# 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} }

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.

## 491 Citations

### A Note on the Sum of Correlated Gamma Random Variables

- BusinessArXiv
- 2011

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

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The distributions of the linear combination αX + βY and the ratio |X/Y | are derived, where X and Y are independent Laplace random variables.

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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

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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

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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…

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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

- Computer Science, MathematicsEntropy
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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

- Business, Mathematics
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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

- Mathematics, Computer ScienceProbability in the Engineering and Informational Sciences
- 2005

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

## 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

- Mathematics
- 1961

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,

- Mathematics
- 1967

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

- Mathematics
- 1982

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…