NBI {gamlss.dist} | R Documentation |
Negative Binomial type I distribution for fitting a GAMLSS
Description
The NBI()
function defines the Negative Binomial type I distribution, a two parameter distribution, for a gamlss.family
object to be used
in GAMLSS fitting using the function gamlss()
.
The functions dNBI
, pNBI
, qNBI
and rNBI
define the density, distribution function, quantile function and random
generation for the Negative Binomial type I, NBI()
, distribution.
Usage
NBI(mu.link = "log", sigma.link = "log")
dNBI(x, mu = 1, sigma = 1, log = FALSE)
pNBI(q, mu = 1, sigma = 1, lower.tail = TRUE, log.p = FALSE)
qNBI(p, mu = 1, sigma = 1, lower.tail = TRUE, log.p = FALSE)
rNBI(n, mu = 1, sigma = 1)
Arguments
mu.link |
Defines the |
sigma.link |
Defines the |
x |
vector of (non-negative integer) quantiles |
mu |
vector of positive means |
sigma |
vector of positive despersion parameter |
p |
vector of probabilities |
q |
vector of quantiles |
n |
number of random values to return |
log , log.p |
logical; if TRUE, probabilities p are given as log(p) |
lower.tail |
logical; if TRUE (default), probabilities are P[X <= x], otherwise, P[X > x] |
Details
Definition file for Negative Binomial type I distribution.
for ,
and
. This
parameterization is equivalent to that used by Anscombe (1950) except he used
instead of
, see also pp. 483-485 of Rigby et al. (2019).
Value
returns a gamlss.family
object which can be used to fit a Negative Binomial type I distribution in the gamlss()
function.
Warning
For values of the d,p,q,r functions switch to the Poisson distribution
Note
is the mean and
is the standard deviation of the Negative Binomial
type I distribution (so
is the dispersion parameter in the usual GLM for the negative binomial type I distribution)
Author(s)
Mikis Stasinopoulos, Bob Rigby and Calliope Akantziliotou
References
Anscombe, F. J. (1950) Sampling theory of the negative bimomial and logarithmic distributiona, Biometrika, 37, 358-382.
Rigby, R. A. and Stasinopoulos D. M. (2005). Generalized additive models for location, scale and shape,(with discussion), Appl. Statist., 54, part 3, pp 507-554.
Rigby, R. A., Stasinopoulos, D. M., Heller, G. Z., and De Bastiani, F. (2019) Distributions for modeling location, scale, and shape: Using GAMLSS in R, Chapman and Hall/CRC, doi:10.1201/9780429298547. An older version can be found in https://www.gamlss.com/.
Stasinopoulos D. M. Rigby R.A. (2007) Generalized additive models for location scale and shape (GAMLSS) in R. Journal of Statistical Software, Vol. 23, Issue 7, Dec 2007, doi:10.18637/jss.v023.i07.
Stasinopoulos D. M., Rigby R.A., Heller G., Voudouris V., and De Bastiani F., (2017) Flexible Regression and Smoothing: Using GAMLSS in R, Chapman and Hall/CRC. doi:10.1201/b21973
(see also https://www.gamlss.com/).
See Also
gamlss.family
, NBII
, PIG
, SI
Examples
NBI() # gives information about the default links for the Negative Binomial type I distribution
# plotting the distribution
plot(function(y) dNBI(y, mu = 10, sigma = 0.5 ), from=0, to=40, n=40+1, type="h")
# creating random variables and plot them
tN <- table(Ni <- rNBI(1000, mu=5, sigma=0.5))
r <- barplot(tN, col='lightblue')
# library(gamlss)
# data(aids)
# h<-gamlss(y~cs(x,df=7)+qrt, family=NBI, data=aids) # fits the model
# plot(h)
# pdf.plot(family=NBI, mu=10, sigma=0.5, min=0, max=40, step=1)