The distribution of the sum of independent gamma random variables

@article{Moschopoulos1985TheDO,
  title={The distribution of the sum of independent gamma random variables},
  author={Panagis G. Moschopoulos},
  journal={Annals of the Institute of Statistical Mathematics},
  year={1985},
  volume={37},
  pages={541-544}
}
  • P. Moschopoulos
  • Published 1 December 1985
  • Mathematics
  • Annals of the Institute of Statistical Mathematics
SummaryThe distribution of the sum ofn independent gamma variates with different parameters is expressed as a single gamma-series whose coefficients are computed by simple recursive relations. 
View on Springer
464 Citations
Highly Influential Citations
46
Background Citations
176
Methods Citations
105
Results Citations
4

464 Citations

Citation Type

Citation Type

On the distribution of the product of independent beta random variables
In this paper, exact distribution of the product of independent beta random variables has been derived and its structural form is given together with recurrence relations for the coefficients of this…
A Note on the Sum of Correlated Gamma Random Variables
TLDR
This Letter obtains exact expressions for the probability density function and the cumulative distribution function of the sum of arbitrarily correlated gamma variables in terms of certain Lauricella functions.
ON THE LINEAR COMBINATION AND RATIO OF LAPLACE RANDOM VARIABLES
The distributions of the linear combination αX + βY and the ratio |X/Y | are derived, where X and Y are independent Laplace random variables.
On the linear combination of normal and Laplace random variables
TLDR
A program in MAPLE is provided to compute the associated percentage points of αX+βY when X and Y are normal and Laplace random variables distributed independently of each other.
Gamma-Series Representations for the Sum of Independent Gamma Random Variables and for the Product of Independent Beta Random Variables
In this work it is shown that using well-known series expansions it is possible to represent a single gamma distribution and also the logarithm of a single beta distribution, as an infinite mixture…
Normal and logistic random variables: distribution of the linear combination
The exact distribution of the linear combination α X  +  β Y is derived when X and Y are normal and logistic random variables distributed independently of each other. Tabulations of the associated…
Near-exact distributions for positive linear combinations of independent non-central Gamma random variables
In this paper near-exact distributions for positive linear combinations of independent non-central Gamma random variables are developed. The authors show that through an adequate factorization of the…
On the Linear Combination of Exponential and Gamma Random Variables
TLDR
A measure of entropy of the linear combination α X + β Y, derived when X and Y are exponential and gamma random variables distributed independently of each other, is investigated.
A Review of Results on Sums of Random Variables
Sums of random variables arise naturally in wireless communications and related areas. Here, we provide a review of the known results on sums of exponential, gamma, lognormal, Rayleigh and Weibull…
ON THE LINEAR COMBINATION OF LAPLACE RANDOM VARIABLES
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…
...
1
2
3
4
5
...

References

SHOWING 1-4 OF 4 REFERENCES
Probability Content of Regions Under Spherical Normal Distributions, IV: The Distribution of Homogeneous and Non-Homogeneous Quadratic Functions of Normal Variables
Abstract : The distribution of homogeneous and non-homogeneous quadratic functions of normal variables is presented. In geometrical terms the probability content is evaluated for a fixed ellipsoid of…
SERIES REPRESENTATIONS OF DISTRIBUTIONS OF QUADRATIC FORMS IN NORMAL VARIABLES, I. CENTRAL CASE,
Abstract : The probability density function (pdf) of a positive definite quadratic form in (central or non-central) normal variables can be represented as a series expansion in a number of different…
Storage capacity of a dam with gamma type inputs
SummaryConsider mutually independent inputsX1,...,Xn onn different occasions into a dam or storage facility. The total input isY=X1+...+Xn. This sum is a basic quantity in many types of stochastic…
The H-function with applications in statistics and other disciplines