QBAD: Quantile-based asymmetric family of distributions

In QBAsyDist: Asymmetric Distributions and Quantile Estimation

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 μ.
phi	This is the scale parameter φ.
alpha	This is the index parameter α.
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

# 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)

QBAsyDist documentation built on Sept. 4, 2019, 1:05 a.m.