QBAsyDist (version 0.1.2)

AND: Quantile-based asymmetric normal distribution

Description

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

Usage

dAND(y, mu, phi, alpha)
pAND(q, mu, phi, alpha)
qAND(beta, mu, phi, alpha)
rAND(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

dAND provides the density, pAND provides the cumulative distribution function, qAND provides the quantile function, and rAND generates a random sample from the quantile-based asymmetric normal distribution.

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 normal distribution (AND)
# Density
rnum<-rnorm(100)
dAND(y=rnum,mu=0,phi=1,alpha=.5)

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

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

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

# }