/
WG.R
153 lines (135 loc) · 6.58 KB
/
WG.R
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
#' The Weibull Geometric family
#'
#' @author Johan David Marin Benjumea, \email{johand.marin@@udea.edu.co}
#'
#' @description
#' The Weibull Geometric distribution
#'
#' @param mu.link defines the mu.link, with "log" link as the default for the mu parameter.
#' @param sigma.link defines the sigma.link, with "log" link as the default for the sigma.
#' @param nu.link defines the nu.link, with "log" link as the default for the nu parameter.
#'
#' @seealso \link{dWG}
#'
#' @details
#' The weibull geometric distribution with parameters \code{mu},
#' \code{sigma} and \code{nu} has density given by
#'
#' \eqn{f(x) = (\sigma \mu^\sigma (1-\nu) x^(\sigma - 1) \exp(-(\mu x)^\sigma))
#' (1- \nu \exp(-(\mu x)^\sigma))^{-2},}
#'
#' for \eqn{x > 0}, \eqn{\mu > 0}, \eqn{\sigma > 0} and \eqn{0 < \nu < 1}.
#'
#' @returns Returns a gamlss.family object which can be used to fit a WG distribution in the \code{gamlss()} function.
#'
#' @example examples/examples_WG.R
#'
#' @references
#'\insertRef{barreto2011weibull}{RelDists}
#'
#' @importFrom gamlss.dist checklink
#' @importFrom gamlss rqres.plot
#' @export
WG <- function (mu.link = "log", sigma.link = "log", nu.link = "logit") {
mstats <- checklink("mu.link", "Weibull Geometric", substitute(mu.link), c("identity", "own"))
dstats <- checklink("sigma.link", "Weibull Geometric", substitute(sigma.link), c("identity", "own"))
vstats <- checklink("nu.link", "Weibull Geometric", substitute(nu.link), c("logit","probit", "own"))
structure(list(family = c("WG", "Weibull Geometric"),
parameters = list(mu = TRUE, sigma = TRUE, nu = TRUE),
nopar = 3,
type = "Continuous",
mu.link = as.character(substitute(mu.link)),
sigma.link = as.character(substitute(sigma.link)),
nu.link = as.character(substitute(nu.link)),
mu.linkfun = mstats$linkfun,
sigma.linkfun = dstats$linkfun,
nu.linkfun = vstats$linkfun,
mu.linkinv = mstats$linkinv,
sigma.linkinv = dstats$linkinv,
nu.linkinv = vstats$linkinv,
mu.dr = mstats$mu.eta,
sigma.dr = dstats$mu.eta,
nu.dr = vstats$mu.eta,
dldm = function(y, mu, sigma, nu) {
exp1 <- exp(-(mu*y)^sigma)
exp2 <- 2/(1 - nu*exp1)
dldm <- sigma/mu - sigma*y*(mu*y)^(sigma - 1) -
exp2*nu*exp1*sigma*(mu*y)^(sigma-1)*y
dldm
},
dldd = function(y, mu, sigma, nu) {
exp1 <- exp(-(mu*y)^sigma)
exp2 <- 2/(1 - nu*exp1)
dldd <- 1/sigma + log(mu) + log(y) - (mu*y)^sigma*log(mu*y) -
exp2*nu*exp1*(mu*y)^sigma*log(mu*y)
dldd
},
dldv = function(y, mu, sigma, nu) {
exp1 <- exp(-(mu*y)^sigma)
exp2 <- 2/(1 - nu*exp1)
dldv <- -(1/(1-nu)) + exp2*exp1
dldv
},
d2ldm2 = function(y, mu, sigma, nu, tau) {
exp1 <- exp(-(mu*y)^sigma)
exp2 <- 2/(1 - nu*exp1)
dldm <- sigma/mu - sigma*y*(mu*y)^(sigma - 1) -
exp2*nu*exp1*sigma*(mu*y)^(sigma-1)*y
d2ldm2 <- -dldm * dldm
d2ldm2
},
d2ldmdd = function(y, mu, sigma, nu, tau) {
exp1 <- exp(-(mu*y)^sigma)
exp2 <- 2/(1 - nu*exp1)
dldm <- sigma/mu - sigma*y*(mu*y)^(sigma - 1) -
exp2*nu*exp1*sigma*(mu*y)^(sigma-1)*y
dldd <- 1/sigma + log(mu) + log(y) - (mu*y)^sigma*log(mu*y) -
exp2*nu*exp1*(mu*y)^sigma*log(mu*y)
d2ldmdd <- -dldm * dldd
d2ldmdd
},
d2ldmdv = function(y, mu, sigma, nu, tau) {
exp1 <- exp(-(mu*y)^sigma)
exp2 <- 2/(1 - nu*exp1)
dldm <- sigma/mu - sigma*y*(mu*y)^(sigma - 1) -
exp2*nu*exp1*sigma*(mu*y)^(sigma-1)*y
dldv <- -(1/(1-nu)) + exp2*exp1
d2ldmdv <- -dldm * dldv
d2ldmdv
},
d2ldd2 = function(y, mu, sigma, nu, tau) {
exp1 <- exp(-(mu*y)^sigma)
exp2 <- 2/(1 - nu*exp1)
dldd <- 1/sigma + log(mu) + log(y) - (mu*y)^sigma*log(mu*y) -
exp2*nu*exp1*(mu*y)^sigma*log(mu*y)
d2ldd2 <- -dldd * dldd
d2ldd2
},
d2ldddv = function(y, mu, sigma, nu, tau) {
exp1 <- exp(-(mu*y)^sigma)
exp2 <- 2/(1 - nu*exp1)
dldd <- 1/sigma + log(mu) + log(y) - (mu*y)^sigma*log(mu*y) -
exp2*nu*exp1*(mu*y)^sigma*log(mu*y)
dldv <- -(1/(1-nu)) + exp2*exp1
d2ldddv <- -dldd * dldv
d2ldddv
},
d2ldv2 = function(y, mu, sigma, nu, tau) {
exp1 <- exp(-(mu*y)^sigma)
exp2 <- 2/(1 - nu*exp1)
dldv <- -(1/(1-nu)) + exp2*exp1
d2ldv2 <- -dldv * dldv
d2ldv2
},
G.dev.incr = function(y, mu, sigma, nu, ...) -2*dWG(y, mu, sigma, nu, log = TRUE),
rqres = expression(rqres(pfun = "pWG", type = "Continuous", y = y, mu = mu, sigma = sigma, nu = nu)),
mu.initial = expression( mu <- rep(0.5, length(y)) ),
sigma.initial = expression( sigma <- rep(0.5, length(y)) ),
nu.initial = expression( nu <- rep(0.5, length(y)) ),
mu.valid = function(mu) all(mu > 0),
sigma.valid = function(sigma) all(sigma > 0),
nu.valid = function(nu) all(nu > 0 & nu < 1),
y.valid = function(y) all(y > 0)
),
class = c("gamlss.family", "family"))
}