qshash

Density, distribution function, quantile function and random generation
for the Sinh-Arcsinh distribution

internal

A comprehensive toolkit for generating continuous test norms in
psychometrics and biometrics, and analyzing model fit. The package offers both
distribution-free modeling using Taylor polynomials and parametric modeling
using the beta-binomial and the 'Sinh-Arcsinh' distribution. Originally developed
for achievement tests, it is applicable to a wide range of mental, physical, or
other test scores dependent on continuous or discrete explanatory variables. The
package provides several advantages: It minimizes deviations from representativeness
in subsamples, interpolates between discrete levels of explanatory variables,
and significantly reduces the required sample size compared to conventional
norming per age group. cNORM enables graphical and analytical evaluation of
model fit, accommodates a wide range of scales including those with negative
and descending values, and even supports conventional norming. It generates
norm tables including confidence intervals. It also includes methods for
addressing representativeness issues through Iterative Proportional Fitting.

Wolfgang Lenhard

cNORM

Continuous Norming

Alexandra Lenhard

Sebastian Gary

WPS publisher 

qshash function

<dl><dt>p</dt>
<dd>vector of probabilities</dd>
<dt>mu</dt>
<dd>location parameter</dd>
<dt>sigma</dt>
<dd>scale parameter (&gt; 0)</dd>
<dt>epsilon</dt>
<dd>skewness parameter</dd>
<dt>delta</dt>
<dd>tail weight parameter (&gt; 0)</dd>
<dt>lower.tail</dt>
<dd>logical; if TRUE, probabilities are P[X &lt;= x]</dd>
<dt>log.p</dt>
<dd>logical; if TRUE, probabilities p are given as log(p)</dd></dl>

Arguments

Sinh-Arcsinh (ShaSh) quantile function — qshash

<dl>

<dt>p</dt>
<dd>vector of probabilities</dd>


<dt>mu</dt>
<dd>location parameter</dd>


<dt>sigma</dt>
<dd>scale parameter (&gt; 0)</dd>


<dt>epsilon</dt>
<dd>skewness parameter</dd>


<dt>delta</dt>
<dd>tail weight parameter (&gt; 0)</dd>


<dt>lower.tail</dt>
<dd>logical; if TRUE, probabilities are P[X &lt;= x]</dd>


<dt>log.p</dt>
<dd>logical; if TRUE, probabilities p are given as log(p)</dd>

</dl>

qshash: Sinh-Arcsinh (ShaSh) quantile function

Description

Usage

Arguments