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A Closed-Form Approximation to the Distribution for the Sum of Independent Non-identically Generalized Gamma Variates and Applications

2021
*
Mathematical Modelling and Engineering Problems
*

Considering this issue, a more accurate

doi:10.18280/mmep.080104
fatcat:4xvdrvob2fee5bwcs2i7i5kqxu
*approximation**of*the*distribution*function is required. ... By assuming the probability density function (PDF)*of*a*generalized*gamma (GG) RV evaluated in terms*of*a proper subset H1,0 1,1 class*of*Fox's H-function (FHF) and the moment-based*approximation*to estimate ... Our main work is focused on the application*of*the sum*of**independent*and not necessarily identical (i.n.i.d) GG*distributions*and its application in WCSs subject to GG fading model. ...##
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The generalized near-integer Gamma distribution: a basis for 'near-exact' approximations to the distribution of statistics which are the product of an odd number of independent Beta random variables

2004
*
Journal of Multivariate Analysis
*

Based on this concept it is shown how a random variable whose exponential has a Beta

doi:10.1016/j.jmva.2003.12.001
fatcat:e23553iftbhdxavtggtpbqujrq
*distribution*may be closely*approximated*by a sum*of**independent*Gamma random variables, giving rise to the*generalized*... A particular near-exact*approximation*to the*distribution**of*the logarithm*of*the product*of*an odd number*of**independent*Beta random variables is shown to be a GNI Gamma*distribution*. ... for a logBeta random variable and for the product*of*an odd number*of**independent*particular Beta random variables. ...##
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Bibliography of distributed approximation beyond bounded degree
[article]

2021
*
arXiv
*
pre-print

This document is an informal bibliography

arXiv:2001.08510v3
fatcat:wjfqufg725fvtluzy62rfjddou
*of*the papers dealing with*distributed**approximation*algorithms. ... These later classes are the focus*of*the current work. ...*Approximation*ratio : 1 − 1 polylog n . Complexity : polylog n. Notes : Extension*of*Paper 31 [9] to a more*general*class*of*graphs. ...##
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New analytical framework for the products of independent RVs with wireless applications

2012
*
2012 IEEE Wireless Communications and Networking Conference (WCNC)
*

A novel analytical framework for evaluating the statistics

doi:10.1109/wcnc.2012.6213927
dblp:conf/wcnc/ChenKLC12
fatcat:gojoyoon5ndznja3von2r73d74
*of*the products*of**independent*random variables is proposed. ... The accuracy*of*the new*approximation*is examined. Numerical results show that it is quite accurate in most regions*of*interest. ... Fig. 1 . 1 Comparison*of*the*approximate*CDF (plus line) and the exact CDF (circle line) for different*distribution*parameters and different numbers*of**independent**generalized*Gamma RVs. ...##
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On the linear combination of independent logistic random variables

2018
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Statistics, Optimization and Information Computing
*

It is shown that the exact

doi:10.19139/soic.v6i3.578
fatcat:2xzr64zcgfcxpnnvre5ys6td3y
*distribution*may be represented as a shifted infinite sum*of**independent*random variables*distributed*as the difference*of*two*independent**Generalized*Integer Gamma*distributions*... In this paper we derive two near-exact*approximations*[5] for the linear combinations*of**independent*logistic random variables, which will have as*distribution*: i) a shifted difference*of*two*Generalized*... [15] develops*approximations*for the*distribution**of*the sum*of*random variables with a*generalized*logistic*distribution*also for the*independent*and identically*distributed*case. ...##
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Novel Approximations to the Statistics of Products of Independent Random Variables and Their Applications in Wireless Communications

2012
*
IEEE Transactions on Vehicular Technology
*

A novel analytical framework for evaluating the statistics

doi:10.1109/tvt.2011.2178441
fatcat:ccut45q75vbpnhfz3uoccnpygy
*of*the product*of**independent*random variables is proposed. ... Numerical results, which are used to check the accuracy*of*the new*approximations*, show that it is quite accurate in most regions*of*interest. ...*Generalized*Gamma*Distribution*Using the Mellin transform and the*approximation*in (23) , the*approximation*to the pdf*of*the product*of*n*independent*normalized*generalized*Gamma RVs can be derived as ...##
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Saddlepoint Approximation to Cumulative Distribution Function for Poisson–Exponential Distribution

2013
*
Modern Applied Science
*

We discuss

doi:10.5539/mas.v7n3p26
fatcat:hwsqdlqdszgpticnjtr6mbhewa
*approximations*to random sum random variable with dependent components assuming existence*of*the moment*generating*function. ... A numerical example*of*continuous*distributions*from the Poisson-Exponential*distribution*is presented. ... ., Kingdom*of*Saudi Arabia. The authors thank the referee for constructive comments. ...##
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On the Approximation of the Generalized-K PDF by a Gamma PDF Using the Moment Matching Method

