qmomeqf: Unnormalized empirical robust moments. sigma_r=Q(3/4)-Q(1/4)...

In dmi3kno/qpd: Tools for Quantile-Parametrized Distribiutions

Unnormalized empirical robust moments.

\sigma_r=Q(3/4)-Q(1/4)

s_r=\frac{Q(3/4)+Q(1/4)-2Q(1/2)}{\sigma_r}

\kappa_r=\frac{Q(7/8)-Q(5/8)+Q(3/8)-Q(1/8)}{\sigma_r}

These are implemented as qdv_eqf, qsk_eqf, and qkr_eqf, respectively. Note that the robust measure of location is the median \mu_r=Q(1/2).

Description

Unnormalized empirical robust moments.

\sigma_r=Q(3/4)-Q(1/4)

s_r=\frac{Q(3/4)+Q(1/4)-2Q(1/2)}{\sigma_r}

\kappa_r=\frac{Q(7/8)-Q(5/8)+Q(3/8)-Q(1/8)}{\sigma_r}

These are implemented as qdv_eqf, qsk_eqf, and qkr_eqf, respectively. Note that the robust measure of location is the median \mu_r=Q(1/2).

Usage

qdv_eqf(x, type = 5, lambda = 0.25)

qsk_eqf(x, type = 5, lambda = 0.25)

qkr_eqf(x, type = 5, lambda = 0.25, zeta = lambda/2)

Arguments

x	numerical sample to compute the quantiles from
type	parameters, passed to quantile function
lambda	probability < 0.5 corresponding to the tail in the robust deviation. Default is 0.25
zeta	probability zeta<lambda corresponding to the tail in robust kurtosis. Default is lambda/2

Value

numeric value of robust moment

Examples

qdv_eqf(1:100) #49.5
qsk_eqf(1:100)
qkr_eqf(1:100)

dmi3kno/qpd documentation built on Sept. 29, 2024, 6:39 p.m.