/
OW.R
191 lines (165 loc) · 8.37 KB
/
OW.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
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
187
188
189
190
191
#' The Odd Weibull family
#'
#' @author Jaime Mosquera Gutiérrez \email{jmosquerag@unal.edu.co}
#'
#' @description
#' The function \code{OW()} defines the Odd Weibull distribution, a three parameter
#' distribution, for a \code{gamlss.family} object to be used in GAMLSS fitting
#' using the function \code{gamlss()}.
#'
#' @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.
#'
#' @details
#' The odd Weibull with parameters \code{mu}, \code{sigma} and \code{nu}
#' has density given by
#'
#' \eqn{f(t) = \left( \frac{\sigma\nu}{t} \right) (\mu t)^\sigma
#' e^{(\mu t)^\sigma} \left(e^{(\mu t)^{\sigma}}-1\right)^{\nu-1}
#' \left[ 1 + \left(e^{(\mu t)^{\sigma}}-1\right)^\nu \right]^{-2}}
#'
#' for x > 0.
#'
#' @returns Returns a gamlss.family object which can be used to fit a OW distribution in the \code{gamlss()} function.
#'
#' @example examples/examples_OW.R
#'
#' @references
#' \insertRef{Cooray2006}{RelDists}
#'
#' @importFrom gamlss.dist checklink
#' @importFrom gamlss rqres.plot
#' @export
OW <- function (mu.link="log", sigma.link="log", nu.link="log") {
mstats <- checklink("mu.link", "Odd Weibull", substitute(mu.link), c("log", "own"))
dstats <- checklink("sigma.link", "Odd Weibull", substitute(sigma.link), c("identity", "log", "own"))
vstats <- checklink("nu.link", "Odd Weibull", substitute(nu.link), c("identity", "log", "own"))
# valid_values <- OW_modifications(valid.values)
# sigma.space <- valid_values$sigma.space
# nu.space <- valid_values$nu.space
structure(list(family = c("OW", "Odd Weibull"),
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) {
prod1 <- (mu*y)^sigma
expT1 <- 1 + ( expm1( prod1 ) )^nu
T1m <- ( sigma*prod1 )/mu
T2m <- sigma*prod1*(nu - 1)*exp(prod1)/
( mu*expm1(prod1) )
T3m <- -( 2*nu*sigma*prod1*exp(prod1)*(expm1(prod1))^(nu-1) )/
(mu*(expT1))
dldm <- sigma/mu + T1m + T2m + T3m
as.numeric(dldm)
},
d2ldm2 = function(y, mu, sigma, nu) {
prod1 <- (mu*y)^sigma
expmT1 <- 1 + ( expm1( prod1 ) )^nu
T1m <- ( sigma*prod1 )/mu
T2m <- sigma*prod1*(nu - 1)*exp(prod1)/
( mu*expm1(prod1) )
T3m <- -( 2*nu*sigma*prod1*exp(prod1)*(expm1(prod1))^(nu-1) )/
(mu*(expmT1))
dldm <- sigma/mu + T1m + T2m + T3m
d2ldm2 <- -dldm*dldm
as.numeric(d2ldm2)
},
dldd = function(y, mu, sigma, nu) {
prod1 <- (mu*y)^sigma
expdT1 <- 1 + ( expm1( prod1 ) )^nu
T1d <- (nu - 1)*exp(prod1)/expm1(prod1)
T2d <- -2*nu*exp(prod1)*(expm1(prod1))^(nu - 1)/expdT1
dldd <- 1/sigma + log(mu*y) + log(mu*y)*prod1*(1 + T1d + T2d)
as.numeric(dldd)
},
d2ldd2 = function(y, mu, sigma, nu) {
