B-beta function of GMM model

\(b_\beta(\theta) = \dfrac{1}{1 + \beta} \int f(x; \theta) ^ {1 + \beta} d x\)

b_beta(lambda, mu, sigma, beta = 0.001, rel.tol = 1e-12)

Arguments

lambda

`numeric` - Vector of mixing proportions of each normal component

mu

`numeric` - Vector of means of each normal component

sigma

`numeric` - Vector of standard deviations of each normal component

beta

`numeric(1)` - parameter corresponds to the beta-divergence induced likelihood

rel.tol

relative accuracy requested.

Value

`numeric(1)`

Examples

set.seed(42)
lambda <- c(0.25, 0.75)
mu <- c(0, 4)
sigma <- c(1, 1)
b_beta(lambda, mu, sigma, beta=0.2)
#> [1] 0.5723572
#> attr(,"abs.error")
#> [1] 5.085423e-13
b_beta(lambda, mu, sigma, beta=1e-3)
#> [1] 0.9970751
#> attr(,"abs.error")
#> [1] 4.26254e-13