QBAsyDist (version 0.1.2)

momQBAD: Method of moments (MoM) estimation for the quantile-based asymmetric family of distributions.

Description

Parameter estimation in the quantile-based asymmetric family of densities by using method of moments are discussed in Section 3.1 of Gijbels et al. (2019a).

Usage

momQBAD(y, f, alpha = NULL)

Arguments

y

This is a vector of quantiles.

f

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

alpha

This is the index parameter \(\alpha\). If \(\alpha\) is unknown, indicate NULL which is default option. In this case, the sample skewness will be used to estimate \(\alpha\). If \(\alpha\) is known, then the value of \(\alpha\) has to be specified in the function.

Value

momQBAD provides the method of moments estimates of the unknown parameters of the 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.

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)
y=rnorm(100)
momQBAD(y=y,f=f_N,alpha=0.5) # If alpha is known with alpha=0.5
momQBAD(y=y,f=f_N) # If alpha is unknown


# 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)
momQBAD(y=y,f=f_La,alpha=0.5) # If alpha is known with alpha=0.5
momQBAD(y=y,f=f_La) # If alpha is unknown
# }