Poisson distribution for fitting a GAMLSS model
This function PO defines the Poisson distribution, an one parameter distribution, for a gamlss.family object to be used in GAMLSS fitting
using the function gamlss(). The functions dPO, pPO, qPO and rPO define the density, distribution function, quantile function and random
generation for the Poisson, PO(), distribution.
PO(mu.link = "log") dPO(x, mu = 1, log = FALSE) pPO(q, mu = 1, lower.tail = TRUE, log.p = FALSE) qPO(p, mu = 1, lower.tail = TRUE, log.p = FALSE) rPO(n, mu = 1)
mu.link |
Defines the |
x |
vector of (non-negative integer) quantiles |
mu |
vector of positive means |
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] |
Definition file for Poisson distribution.
f(y|μ)=e^(-μ)*μ^y/Γ(y+1)
for y=0,1,2,... and μ>0.
returns a gamlss.family object which can be used to fit a Poisson distribution in the gamlss() function.
mu is the mean of the Poisson distribution
Bob Rigby, Mikis Stasinopoulos, and Kalliope Akantziliotou
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 https://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 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, https://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.
gamlss.family, NBI, NBII,
SI, SICHEL
PO()# gives information about the default links for the Poisson distribution # fitting data using PO() # plotting the distribution plot(function(y) dPO(y, mu=10 ), from=0, to=20, n=20+1, type="h") # creating random variables and plot them tN <- table(Ni <- rPO(1000, mu=5)) r <- barplot(tN, col='lightblue') # library(gamlss) # data(aids) # h<-gamlss(y~cs(x,df=7)+qrt, family=PO, data=aids) # fits the constant+x+qrt model # plot(h) # pdf.plot(family=PO, mu=10, min=0, max=20, step=1)
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