QBAsyDist (version 0.1.2)

momATD: Method of moments (MoM) estimation for the quantile-based asymmetric Student's-\(t\) distribution.

Description

Parameter estimation in the quantile-based asymmetric Student's-\(t\) distribution by using method of moments are discussed in Gijbels et al. (2019a). We here used the first four sample moments to estimate parameter \(\theta=(\mu,\phi,\alpha,\nu)\) under the assumption that the first four population moments exist, which needs to assume \(\nu>4\).

Usage

momATD(y, alpha = NULL)

Arguments

y

This is a vector of quantiles.

alpha

This is the index parameter \(\alpha\). If \(\alpha\) is unknown, indicate NULL which is the 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

momATD 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
y=rnorm(100)
momATD(y=y,alpha=0.5) # If alpha is known with alpha=0.5
momATD(y=y) # If alpha is unknown

# }