QBAsyDist (version 0.1.2)

GTEF: Generalized tick-exponential family

Description

Density, cumulative distribution function, quantile function and random sample generation from the generalized tick-exponential family (GTEF) of densities discusse in Gijbels et al. (2019b).

Usage

dGTEF(y, eta, phi, alpha, p, g)
pGTEF(q, eta, phi, alpha, p, g)
qGTEF(beta, eta, phi, alpha, p, g, lower = -Inf, upper = Inf)
rGTEF(n, eta, phi, alpha, p, g, lower = -Inf, upper = Inf)

Arguments

y, q

These are each a vector of quantiles.

eta

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

phi

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

alpha

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

p

This is the shape parameter, which must be positive.

g

This is the "link" function. The function \(g\) is to be differentiated. Therefore, \(g\) must be written as a function. For example, g<-function(y){log(y)} for log link function.

beta

This is a vector of probabilities.

lower

This is the lower limit of the domain (support of the random variable) \(f_{\alpha}^g(y;\eta,\phi)\), default -Inf.

upper

This is the upper limit of the domain (support of the random variable) \(f_{\alpha}^g(y;\eta,\phi)\), default Inf.

n

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

Value

dGTEF provides the density, pGTEF provides the cumulative distribution function, qGTEF provides the quantile function, and rGTEF generates a random sample from the generalized tick-exponential family of densities. The length of the result is determined by \(n\) for rGTEF, and is the maximum of the lengths of the numerical arguments for the other functions.

References

Gijbels, I., Karim, R. and Verhasselt, A. (2019b). Quantile estimation in a generalized asymmetric distributional setting. To appear in Springer Proceedings in Mathematics & Statistics, Proceedings of `SMSA 2019', the 14th Workshop on Stochastic Models, Statistics and their Application, Dresden, Germany, in March 6--8, 2019. Editors: Ansgar Steland, Ewaryst Rafajlowicz, Ostap Okhrin.

Examples

# NOT RUN {
# For identiy link function
y=rnorm(100)
g_id<-function(y){y}
dGTEF(y,eta=0,phi=1,alpha=0.5,p=2,g=g_id)

# cumulative distribution function
pGTEF(q=y,eta=10,phi=1,alpha=0.5,p=2,g=g_id)

# Quantile function
beta=c(0.25,0.5,0.75)
qGTEF(beta=beta,eta=10,phi=1,alpha=0.5,p=2,g=g_id)

# random sample generation
rGTEF(n=100,eta=10,phi=1,alpha=.5,p=2,g=g_id,lower = -Inf, upper = Inf)

# For log link function
y=rexp(100)
g_log<-function(y){log(y)}
dGTEF(y,eta=10,phi=1,alpha=0.5,p=2,g=g_log)

# cumulative distribution function
pGTEF(q=y,eta=10,phi=1,alpha=0.5,p=2,g=g_log)

# Quantile function
g_log<-function(y){log(y)}
#' beta=c(0.25,0.5,0.75)
qGTEF(beta=beta,eta=10,phi=1,alpha=0.5,p=2,g=g_log,lower = 0, upper = Inf)

# random sample generation
rGTEF(n=100,eta=10,phi=1,alpha=.5,p=2,g=g_log,lower = 0, upper = Inf)




# }