The function WARING()
defines the Waring distribution, a two parameter
distribution, for a gamlss.family
object to be used in GAMLSS fitting
using the function gamlss()
, with mean equal to the parameter mu
and scale parameter sigma
. The functions dWARING
, pWARING
, qWARING
and rWARING
define the density, distribution function, quantile function and random generation for the WARING
parameterization of the Waring distribution.
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mu.link |
Defines the |
sigma.link |
Defines the |
x |
vector of (non-negative integer) quantiles. |
q |
vector of quantiles. |
p |
vector of probabilities. |
n |
number of random values to return. |
mu |
vector of positive |
sigma |
vector of positive |
lower.tail |
logical; if |
log, log.p |
logical; if |
max.value |
constant; generates a sequence of values for the cdf function. |
The Waring distribution has density,
f(y|mu, sigma)= ((1+sigma) Gamma(y+mu/sigma) Gamma((mu+sigma+1)/sigma))/(sigma Gamma(y+(mu+1)/sigma+2) Gamma(mu/sigma))
for y=0,1,2,…, mu>0 and sigma>0.
Returns a gamlss.family
object which can be used to fit a Waring distribution in the gamlss()
function.
Fiona McElduff, Bob Rigby and Mikis Stasinopoulos. f.mcelduff@ich.ucl.ac.uk
Wimmer, G. and Altmann, G. (1999) Thesaurus of univariate discrete probability distributions. Stamm.
gamlss.family
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Questions? Problems? Suggestions? Tweet to @rdrrHQ or email at ian@mutexlabs.com.
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