ZABB: Zero inflated and zero adjusted Binomial distribution for... In gamlss.dist: Distributions for Generalized Additive Models for Location Scale and Shape

Description

The function `ZIBB` defines the zero inflated beta binomial distribution, a three parameter distribution, for a `gamlss.family` object to be used in GAMLSS fitting using the function `gamlss()`. The functions `dZIBB`, `pZIBB`, `qZIBB` and `rZINN` define the density, distribution function, quantile function and random generation for the zero inflated beta binomial, `ZIBB`, distribution.

The function `ZABB` defines the zero adjusted beta binomial distribution, a three parameter distribution, for a `gamlss.family` object to be used in GAMLSS fitting using the function `gamlss()`. The functions `dZABB`, `pZABB`, `qZABB` and `rZABB` define the density, distribution function, quantile function and random generation for the zero inflated beta binomial, `ZABB()`, distribution.

Usage

 ``` 1 2 3 4 5 6 7 8 9 10 11 12 13 14``` ```ZABB(mu.link = "logit", sigma.link = "log", nu.link = "logit") ZIBB(mu.link = "logit", sigma.link = "log", nu.link = "logit") dZIBB(x, mu = 0.5, sigma = 0.5, nu = 0.1, bd = 1, log = FALSE) dZABB(x, mu = 0.5, sigma = 0.1, nu = 0.1, bd = 1, log = FALSE) pZIBB(q, mu = 0.5, sigma = 0.5, nu = 0.1, bd = 1, lower.tail = TRUE, log.p = FALSE) pZABB(q, mu = 0.5, sigma = 0.1, nu = 0.1, bd = 1, lower.tail = TRUE, log.p = FALSE) qZIBB(p, mu = 0.5, sigma = 0.5, nu = 0.1, bd = 1, lower.tail = TRUE, log.p = FALSE) qZABB(p, mu = 0.5, sigma = 0.1, nu = 0.1, bd = 1, lower.tail = TRUE, log.p = FALSE) rZIBB(n, mu = 0.5, sigma = 0.5, nu = 0.1, bd = 1) rZABB(n, mu = 0.5, sigma = 0.1, nu = 0.1, bd = 1) ```

Arguments

 `mu.link` Defines the `mu.link`, with "logit" link as the default for the `mu` parameter. Other links are "probit" and "cloglog"'(complementary log-log) `sigma.link` Defines the `sigma.link`, with "log" link as the default for the `sigma` parameter. `nu.link` Defines the `sigma.link`, with "logit" link as the default for the `mu` parameter. Other links are "probit" and "cloglog"'(complementary log-log) `x` vector of (non-negative integer) quantiles `mu` vector of positive probabilities `sigma` vector of positive dispertion parameter `nu` vector of positive probabilities `bd` vector of binomial denominators `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

For the definition of the distributions see Rigby and Stasinopoulos (2010) below.

Value

The functions `ZIBB` and `ZABB` return a `gamlss.family` object which can be used to fit a zero inflated or zero adjusted beta binomial distribution respectively in the `gamlss()` function.

Author(s)

Mikis Stasinopoulos [email protected], Bob Rigby

References

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.

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.org/).

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.

Rigby, R. A. and Stasinopoulos D. M. (2010) The gamlss.family distributions, (distributed with this package or see http://www.gamlss.org/)

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`
 ```1 2 3 4 5 6 7``` ```ZIBB() ZABB() # creating data and plotting them dat <- rZIBB(1000, mu=.5, sigma=.5, nu=0.1, bd=10) r <- barplot(table(dat), col='lightblue') dat1 <- rZABB(1000, mu=.5, sigma=.2, nu=0.1, bd=10) r1 <- barplot(table(dat1), col='lightblue') ```