prod1 <- (mu*y)^sigma
expdT1 <- 1 + ( expm1( prod1 ) )^nu
T1d <- (nu - 1)*exp(prod1)/expm1(prod1)
T2d <- -2*nu*exp(prod1)*(expm1(prod1))^(nu - 1)/expdT1
dldd <- 1/sigma + log(mu*y) + log(mu*y)*prod1*(1 + T1d + T2d)
d2ldd2 <- -dldd*dldd
as.numeric(d2ldd2)
},
dldv = function(y, mu, sigma, nu) {
prod1 <- (mu*y)^sigma
expvT1 <- 1 + ( expm1( prod1 ) )^nu
dldv <- 1/nu + log(expm1(prod1))*(1 - 2*(expm1(prod1))^nu/expvT1)
as.numeric(dldv)
},
d2ldv2 = function(y, mu, sigma, nu) {
prod1 <- (mu*y)^sigma
expvT1 <- 1 + ( expm1( prod1 ) )^nu
dldv <- 1/nu + log(expm1(prod1))*(1 - 2*(expm1(prod1))^nu/expvT1)
d2ldv2 <- -dldv*dldv
as.numeric(d2ldv2)
},
d2ldmdd = function(y, mu, sigma, nu) {
prod1 <- (mu*y)^sigma
expT1 <- 1 + ( expm1( prod1 ) )^nu
T1m <- ( sigma*prod1 )/mu
T2m <- sigma*prod1*(nu - 1)*exp(prod1)/
( mu*expm1(prod1) )
T3m <- -( 2*nu*sigma*prod1*exp(prod1)*(expm1(prod1))^(nu-1) )/
(mu*(expT1))
dldm <- sigma/mu + T1m + T2m + T3m
expdT1 <- 1 + ( expm1( prod1 ) )^nu
T1d <- (nu - 1)*exp(prod1)/expm1(prod1)
T2d <- -2*nu*exp(prod1)*(expm1(prod1))^(nu - 1)/expdT1
dldd <- 1/sigma + log(mu*y) + log(mu*y)*prod1*(1 + T1d + T2d)
d2ldmdd <- -dldm*dldd
as.numeric(d2ldmdd)
},
d2ldmdv = function(y, mu, sigma, nu) {
prod1 <- (mu*y)^sigma
expT1 <- 1 + ( expm1( prod1 ) )^nu
T1m <- ( sigma*prod1 )/mu
T2m <- sigma*prod1*(nu - 1)*exp(prod1)/
( mu*expm1(prod1) )
T3m <- -( 2*nu*sigma*prod1*exp(prod1)*(expm1(prod1))^(nu-1) )/
(mu*(expT1))
dldm <- sigma/mu + T1m + T2m + T3m
expvT1 <- 1 + ( expm1( prod1 ) )^nu
dldv <- 1/nu + log(expm1(prod1))*(1 - 2*(expm1(prod1))^nu/expvT1)
d2ldmdv <- -dldm*dldv
as.numeric(d2ldmdv)
},
d2ldddv = function(y, mu, sigma, nu) {
prod1 <- (mu*y)^sigma
expdT1 <- 1 + ( expm1( prod1 ) )^nu
T1d <- (nu - 1)*exp(prod1)/expm1(prod1)
T2d <- -2*nu*exp(prod1)*(expm1(prod1))^(nu - 1)/expdT1
dldd <- 1/sigma + log(mu*y) + log(mu*y)*prod1*(1 + T1d + T2d)
expvT1 <- 1 + ( expm1( prod1 ) )^nu
dldv <- 1/nu + log(expm1(prod1))*(1 - 2*(expm1(prod1))^nu/expvT1)
d2ldddv <- -dldd*dldv
as.numeric(d2ldddv)
},
G.dev.incr = function(y, mu, sigma, nu, ...) -2*dOW(y, mu, sigma, nu, log = TRUE),
rqres = expression(rqres(pfun = "pOW", type = "Continuous", y = y, mu = mu, sigma = sigma, nu = nu)),
mu.initial = expression(mu <- rep(1/mean(y), length(y))),
# Increasing hazard as default
sigma.initial = expression(sigma <- rep(2, length(y))),
nu.initial = expression(nu <- rep(6, length(y))),
mu.valid = function(mu) all(mu > 0),
sigma.valid = function(sigma) all(sigma > 1),
nu.valid = function(nu) all(nu > 1),
# sigma.valid = sigma.space,
# nu.valid = nu.space,
y.valid = function(y) all(y > 0)
),
class = c("gamlss.family", "family"))
}