Description Usage Arguments Functions Note References Examples
The bimodal extension of the generalized GammaDistribution (BEGG) was first introduced by Bulut et. al. in 2015. It is a scale mixture of the generalized gamma distribution that is almost always bimodal. The two modes can have different shapes, depending on the parameters α, β, δ0, δ1, η, ε, μ and σ.
1 2 3 4 
x 
vector of quantiles. 
alpha 
a positive number. Controls the kurtosis of the distribution. The distribution is leptokurtic for α ϵ (0,2) and β = 1. It is platikurtic for α > 2 and β = 1. 
beta 
a positive number. Controls the kurtosis of the distribution. 
delta0 
a positive number. Controls the bimodality. If δ0 = δ1, the density function will have two modes with the same height. If δ0 = δ1 = 0, the distribution will be unimodal. 
delta1 
a positive number. Controls the bimodality. 
eta 
a positive number. Controls the tail thickness of the distribution. 
eps 
numeric. Controls the skewness of the distribution. When ε = 0, the distribution will be symmetric with two modes with different height. 
mu 
numeric. The location parameter of the distribution. Defaults to 0. 
sigma 
a positive number. The scaling parameter of the distribution. Defaults to 1. 
order 
integer vector. Specifies all orders for which the raw moments shall be calculated. 
dBEGG
: density function
mBEGG
: raw moments
This distribution is included in package momcalc because it is a
good test case for function is.unimodal
and the raw moments are
known.
Çankaya, M. N.; Bulut, Y. M.; Doğru, F. Z. & Arslan, O.(2015). A bimodal extension of the generalized gamma distribution. Revista Colombiana de Estadística, 38(2), 371384.
1 2 3 4 5 6 7 8 9 10 11 12 13 14  # The first 3 examples are the same as in the paper:
par(mfrow=c(2, 2))
x < seq(2, 2, .01)
y < dBEGG(x, alpha = 2, beta = 2, delta0 = 1, delta1 = 4, eta = 1, eps = 0)
plot(x, y, type = "l", ylab = "")
x < seq(2, 3, .01)
y < dBEGG(x, alpha = 2, beta = 1, delta0 = 0, delta1 = 2, eta = 1, eps = 0.5)
plot(x, y, type = "l", ylab = "")
x < seq(2.5, 1.5, .01)
y < dBEGG(x, alpha = 3, beta = 2, delta0 = 4, delta1 = 2, eta = 2, eps = 0.3)
plot(x, y, type = "l", ylab = "")
x < seq(4, 2, .01)
y < dBEGG(x, alpha = 2, beta = 1, delta0 = 0, delta1 = 0, eta = 1, eps = 0.7)
plot(x, y, type = "l", ylab = "")

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