QBAsyDist (version 0.1.2)

ALoD: Quantile-based asymmetric logistic distribution

Description

Density, cumulative distribution function, quantile function and random sample generation from the quantile-based asymmetric logistic distribution (ALoD) proposed in Gijbels et al. (2019a).

Usage

dALoD(y, mu, phi, alpha)
pALoD(q, mu, phi, alpha)
qALoD(beta, mu, phi, alpha)
rALoD(n, mu, phi, alpha)

Arguments

y, q

These are each a vector of quantiles.

mu

This is the location parameter \(\mu\).

phi

This is the scale parameter \(\phi\).

alpha

This is the index parameter \(\alpha\).

beta

This is a vector of probabilities.

n

This is the number of observations, which must be a positive integer that has length 1.

Value

dALoD provides the density, pALoD provides the cumulative distribution function, qALoD provides the quantile function, and rALoD generates a random sample from the quantile-based asymmetric logistic distribution. The length of the result is determined by \(n\) for rALoD, and is the maximum of the lengths of the numerical arguments for the other functions.

References

Gijbels, I., Karim, R. and Verhasselt, A. (2019a). On quantile-based asymmetric family of distributions: properties and inference. International Statistical Review, https://doi.org/10.1111/insr.12324.

See Also

dQBAD, pQBAD, qQBAD, rQBAD

Examples

# NOT RUN {
# Quantile-based asymmetric logistic distribution (ALoD)
# Density
rnum<-rnorm(100)
dALoD(y=rnum,mu=0,phi=1,alpha=.5)

# Distribution function
pALoD(q=rnum,mu=0,phi=1,alpha=.5)

# Quantile function
beta<-c(0.25,0.5,0.75)
qALoD(beta=beta,mu=0,phi=1,alpha=.5)

# random sample generation
rALoD(n=100,mu=0,phi=1,alpha=.5)

# }