BEGG: Bimodal extension of the generalized Gamma-Distribution

In CharlotteJana/momcalc: Symbolic Moment Calculation

Description

The bimodal extension of the generalized Gamma-Distribution (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.

Usage

dBEGG(x, alpha, beta, delta0, delta1, eta, eps, mu = 0, sigma = 1)

mBEGG(alpha, beta, delta0, delta1, eta, eps, mu = 0, sigma = 1,
  order = 1:4)

Arguments

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.

Functions

• dBEGG: density function

• mBEGG: raw moments

Note

This distribution is included in package momcalc because it is a good test case for function is.unimodal and the raw moments are known.

References

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), 371-384.

Examples

 # 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 = "")

CharlotteJana/momcalc documentation built on Oct. 17, 2019, 7:21 a.m.