of the population types must converge to a non-random constant (Equation (1)). Ensuring this can not happen provides the desired continuity conditions.

ON THE LINEAR COMBINATION OF LAPLACE RANDOM VARIABLES

2005 ◽  
Vol 19 (4) ◽  
pp. 463-470 ◽  
Author(s):  
Saralees Nadarajah ◽  
Samuel Kotz
Keyword(s):  
Fuzzy Sets ◽  
Linear Combination ◽  
Random Variables ◽  
Percentage Points ◽  
Automation Control

The distribution of the linear combination αX + βY is derived when X and Y are independent Laplace random variables. Extensive tabulations of the associated percentage points are also given. The work is motivated by examples in automation, control, fuzzy sets, neurocomputing, and other areas of informational sciences.

scholarly journals The general theory of canonical correlation and its relation to functional analysis

1961 ◽  
Vol 2 (2) ◽  
pp. 229-242 ◽  
Author(s):  
E. J. Hannan
Keyword(s):  
Linear Combination ◽  
Canonical Correlation ◽  
Random Variables ◽  
Random Variable ◽  
Finite Variance ◽  
Finite Sample ◽  
Standard Description ◽  
Joint Distributions ◽  
Gaussian Case ◽  
The Relationship

The classical theory of canonical correlation is concerned with a standard description of the relationship between any linear combination of ρ random variablesxs, and any linear combination ofqrandom variablesytinsofar as this relation can be described in terms of correlation. Lancaster [1] has extended this theory, forp=q= 1, to include a description of the correlation of any function of a random variablexand any function of a random variabley(both functions having finite variance) for a class of joint distributions ofxandywhich is very general. It is the purpose of this paper to derive Lancaster's results from general theorems concerning the spectral decomposition of operators on a Hilbert space. These theorems lend themselves easily to the generalisation of the theory to situations wherepandqare not finite. In the case of Gaussian, stationary, processes this generalisation is equivalent to the classical spectral theory and corresponds to a canonical reduction of a (finite) sample of data which is basic. The theory also then extends to any number of processes. In the Gaussian case, also, the present discussion-is connected with the results of Gelfand and Yaglom [2] relating to the amount of information in one random process about another.

Asymptotic Normality of a Class of Nonparametric Statistics

1987 ◽  
Vol 3 (3) ◽  
pp. 313-347 ◽  
Author(s):  
Munsup Seoh ◽  
Madan L. Puri
Keyword(s):  
Asymptotic Normality ◽  
Order Statistics ◽  
Linear Combination ◽  
Linear Function ◽  
Random Variables ◽  
Weighted Sum ◽  
Rank Statistics ◽  
Concomitants Of Order Statistics ◽  
Signed Rank ◽  
Special Cases

Asymptotic normality is established for a class of statistics which includes as special cases weighted sum of independent and identically distributed (i.i.d.) random variables, unsigned linear rank statistics, signed rank statistics, linear combination of functions of order statistics, and linear function of concomitants of order statistics. The results obtained unify as well as extend a number of known results.

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