TY - JOUR

T1 - Development and comparative study of two near-exact approximations to the distribution of the product of an odd number of independent Beta random variables

AU - Coelho, Carlos Manuel Agra

PY - 2007/1/1

Y1 - 2007/1/1

N2 - Using the concept of near-exact approximation to a distribution we developed two different near-exact approximations to the distribution of the product of an odd number of particular independent Beta random variables (r.v.'s). One of them is a particular generalized near-integer Gamma (GNIG) distribution and the other is a mixture of two GNIG distributions. These near-exact distributions are mostly adequate to be used as a basis for approximations of distributions of several statistics used in multivariate analysis. By factoring the characteristic function (c.f.) of the logarithm of the product of the Beta r.v.'s, and then replacing a suitably chosen factor of that c.f. by an adequate asymptotic result it is possible to obtain what we call a near-exact c.f., which gives rise to the near-exact approximation to the exact distribution. Depending on the asymptotic result used to replace the chosen pails of the c.f., one may obtain different near-exact approximations. Moments from the two near-exact approximations developed are compared with the exact ones. The two approximations are also compared with each other, namely in terms of moments and quantiles. (c) 2006 Elsevier B.V. All rights reserved.

AB - Using the concept of near-exact approximation to a distribution we developed two different near-exact approximations to the distribution of the product of an odd number of particular independent Beta random variables (r.v.'s). One of them is a particular generalized near-integer Gamma (GNIG) distribution and the other is a mixture of two GNIG distributions. These near-exact distributions are mostly adequate to be used as a basis for approximations of distributions of several statistics used in multivariate analysis. By factoring the characteristic function (c.f.) of the logarithm of the product of the Beta r.v.'s, and then replacing a suitably chosen factor of that c.f. by an adequate asymptotic result it is possible to obtain what we call a near-exact c.f., which gives rise to the near-exact approximation to the exact distribution. Depending on the asymptotic result used to replace the chosen pails of the c.f., one may obtain different near-exact approximations. Moments from the two near-exact approximations developed are compared with the exact ones. The two approximations are also compared with each other, namely in terms of moments and quantiles. (c) 2006 Elsevier B.V. All rights reserved.

KW - near-exact approximations

KW - mixtures

KW - generalized near-integer Gamma distribution

KW - independent random variables

KW - multivariate analysis

U2 - 10.1016/j.jspi.2006.09.005

DO - 10.1016/j.jspi.2006.09.005

M3 - Article

SN - 0378-3758

VL - 137

SP - 1560

EP - 1575

JO - Journal Of Statistical Planning And Inference

JF - Journal Of Statistical Planning And Inference

IS - 5

ER -