2009
*
2009 IEEE Wireless Communications and Networking Conference
*

The region-wise

doi:10.1109/wcnc.2009.4917849
dblp:conf/wcnc/Al-AhmadiY09
fatcat:ihjhrxzwqzcnhbffd7do2qxini
*approximation*obtained by the adjusted moment matching method is used to wellapproximate the PDF*of*the sum*of*identically and*independent**generalized*-K random variables. ... The accuracy*of*this*approximation*in the lower and upper tail regions is enhanced by adjusting the parameters*of*the*approximating*Gamma*distribution*in each region. ... ON THE*APPROXIMATION**OF*THE PDF*OF*THE SUM*OF**INDEPENDENT*GENERALIZEK-K RVS The results obtained in Section III can also be used to*approximate*the PDF*of*the sum*of**independent**generalized*-K RVs since ...##
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Comparison of Maximum Likelihood and GAN-based training of Real NVPs
[article]

2017
*
arXiv
*
pre-print

We show that an

arXiv:1705.05263v1
fatcat:tjxqumbrybenhgwzknqqqw3f3a
*independent*critic trained to*approximate*Wasserstein distance between the validation set and the*generator**distribution*helps detect overfitting. ... We then compare the*generated*samples, exact log-probability densities and*approximate*Wasserstein distances. ... We were able to measure the gap between the unbiased KL estimate log q(z|x) − log p(z) and its*approximation*from GAN. ...##
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Practical Small-Sample Asymptotics for Regression Problems

1996
*
Journal of the American Statistical Association
*

Saddlepoint

doi:10.2307/2291660
fatcat:b7hhwjucevaz7jwj3ikygg66ey
*approximations*are derived for sums*of**independent*, but not necessarily identically*distributed*, random variables, along with*generalizations*to estimating equations and multivariate problems ... We give*general*formulae for the*distribution**of*the coefficients in a*generalized*linear model with both canonical and non-canonical link functions, and illustrate the accuracy*of*our*approximations*with ... Field (1982) derives*approximations*in the case*of**independent*and identically*distributed*random variables. ...##
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Practical Small-Sample Asymptotics for Regression Problems

1996
*
Journal of the American Statistical Association
*

Saddlepoint

doi:10.1080/01621459.1996.10476933
fatcat:6oiehr2zh5arvloc2vlb5zkaye
*approximations*are derived for sums*of**independent*, but not necessarily identically*distributed*, random variables, along with*generalizations*to estimating equations and multivariate problems ... We give*general*formulae for the*distribution**of*the coefficients in a*generalized*linear model with both canonical and non-canonical link functions, and illustrate the accuracy*of*our*approximations*with ... Field (1982) derives*approximations*in the case*of**independent*and identically*distributed*random variables. ...##
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On the approximation of the generalized-Κ distribution by a gamma distribution for modeling composite fading channels

2010
*
IEEE Transactions on Wireless Communications
*

Moreover, the approach introduced in this paper can be used to well-

doi:10.1109/twc.2010.02.081266
fatcat:clmxuf3nvzcwdel7gqa4wrij3u
*approximate*the*distribution**of*the sum*of**independent**generalized*-random variables by a Gamma*distribution*; the need for such results ... In this paper, the*approximation**of*the*generalized*-PDF by a Gamma PDF using the moment matching method is explored. ... ACKNOWLEDGMENT The authors would like thank Sebastian Szyszkowicz for his helpful discussions during early stages*of*this work. ...##
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On the Exact and Near-Exact Distributions of the Product of Generalized Gamma Random Variables and the Generalized Variance

2014
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Communications in Statistics - Theory and Methods
*

In this paper the authors first obtain the exact

doi:10.1080/03610926.2013.783073
fatcat:cmfrclgcrbgkvmyvt3v4tlvary
*distribution**of*the logarithm*of*the product*of**independent**generalized*Gamma r.v.' ... Numerical studies are carried out to assess the precision*of*different*approximations*to the exact*distribution*and they show the high accuracy*of*the*approximations*provided by the near-exact*distributions*... A), the importance*of*the*distribution**of*the product*of**independent**generalized*Gamma r.v.' ...##
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Page 1626 of Mathematical Reviews Vol. , Issue 82d
[page]

1982
*
Mathematical Reviews
*

In this paper it is shown that the probability

*distribution**of*q(n;a,c) can be*approximated*by the difference*of*two*independent*type III variables. ... Author’s summary: “The randomized gamma*distribution*is defined as a*generalization**of*the*distribution**of*a lattice Poisson random sum*of**independent*three-parameter gamma variables. ...##
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On the distribution of linear functions of independent F and U variates

1996
*
Statistics and Probability Letters
*

This paper is concerned with the

doi:10.1016/0167-7152(95)00030-5
fatcat:gr3jgqbaqbghhpmfjjmhn64ara
*distributions**of*linear functions*of**independent*U and F variates. ... Useful and accurate*approximations*are considered for the linear combinations*of*two*independent*U variates as well as the linear combinations*of*two*independent*F variates. ... The*distribution**of*linear functions*of*two*independent*U variates In this section we will consider some*approximations*to the*distributions**of*linear compound for h = 1, 2, 3. ...
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