# momQBAD: Method of moments (MoM) estimation for the quantile-based... In QBAsyDist: Asymmetric Distributions and Quantile Estimation

## 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

 `1` ```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 α. If α is unknown, indicate NULL which is default option. In this case, the sample skewness will be used to estimate α. If α is known, then the value of α 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

 ``` 1 2 3 4 5 6 7 8 9 10 11``` ```# 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 ```

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