EEN: Extended Exp-Normal Distribution
In bistoonh/NewDists: The GOGaG and EEG family of distributions.

Description Usage Arguments Value Author(s) References Examples

These functions provide information about the Extended Exp-Normal distribution. dEEN gives the density, pEEN gives the distribution function, qEEN gives the quantile function, rEEN generates random deviates, mEEN gives the mean function, vEEN gives the variance function, sEEN gives the skewness function, kEEN gives the kurtosis function, and entEEN gives the Rrnyi or Shannon entropy function due to Alizadeh et al. (2018) specified by the pdf

f(x;α ,β ,μ ,σ )=\frac{φ ≤ft( \frac{x-μ}{σ} \right)Φ {{≤ft( \frac{x-μ}{σ} \right)}^{α -1}}≤ft[ α +≤ft( β -α \right) Φ {{≤ft( \frac{x-μ}{σ} \right)}^{β }} \right]}{{{≤ft[ Φ {{≤ft( \frac{x-μ}{σ} \right)}^{α }}+1-Φ {{≤ft(\frac{x-μ}{σ} \right)}^{β }} \right]}^{2}}},

where α, β, σ > 0.

dEEN(x, alpha, beta, mu = 0, sigma = 1, log = FALSE)
pEEN(x, alpha, beta, mu = 0, sigma = 1)
qEEN(p, alpha, beta, mu = 0, sigma = 1)
rEEN(n, alpha, beta, mu = 0, sigma = 1)
mEEN(alpha, beta, mu = 0, sigma = 1)
vEEN(alpha, beta, mu = 0, sigma = 1)
sEEN(alpha, beta, mu = 0, sigma = 1)
kEEN(alpha, beta, mu = 0, sigma = 1)
entEEN(gamma, alpha, beta, mu = 0, sigma = 1, explain = FALSE)

`x`	Scaler or vector of values at which the pdf or cdf needs to be computed
`p`	Scaler or vector of probabilities at which the quantile needs to be computed
`n`	Number of random numbers to be generated
`alpha`	The value of the first shape parameter. Must be positive and finite.
`beta`	The value of the second shape parameter. Must be positive and finite.
`mu`	Value of mean. Must be finite.
`sigma`	Value of standard deviations. Must be positive and finite.
`log`	Logical; if TRUE, probabilities p are given as log(p).
`gamma`	The gamma in Rrnyi entropy. if gamma = 1, the Shannon entropy is returned.
`explain`	Logical; if TRUE, explain Rrnyi or Shannon entropy is returned.

An object of the same length as x, giving the pdf or cdf values computed at x or an object of the same length as p, giving the quantile values computed at p or an object of the same length as n, giving the random numbers generated or an object of the same length as gamma, giving the entropy (Rrnyi or Shannon) or an object giving the values of mean, variance, skewness, or kurtosis.

Bistoon Hosseini, Mahmoud Afshari

Alizadeh, Morad, Mahmoud Afshari, Bistoon Hosseini, and Thiago G. Ramires. "Extended exp-G family of distributions: Properties, applications and simulation." Communications in Statistics-Simulation and Computation (2018): 1-16.

x = runif(10, min= -1 , max = 1)
dEEN(x, alpha = 0.5, beta = 1.2, mu = -2, sigma = 0.2, log = FALSE)
pEEN(x, alpha = 0.5, beta = 1.2, mu = 1, sigma = 1.1)
qEEN(x, alpha = 0.5, beta = 1.2, mu = .5, sigma = 11)
rEEN(n = 10, alpha = 0.5, beta = 1.2, mu = 0, sigma = 1)
mEEN(alpha = 0.5, beta = 1.2, mu = 10, sigma = .1)
vEEN(alpha = 0.5, beta = 1.2, mu = 2, sigma = 3)
sEEN(alpha = 0.5, beta = 1.2, mu = 1, sigma = 1)
kEEN(alpha = 0.5, beta = 1.2, mu = 0, sigma = 2)
entEEN(gamma = c(.5, 1, 1.5), alpha = 0.5, beta = 1.2, mu = 0, sigma = 1, explain = TRUE)