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A saddlepoint approximation to the distribution of the sum of independent non‐identically beta random variables
Author(s) -
Nadarajah Saralees,
Jiang Xiao,
Chu Jeffrey
Publication year - 2015
Publication title -
statistica neerlandica
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.52
H-Index - 39
eISSN - 1467-9574
pISSN - 0039-0402
DOI - 10.1111/stan.12051
Subject(s) - mathematics , independent and identically distributed random variables , beta distribution , random variable , beta (programming language) , illustration of the central limit theorem , distribution (mathematics) , statistics , sum of normally distributed random variables , mathematical analysis , computer science , programming language
The exact distribution of the sum of more than two independent beta random variables has not been known. Even in terms of approximations, only the normal approximation is known for the sum. Motivated by Murakami [Statistica Neerlandica, 2014, doi:10.1111/stan.12032], we derive here a saddlepoint approximation for the distribution of sum. An extensive simulation study shows that it always performs better than the normal approximation.