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

Toufik Chaayra, Hussain Ben-azza, Faissal El Bouanani
2021 Mathematical Modelling and Engineering Problems  
Considering this issue, a more accurate 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.  ... 
doi:10.18280/mmep.080104 fatcat:4xvdrvob2fee5bwcs2i7i5kqxu

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

Carlos A. Coelho
2004 Journal of Multivariate Analysis  
Based on this concept it is shown how a random variable whose exponential has a Beta 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.  ... 
doi:10.1016/j.jmva.2003.12.001 fatcat:e23553iftbhdxavtggtpbqujrq

Bibliography of distributed approximation beyond bounded degree [article]

Laurent Feuilloley
2021 arXiv   pre-print
This document is an informal bibliography 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.  ... 
arXiv:2001.08510v3 fatcat:wjfqufg725fvtluzy62rfjddou

New analytical framework for the products of independent RVs with wireless applications

Yunfei Chen, George K. Karagiannidis, Hao Lu, Ning Cao
2012 2012 IEEE Wireless Communications and Networking Conference (WCNC)  
A novel analytical framework for evaluating the statistics 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.  ... 
doi:10.1109/wcnc.2012.6213927 dblp:conf/wcnc/ChenKLC12 fatcat:gojoyoon5ndznja3von2r73d74

On the linear combination of independent logistic random variables

Filipe J. Marques
2018 Statistics, Optimization and Information Computing  
It is shown that the exact 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.  ... 
doi:10.19139/soic.v6i3.578 fatcat:2xzr64zcgfcxpnnvre5ys6td3y

Novel Approximations to the Statistics of Products of Independent Random Variables and Their Applications in Wireless Communications

Yunfei Chen, George K. Karagiannidis, Hao Lu, Ning Cao
2012 IEEE Transactions on Vehicular Technology  
A novel analytical framework for evaluating the statistics 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  ... 
doi:10.1109/tvt.2011.2178441 fatcat:ccut45q75vbpnhfz3uoccnpygy

Saddlepoint Approximation to Cumulative Distribution Function for Poisson–Exponential Distribution

Alya O. Almutair, Heng Chin Low
2013 Modern Applied Science  
We discuss 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.  ... 
doi:10.5539/mas.v7n3p26 fatcat:hwsqdlqdszgpticnjtr6mbhewa

On the Approximation of the Generalized-K PDF by a Gamma PDF Using the Moment Matching Method

Saad Al-Ahmadi, Halim Yanikomeroglu
2009 2009 IEEE Wireless Communications and Networking Conference  
The region-wise 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  ... 
doi:10.1109/wcnc.2009.4917849 dblp:conf/wcnc/Al-AhmadiY09 fatcat:ihjhrxzwqzcnhbffd7do2qxini

Comparison of Maximum Likelihood and GAN-based training of Real NVPs [article]

Ivo Danihelka, Balaji Lakshminarayanan, Benigno Uria, Daan Wierstra, Peter Dayan
2017 arXiv   pre-print
We show that an 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.  ... 
arXiv:1705.05263v1 fatcat:tjxqumbrybenhgwzknqqqw3f3a

Practical Small-Sample Asymptotics for Regression Problems

Robert L. Strawderman, George Casella, Martin T. Wells
1996 Journal of the American Statistical Association  
Saddlepoint 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.  ... 
doi:10.2307/2291660 fatcat:b7hhwjucevaz7jwj3ikygg66ey

Practical Small-Sample Asymptotics for Regression Problems

Robert L. Strawderman, George Casella, Martin T. Wells
1996 Journal of the American Statistical Association  
Saddlepoint 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.  ... 
doi:10.1080/01621459.1996.10476933 fatcat:6oiehr2zh5arvloc2vlb5zkaye

On the approximation of the generalized-Κ distribution by a gamma distribution for modeling composite fading channels

Saad Al-Ahmadi, Halim Yanikomeroglu
2010 IEEE Transactions on Wireless Communications  
Moreover, the approach introduced in this paper can be used to well-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.  ... 
doi:10.1109/twc.2010.02.081266 fatcat:clmxuf3nvzcwdel7gqa4wrij3u

On the Exact and Near-Exact Distributions of the Product of Generalized Gamma Random Variables and the Generalized Variance

Carlos A. Coelho, Barry C. Arnold
2014 Communications in Statistics - Theory and Methods  
In this paper the authors first obtain the exact 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.'  ... 
doi:10.1080/03610926.2013.783073 fatcat:cmfrclgcrbgkvmyvt3v4tlvary

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.  ... 

On the distribution of linear functions of independent F and U variates

Jack C. Lee, Ling Hu
1996 Statistics and Probability Letters  
This paper is concerned with the 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.  ... 
doi:10.1016/0167-7152(95)00030-5 fatcat:gr3jgqbaqbghhpmfjjmhn64ara
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