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Random Variable
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(7)
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The Algebra of Random Variables
The Algebra of Random Variables,M. D. Springer
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The Algebra of Random Variables
(
Citations: 205
)
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M. D. Springer
Published in 1979.
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Citation Context
(80)
...We refer to
16
or
15
for its definition, properties and applications in statistics...
T. PhamGia
,
et al.
Testing the equality of several covariance matrices
...This apparently paradoxical behavior is an example of how the algebra of random variables with uncertainty is quite different from the algebra of deterministic variables; see [
56
]...
Jari P. Kaipio
,
et al.
The Bayesian Framework for Inverse Problems in Heat Transfer
...Then, according to common practice in statistics [31], [
32
], we can accurately approximate ξ by a single chisquare variable to simplify the relevant analysis...
Q. T. Zhang
.
Theoretical Performance and Thresholds of the Multitaper Method for Sp...
...Products of random variables of various types of distributions have been investigated and their distributions determined in [2], [
3
]...
...In their analysis, the authors of [13] have exploited the fact that a product of Hfunctions is also an Hfunction [
3
]...
...In this paper, we employ the Mellin transform [
3
], [14], [15] to derive the expression for PDF of the product of Nakagamim or Gamma distributed random variables...
...The Mellin transform of a product of random variables is the product of the Mellin transforms of the individual random variables [
3
], [15]...
...The Mellin transform has been employed previously in similar applications such as determining the PDF of product of beta, gamma and Rayleigh distributed variables [
3
], [7], [15]; however, the inverse Mellin transform and the resultant PDF is expressed in these contributions in the form of Meijer’s G function...
...Next, according to the properties of the Mellin transform, the transform of the product of random variables is equal to the product of the Mellin transforms of the individual random variables [
3
], [15]...
...In terms of probability theory, fX (x) in (1) denotes the PDF of the random variable X .T he inverse Mellin transform is defined as [
3
]...
...Here, we use the property of Mellin transform whereby if M [f (t) ,z ]= F (z), then [
3
], [17]...
...If we use the variable transform of (z +1 )/2 → z in the above equation, this does not affect the path of integration [
3
]...
...From the Residue Theorem [
3
], [17], [19], we know that the complex integral at the righthand side of the above equation can be computed by summing the residues of the integrand associated with all its poles...
...of z = −j. Consequently, using the corresponding relationship characterizing the residues of multiple poles [
3
], [18], [19] and...
Sohail Ahmed
,
et al.
Probability Distributions of Products of Rayleigh and Nakagamim Varia...
...Moreover, the generalized�� distribution belongs to the (Fox) �� function distributions family [
18
]...
...We propose using the Gamma distribution due to the following reasons: (i) Gamma distribution is a TypeIII Pearson distribution which is widely used in fitting distributions for positive RVs by matching the first and second moments [
18
], and (ii) since the PDF in (3) corresponds to the product of two Gamma RVs, one of the corresponding Gamma PDFs will dominate for large values of �� �� or �� �� [7]...
Saad AlAhmadi
,
et al.
On the approximation of the generalizedKappa distribution by a gamma ...
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Citations
(205)
Testing the equality of several covariance matrices
(
Citations: 1
)
T. PhamGia
,
N. Turkkan
Journal:
Journal of Statistical Computation and Simulation  J STAT COMPUT SIM
, vol. aheadofp, no. aheadofp, pp. 114, 2011
The Bayesian Framework for Inverse Problems in Heat Transfer
(
Citations: 1
)
Jari P. Kaipio
,
Colin Fox
Journal:
Heat Transfer Engineering  HEAT TRANSFER ENG
, vol. 32, no. 9, pp. 718753, 2011
A New Formula for the BER of Binary Modulations with DualBranch Selection over GeneralizedK
Imran Shafique Ansari
,
Saad AlAhmadi
,
Ferkan Yilmaz
,
MohamedSlim Alouini
,
Halim Yanikomeroglu
Journal:
IEEE Transactions on Communications  TCOM
, vol. 59, no. 10, pp. 26542658, 2011
An Exact ClosedForm Expression for the BER of Binary Modulations with DualBranch Selection over GeneralizedK Fading
Imran Shafique Ansari
,
Saad AlAhmadi
,
Ferkan Yilmaz
,
MohamedSlim Alouini
,
Halim Yanikomeroglu
Conference:
Vehicular Technology, IEEE Conference  VTC Spring
, pp. 14, 2011
CSTII’s recognition domain for acceptor substrates in α(2→8)sialylations
Wenling Li
,
Ping Zhang
,
Amir J. Zuccolo
,
Ruxiang Blake Zheng
,
ChangChun Ling
Journal:
Carbohydrate Research  CARBOHYD RES
, vol. 346, no. 13, pp. 16921704, 2011