# 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

 ```1 2 3 4``` ```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

 ``` 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 = "") ```

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