/
dEGG.R
166 lines (156 loc) · 4.98 KB
/
dEGG.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
#' The four parameter Exponentiated Generalized Gamma distribution
#'
#' @author Amylkar Urrea Montoya, \email{amylkar.urrea@@udea.edu.co}
#'
#' @description
#' Density, distribution function, quantile function,
#' random generation and hazard function for the four parameter Exponentiated Generalized Gamma distribution
#' with parameters \code{mu}, \code{sigma}, \code{nu} and \code{tau}.
#'
#' @param x,q vector of quantiles.
#' @param p vector of probabilities.
#' @param n number of observations.
#' @param mu parameter.
#' @param sigma parameter.
#' @param nu parameter.
#' @param tau parameter.
#' @param log,log.p logical; if TRUE, probabilities p are given as log(p).
#' @param lower.tail logical; if TRUE (default), probabilities are P[X <= x], otherwise, P[X > x].
#'
#' @details
#' Four-Parameter Exponentiated Generalized Gamma distribution with parameters \code{mu},
#' \code{sigma}, \code{nu} and \code{tau} has density given by
#'
#' \eqn{f(x) = \frac{\nu \sigma}{\mu \Gamma(\tau)} \left(\frac{x}{\mu}\right)^{\sigma \tau -1} \exp\left\{ - \left( \frac{x}{\mu} \right)^\sigma \right\} \left\{ \gamma_1\left( \tau, \left( \frac{x}{\mu} \right)^\sigma \right) \right\}^{\nu-1} ,}
#'
#' for x > 0.
#'
#' @return
#' \code{dEGG} gives the density, \code{pEGG} gives the distribution
#' function, \code{qEGG} gives the quantile function, \code{rEGG}
#' generates random deviates and \code{hEGG} gives the hazard function.
#'
#' @example examples/examples_dEGG.R
#'
#' @references
#' \insertRef{almalki2014modifications}{RelDists}
#'
#' \insertRef{cordeiro2011}{RelDists}
#'
#' @importFrom Rdpack reprompt
#'
#' @export
dEGG <- function(x, mu, sigma,
nu, tau, log=FALSE){
if (any(x <= 0))
stop(paste("x must be positive", "\n", ""))
if (any(mu <= 0))
stop(paste("mu must be positive", "\n", ""))
if (any(sigma <= 0))
stop(paste("sigma must be positive", "\n", ""))
if (any(nu <= 0))
stop(paste("nu must be positive", "\n", ""))
if (any(tau <= 0))
stop(paste("tau must be postive", "\n", ""))
A <- log(nu * sigma) - log(mu * base::gamma(tau))
B <- (sigma * tau - 1) * log(x / mu) - (x / mu)^sigma
t <- (x / mu)^sigma
C <- (nu - 1) * log(zipfR::Igamma(tau, t) / base::gamma(tau))
loglik <- A + B + C
if (log == FALSE)
density <- exp(loglik)
else
density <- loglik
return(density)
}
#' @export
#' @rdname dEGG
pEGG <- function(q, mu, sigma, nu, tau,
lower.tail=TRUE, log.p=FALSE){
if (any(mu <= 0))
stop(paste("mu must be positive", "\n", ""))
if (any(sigma <= 0))
stop(paste("sigma must be positive", "\n", ""))
if (any(nu <= 0))
stop(paste("nu must be positive", "\n", ""))
if (any(tau <= 0))
stop(paste("tau must be postive", "\n", ""))
t <- (q / mu)^sigma
cdf <- (zipfR::Igamma(tau, t) / base::gamma(tau))^nu
if (lower.tail == TRUE)
cdf <- cdf
else cdf <- 1 - cdf
if (log.p == FALSE)
cdf <- cdf
else cdf <- log(cdf)
cdf
}
#' @export
#' @rdname dEGG
qEGG <- function(p, mu, sigma, nu, tau,
lower.tail=TRUE, log.p=FALSE){
if (any(mu <= 0))
stop(paste("mu must be positive", "\n", ""))
if (any(sigma <= 0))
stop(paste("sigma must be positive", "\n", ""))
if (any(nu <= 0))
stop(paste("nu must be positive", "\n", ""))
if (any(tau <= 0))
stop(paste("tau must be postive", "\n", ""))
if (log.p == TRUE)
p <- exp(p)
else p <- p
if (lower.tail == TRUE)
p <- p
else p <- 1 - p
if (any(p < 0) | any(p > 1))
stop(paste("p must be between 0 and 1", "\n", ""))
fda <- function(x, mu, sigma, nu, tau){
t <- (x / mu)^sigma
cdf <- (zipfR::Igamma(tau, t) / base::gamma(tau))^nu
cdf
}
fda1 <- function(x, mu, sigma, nu, tau, p) {
fda(x, mu, sigma, nu, tau) - p
}
r_de_la_funcion <- function(mu, sigma, nu, tau, p) {
uniroot(fda1, interval=c(0, 1e+06), mu, sigma, nu, tau, p)$root
}
r_de_la_funcion <- Vectorize(r_de_la_funcion)
q <- r_de_la_funcion(mu, sigma, nu, tau, p)
q
}
#' @importFrom stats runif
#' @export
#' @rdname dEGG
rEGG <- function(n, mu, sigma, nu, tau){
if (any(mu <= 0))
stop(paste("mu must be positive", "\n", ""))
if (any(sigma <= 0))
stop(paste("sigma must be positive", "\n", ""))
if (any(nu <= 0))
stop(paste("nu must be positive", "\n", ""))
if (any(tau <= 0))
stop(paste("tau must be postive", "\n", ""))
n <- ceiling(n)
p <- runif(n)
r <- qEGG(p, mu, sigma, nu, tau)
r
}
#' @export
#' @rdname dEGG
hEGG <- function(x, mu, sigma, nu, tau){
if (any(x <= 0))
stop(paste("x must be positive", "\n", ""))
if (any(mu <= 0))
stop(paste("mu must be positive", "\n", ""))
if (any(sigma <= 0))
stop(paste("sigma must be positive", "\n", ""))
if (any(nu <= 0))
stop(paste("nu must be positive", "\n", ""))
if (any(tau <= 0))
stop(paste("tau must be postive", "\n", ""))
h <- dEGG(x, mu, sigma, nu, tau, log=FALSE) /
pEGG(q=x, mu, sigma, nu, tau, lower.tail=FALSE, log.p=FALSE)
h
}