In this note we consider an alternative approach to compute the distribution of the sum of independent exponential random variables. In particular, by considering the logarithmic relation between exponential and beta distribution functions and by considering the Wilks’ integral representation for the product of independent beta random variables, we provide a closed-form expression for the distribution of the sum of independent exponential random variables. The expression we obtain is simpler than the ones previously obtained in the literature.

On the distribution of sums of independent exponential random variables via Wilks' integral representation

FAVARO, STEFANO;
2010-01-01

Abstract

In this note we consider an alternative approach to compute the distribution of the sum of independent exponential random variables. In particular, by considering the logarithmic relation between exponential and beta distribution functions and by considering the Wilks’ integral representation for the product of independent beta random variables, we provide a closed-form expression for the distribution of the sum of independent exponential random variables. The expression we obtain is simpler than the ones previously obtained in the literature.
2010
109
1035
1042
http://www.springer.com/math/journal/10440
Beta random variables; Exponential random variables; product and sum of independent random variables; Wilks’ integral representation
S. Favaro; S.G. Walker
File in questo prodotto:
File Dimensione Formato  
AAM.pdf

Accesso riservato

Tipo di file: POSTPRINT (VERSIONE FINALE DELL’AUTORE)
Dimensione 330.6 kB
Formato Adobe PDF
330.6 kB Adobe PDF   Visualizza/Apri   Richiedi una copia

I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.

Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/2318/58830
Citazioni
  • ???jsp.display-item.citation.pmc??? ND
  • Scopus 12
  • ???jsp.display-item.citation.isi??? 10
social impact