QBAsyDist (version 0.1.2)

ATD: Quantile-based asymmetric Student's-t distribution

Description

Density, cumulative distribution function, quantile function and random sample generation from the quantile-based asymmetric Student's-\(t\) distribution (ATD) proposed in Gijbels et al. (2019a).

Usage

dATD(y, mu, phi, alpha, nu)
pATD(q, mu, phi, alpha, nu)
qATD(beta, mu, phi, alpha, nu)
rATD(n, mu, phi, alpha, nu)

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 \(\alpha\).

nu

This is the degrees of freedom parameter \(\nu\), which must be positive.

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

dATD provides the density, pATD provides the cumulative distribution function, qATD provides the quantile function, and rATD generates a random sample from the quantile-based asymmetric Student's-\(t\) distribution. The length of the result is determined by \(n\) for rATD, 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 Student's-\eqn{t} distribution (ATD)
# Density
rnum<-rnorm(100)
dATD(rnum,mu=0,phi=1,alpha=0.5,nu=10)

# Distribution function
pATD(rnum,mu=0,phi=1,alpha=0.5,nu=10)

# Quantile function
beta<-c(0.25,0.5,0.75)
qATD(beta=beta,mu=0,phi=1,alpha=.5,nu=10)

# random sample generation
rATD(n=100,mu=0,phi=1,alpha=.5,nu=10)

# }