QBAsyDist (version 0.1.2)

QBAD: Quantile-based asymmetric family of distributions

Description

Density, cumulative distribution function, quantile function and random sample generation from the quantile-based asymmetric family of densities defined in Gijbels et al. (2019a).

Usage

dQBAD(y, mu, phi, alpha, f)
pQBAD(q, mu, phi, alpha, F)
qQBAD(beta, mu, phi, alpha, F, QF = NULL)
rQBAD(n, mu, phi, alpha, F, QF = NULL)

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 \(\alpha\).

f

This is the reference density function \(f\) which is a standard version of a unimodal and symmetric around 0 density.

F

This is the cumulative distribution function \(F\) of a unimodal and symmetric around 0 reference density function \(f\).

beta

This is a vector of probabilities.

QF

This is the quantile function of the reference density \(f\).

n

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

Value

dQBAD provides the density, pQBAD provides the cumulative distribution function, qQBAD provides the quantile function, and rQBAD generates a random sample from the quantile-based asymmetric family of distributions. The length of the result is determined by \(n\) for rQBAD, 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.

Examples

# NOT RUN {
# Example 1: Let F be a standard normal cumulative distribution function then
f_N<-function(s){dnorm(s, mean = 0,sd = 1)} # density function of N(0,1)
F_N<-function(s){pnorm(s, mean = 0,sd = 1)} # distribution function of N(0,1)
QF_N<-function(beta){qnorm(beta, mean = 0, sd = 1, lower.tail = TRUE, log.p = FALSE)}
rnum<-rnorm(100)
beta=c(0.25,0.50,0.75)

# Density
dQBAD(y=rnum,mu=0,phi=1,alpha=.5,f=f_N)

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

# Quantile function
qQBAD(beta=beta,mu=0,phi=1,alpha=.5,F=F_N,QF=QF_N)
qQBAD(beta=beta,mu=0,phi=1,alpha=.5,F=F_N)

# random sample generation
rQBAD(n=100,mu=0,phi=1,alpha=.5,QF=QF_N)
rQBAD(n=100,mu=0,phi=1,alpha=.5,F=F_N)



# Example 2: Let F be a standard Laplace cumulative distribution function then
f_La<-function(s){0.5*exp(-abs(s))} # density function of Laplace(0,1)
F_La<-function(s){0.5+0.5*sign(s)*(1-exp(-abs(s)))} # distribution function of Laplace(0,1)
QF_La<-function(beta){-sign(beta-0.5)*log(1-2*abs(beta-0.5))}
rnum<-rnorm(100)
beta=c(0.25,0.50,0.75)

# Density
dQBAD(y=rnum,mu=0,phi=1,alpha=.5,f=f_La)

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

# Quantile function
qQBAD(beta=c(0.25,0.50,0.75),mu=0,phi=1,alpha=.5,F=F_La,QF=QF_La)
qQBAD(beta=c(0.25,0.50,0.75),mu=0,phi=1,alpha=.5,F=F_La)

# random sample generation
rQBAD(n=100,mu=0,phi=1,alpha=.5,QF=QF_La)
rQBAD(n=100,mu=0,phi=1,alpha=.5,F=F_La)

# }