Description Usage Arguments Details Value Author(s) References See Also Examples
The BNB()
function defines the beta negative binomial distribution, a three parameter distribution, for a gamlss.family
object to be used in GAMLSS fitting using the function gamlss()
.
The functions dBNB
, pBNB
, qBNB
and rBNB
define the density, distribution function, quantile function and random
generation for the beta negative binomial distribution, BNB()
.
The functions ZABNB()
and ZIBNB()
are the zero adjusted (hurdle) and zero inflated versions of the beta negative binomial distribution, respectively. That is four parameter distributions.
The functions dZABNB
, dZIBNB
, pZABNB
,pZIBNB
, qZABNB
qZIBNB
rZABNB
and rZIBNB
define the probability, cumulative, quantile and random
generation functions for the zero adjusted and zero inflated beta negative binomial distributions, ZABNB()
, ZIBNB()
, respectively.
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 | BNB(mu.link = "log", sigma.link = "log", nu.link = "log")
dBNB(x, mu = 1, sigma = 1, nu = 1, log = FALSE)
pBNB(q, mu = 1, sigma = 1, nu = 1, lower.tail = TRUE, log.p = FALSE)
qBNB(p, mu = 1, sigma = 1, nu = 1, lower.tail = TRUE, log.p = FALSE,
max.value = 10000)
rBNB(n, mu = 1, sigma = 1, nu = 1, max.value = 10000)
ZABNB(mu.link = "log", sigma.link = "log", nu.link = "log",
tau.link = "logit")
dZABNB(x, mu = 1, sigma = 1, nu = 1, tau = 0.1, log = FALSE)
pZABNB(q, mu = 1, sigma = 1, nu = 1, tau = 0.1, lower.tail = TRUE,
log.p = FALSE)
qZABNB(p, mu = 1, sigma = 1, nu = 1, tau = 0.1, lower.tail = TRUE,
log.p = FALSE, max.value = 10000)
rZABNB(n, mu = 1, sigma = 1, nu = 1, tau = 0.1, max.value = 10000)
ZIBNB(mu.link = "log", sigma.link = "log", nu.link = "log",
tau.link = "logit")
dZIBNB(x, mu = 1, sigma = 1, nu = 1, tau = 0.1, log = FALSE)
pZIBNB(q, mu = 1, sigma = 1, nu = 1, tau = 0.1, lower.tail = TRUE,
log.p = FALSE)
qZIBNB(p, mu = 1, sigma = 1, nu = 1, tau = 0.1, lower.tail = TRUE,
log.p = FALSE, max.value = 10000)
rZIBNB(n, mu = 1, sigma = 1, nu = 1, tau = 0.1, max.value = 10000)
|
mu.link |
The link function for |
sigma.link |
The link function for |
nu.link |
The link function for |
tau.link |
The link function for |
x |
vector of (non-negative integer) |
mu |
vector of positive means |
sigma |
vector of positive dispersion parameter |
nu |
vector of a positive parameter |
tau |
vector of probabilities |
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] |
p |
vector of probabilities |
q |
vector of quantiles |
n |
number of random values to return |
max.value |
a constant, set to the default value of 10000 for how far the algorithm should look for q |
The probability function of the BNB
is
f(y|μ,σ, ν)=(Γ(y+1/ν)Β(y+(μν)/σ, 1/σ+1/ν +1 )/(Γ(y+1) Γ(1/ν) Β((μν)/σ, 1/σ+1) )
for y=0,1,2,3,..., μ>0, σ>0 and ν>0.
The distribution has mean μ.
returns a gamlss.family
object which can be used to fit a Poisson distribution in the gamlss()
function.
Bob Rigby and Mikis Stasinopoulos d.stasinopoulos@londonmrt.ac.uk
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. An older version can be found in http://www.gamlss.com/.
Stasinopoulos D. M., Rigby R.A. and Akantziliotou C. (2006) Instructions on how to use the GAMLSS package in R. Accompanying documentation in the current GAMLSS help files, (see also http://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, http://www.jstatsoft.org/v23/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.
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 | BNB() # gives information about the default links for the beta negative binomial
# plotting the distribution
plot(function(y) dBNB(y, mu = 10, sigma = 0.5, nu=2), from=0, to=40, n=40+1, type="h")
# creating random variables and plot them
tN <- table(Ni <- rBNB(1000, mu=5, sigma=0.5, nu=2))
r <- barplot(tN, col='lightblue')
ZABNB()
ZIBNB()
# plotting the distribution
plot(function(y) dZABNB(y, mu = 10, sigma = 0.5, nu=2, tau=.1),
from=0, to=40, n=40+1, type="h")
plot(function(y) dZIBNB(y, mu = 10, sigma = 0.5, nu=2, tau=.1),
from=0, to=40, n=40+1, type="h")
## Not run:
library(gamlss)
data(species)
species <- transform(species, x=log(lake))
m6 <- gamlss(fish~ pb(x), sigma.fo=~1, data=species, family=BNB)
## End(Not run)
|
Loading required package: MASS
GAMLSS Family: BNB Beta Negative Binomial
Link function for mu : log
Link function for sigma: log
Link function for nu : log
GAMLSS Family: ZABNB zero adjusted BNB
Link function for mu : log
Link function for sigma: log
Link function for nu : log
Link function for tau : logit
GAMLSS Family: ZIBNB
Link function for mu : log
Link function for sigma: log
Link function for nu : log
Link function for tau : logit
Loading required package: splines
Loading required package: gamlss.data
Loading required package: nlme
Loading required package: parallel
********** GAMLSS Version 5.0-2 **********
For more on GAMLSS look at http://www.gamlss.org/
Type gamlssNews() to see new features/changes/bug fixes.
GAMLSS-RS iteration 1: Global Deviance = 632.2582
GAMLSS-RS iteration 2: Global Deviance = 629.5883
GAMLSS-RS iteration 3: Global Deviance = 626.2913
GAMLSS-RS iteration 4: Global Deviance = 623.5843
GAMLSS-RS iteration 5: Global Deviance = 622.0562
GAMLSS-RS iteration 6: Global Deviance = 621.4817
GAMLSS-RS iteration 7: Global Deviance = 621.3382
GAMLSS-RS iteration 8: Global Deviance = 621.3034
GAMLSS-RS iteration 9: Global Deviance = 621.2998
GAMLSS-RS iteration 10: Global Deviance = 621.2993
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