# On the distribution of the sum of dependent standard normally distributed random variables using copulas

@inproceedings{Schneider2021OnTD, title={On the distribution of the sum of dependent standard normally distributed random variables using copulas}, author={Walter Schneider}, year={2021} }

The distribution function of the sum Z of two standard normally distributed random variables X and Y is computed with the concept of copulas to model the dependency between X and Y . By using implicit copulas such as the Gaussor t-copula as well as Archimedean Copulas such as the Clayton-, Gumbelor Frank-copula, a wide variety of different dependencies can be covered. For each of these copulas an analytical closed form expression for the corresponding joint probability density function fX,Y is… Expand

#### References

SHOWING 1-10 OF 13 REFERENCES

Determining Distribution for the Product of Random Variables by Using Copulas

- Mathematics
- Risks
- 2019

Determining distributions of the functions of random variables is one of the most important problems in statistics and applied mathematics because distributions of functions have wide range of… Expand

On computing the distribution function of the sum of independent random variables

- Mathematics, Computer Science
- Comput. Oper. Res.
- 2001

Abstract We present an efficient approach to the determination of the convolution of random variables when their probability density functions are given as continuous functions over finite support.… Expand

Analyzing Dependent Data with Vine Copulas

- Mathematics, Computer Science
- Lecture Notes in Statistics
- 2019

This textbook provides a step-by-step introduction to the class of vine copulas, their statistical inference and applications, and demonstrates how the R package VineCopula can be used to explore and build statistical dependence models from scratch. Expand

An Introduction to Copulas

- Computer Science
- Technometrics
- 2000

This book is aimed at graduate students in statistics or mathematics, and practicing statisticians, and requires proficiency in advanced calculus, and can serve as a very good reference on the exciting topic of wavelets. Expand

A copula-based approach to account for dependence in stress-strength models

- Mathematics
- 2013

The focus of stress-strength models is on the evaluation of the probability R = P(Y < X) that stress Y experienced by a component does not exceed strength X required to overcome it. In reliability… Expand

A stress–strength model with dependent variables to measure household financial fragility

- Computer Science, Mathematics
- Stat. Methods Appl.
- 2012

It is pointed out that neglecting the existing dependence in fact overestimates the actual household fragility, and it is shown that the proposed method improves the estimation of household financial fragility. Expand

On the distribution of the sum of independent uniform random variables

- Mathematics
- 2009

Motivated by an application in change point analysis, we derive a closed form for the density function of the sum of n independent, non-identically distributed, uniform random variables.

An Inequality for the Sum of Independent Bounded Random Variables

- Mathematics
- 2012

We give a simple inequality for the sum of independent, bounded random variables. This inequality improves on the celebrated result of Hoeffding in a special case. It is optimal in the limit where… Expand

Quantitative Risk Management

- Economics, Computer Science
- International Encyclopedia of Statistical Science
- 2011

The book’s methodology draws on diverse quantitative disciplines, from mathematical finance and statistics to econometrics and actuarial mathematics, to satisfactorily address extreme outcomes and the dependence of key risk drivers. Expand

Probability, Random Variables and Stochastic Processes

- Mathematics, Computer Science
- 1965

This chapter discusses the concept of a Random Variable, the meaning of Probability, and the axioms of probability in terms of Markov Chains and Queueing Theory. Expand