dBetacBinom

Gives the density at <code>x</code> under the Beta Compound-Binomial distribution, where the Compound-Binomial distribution is Lord's two-term approximation.

Package providing a number of functions for working with Two- and
Four-parameter Beta and closely related distributions (i.e., the Gamma-
Binomial-, and Beta-Binomial distributions).
Includes, among other things:
- d/p/q/r functions for Four-Parameter Beta distributions and Generalized
"Binomial" (continuous) distributions, and d/p/r- functions for Beta-
Binomial distributions.
- d/p/q/r functions for Two- and Four-Parameter Beta distributions
parameterized in terms of their means and variances rather than their
shape-parameters.
- Moment generating functions for Binomial distributions, Beta-Binomial
distributions, and observed value distributions.
- Functions for estimating classification accuracy and consistency,
making use of the Classical Test-Theory based 'Livingston and Lewis' (L&L)
and 'Hanson and Brennan' approaches.
A shiny app is available, providing a GUI for the L&L approach when used
for binary classifications. For url to the app, see documentation for the
LL.CA() function.
Livingston and Lewis (1995) <doi:10.1111/j.1745-3984.1995.tb00462.x>.
Lord (1965) <doi:10.1007/BF02289490>.
Hanson (1991) <https://files.eric.ed.gov/fulltext/ED344945.pdf>.

Haakon Haakstad

betafunctions

Functions for Working with Two- And Four-Parameter Beta
Probability Distributions and Psychometric Analysis of
Classifications

dBetacBinom function

<dl><dt>x</dt>
<dd>Value of <code>x</code> (a specific number of successes).</dd>
<dt>N</dt>
<dd>Number of trials.</dd>
<dt>k</dt>
<dd>Lord's k (see documentation for the <code>Lords.k()</code> function).</dd>
<dt>l</dt>
<dd>The lower-bound location parameter of the four-parameter Beta distribution.</dd>
<dt>u</dt>
<dd>The upper-bound location parameter of the four-parameter Beta distribution.</dd>
<dt>alpha</dt>
<dd>The first shape-parameter of the four-parameter Beta distribution.</dd>
<dt>beta</dt>
<dd>The second shape-parameter of the four-parameter Beta distribution.
# Assume some variable follows a Beta compound Binomial distribution with 100
# trials, Lord's k = 1, and probabilities of successful trials drawn from a
# four-parameter Beta distribution with location-parameters l = .15 and u =
# .85, and shape parameters alpha = 6 and beta = 4. To compute the
# probability density at a specific point of the distribution (e.g., 50):
dBetacBinom(x = 50, N = 100, k = 1, l = .15, u = .85, alpha = 6, beta = 4)</dd></dl>

Arguments

Probability Mass function for Lord's Beta Compound Binomial Distribution. — dBetacBinom

<dl>

<dt>x</dt>
<dd>Value of <code>x</code> (a specific number of successes).</dd>


<dt>N</dt>
<dd>Number of trials.</dd>


<dt>k</dt>
<dd>Lord's k (see documentation for the <code>Lords.k()</code> function).</dd>


<dt>l</dt>
<dd>The lower-bound location parameter of the four-parameter Beta distribution.</dd>


<dt>u</dt>
<dd>The upper-bound location parameter of the four-parameter Beta distribution.</dd>


<dt>alpha</dt>
<dd>The first shape-parameter of the four-parameter Beta distribution.</dd>


<dt>beta</dt>
<dd>The second shape-parameter of the four-parameter Beta distribution.
# Assume some variable follows a Beta compound Binomial distribution with 100
# trials, Lord's k = 1, and probabilities of successful trials drawn from a
# four-parameter Beta distribution with location-parameters l = .15 and u =
# .85, and shape parameters alpha = 6 and beta = 4. To compute the
# probability density at a specific point of the distribution (e.g., 50):
dBetacBinom(x = 50, N = 100, k = 1, l = .15, u = .85, alpha = 6, beta = 4)</dd>

</dl>

dBetacBinom: Probability Mass function for Lord's Beta Compound Binomial Distribution.

Description

Usage

Arguments