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Density function, distribution function and random generation for nine parametric bivariate extreme value models.
dbvevd(x, dep, asy = c(1, 1), alpha, beta, model = c("log", "alog",
"hr", "neglog", "aneglog", "bilog", "negbilog", "ct", "amix"),
mar1 = c(0, 1, 0), mar2 = mar1, log = FALSE)
pbvevd(q, dep, asy = c(1, 1), alpha, beta, model = c("log", "alog",
"hr", "neglog", "aneglog", "bilog", "negbilog", "ct", "amix"),
mar1 = c(0, 1, 0), mar2 = mar1, lower.tail = TRUE)
rbvevd(n, dep, asy = c(1, 1), alpha, beta, model = c("log", "alog",
"hr", "neglog", "aneglog", "bilog", "negbilog", "ct", "amix"),
mar1 = c(0, 1, 0), mar2 = mar1)
A vector of length two or a matrix with two columns, in which case the density/distribution is evaluated across the rows.
Number of observations.
Dependence parameter for the logistic, asymmetric logistic, Husler-Reiss, negative logistic and asymmetric negative logistic models.
A vector of length two, containing the two asymmetry parameters for the asymmetric logistic and asymmetric negative logistic models.
Alpha and beta parameters for the bilogistic, negative bilogistic, Coles-Tawn and asymmetric mixed models.
The specified model; a character string. Must be
either "log"
(the default), "alog"
, "hr"
,
"neglog"
, "aneglog"
, "bilog"
,
"negbilog"
, "ct"
or "amix"
(or any unique
partial match), for the logistic, asymmetric logistic,
Husler-Reiss, negative logistic, asymmetric negative logistic,
bilogistic, negative bilogistic, Coles-Tawn and asymmetric
mixed models respectively. If parameter arguments are given
that do not correspond to the specified model those arguments
are ignored, with a warning.
Vectors of length three containing marginal parameters, or matrices with three columns where each column represents a vector of values to be passed to the corresponding marginal parameter.
Logical; if TRUE
, the log density is returned.
Logical; if TRUE
(default), the
distribution function is returned; the survivor function
is returned otherwise.
dbvevd
gives the density function, pbvevd
gives the
distribution function and rbvevd
generates random deviates,
for one of nine parametric bivariate extreme value models.
Define
In each of the bivariate distributions functions
model = "log"
(Gumbel, 1960)
The bivariate logistic distribution function with
parameter
model = "alog"
(Tawn, 1988)
The bivariate asymmetric logistic distribution function with
parameters
model = "hr"
(Husler and Reiss, 1989)
The Husler-Reiss distribution function with parameter
model = "neglog"
(Galambos, 1975)
The bivariate negative logistic distribution function
with parameter
model = "aneglog"
(Joe, 1990)
The bivariate asymmetric negative logistic distribution function
with parameters parameters
model = "bilog"
(Smith, 1990)
The bilogistic distribution function with
parameters
model = "negbilog"
(Coles and Tawn, 1994)
The negative bilogistic distribution function with
parameters
model = "ct"
(Coles and Tawn, 1991)
The Coles-Tawn distribution function with
parameters
model = "amix"
(Tawn, 1988)
The asymmetric mixed distribution function with
parameters abvevd
.
Coles, S. G. and Tawn, J. A. (1991) Modelling extreme multivariate events. J. Roy. Statist. Soc., B, 53, 377--392.
Coles, S. G. and Tawn, J. A. (1994) Statistical methods for multivariate extremes: an application to structural design (with discussion). Appl. Statist., 43, 1--48.
Galambos, J. (1975) Order statistics of samples from multivariate distributions. J. Amer. Statist. Assoc., 70, 674--680.
Gumbel, E. J. (1960) Distributions des valeurs extremes en plusieurs dimensions. Publ. Inst. Statist. Univ. Paris, 9, 171--173.
Husler, J. and Reiss, R.-D. (1989) Maxima of normal random vectors: between independence and complete dependence. Statist. Probab. Letters, 7, 283--286.
Joe, H. (1990) Families of min-stable multivariate exponential and multivariate extreme value distributions. Statist. Probab. Letters, 9, 75--81.
Joe, H. (1997) Multivariate Models and Dependence Concepts, London: Chapman & Hall.
Smith, R. L. (1990) Extreme value theory. In Handbook of Applicable Mathematics (ed. W. Ledermann), vol. 7. Chichester: John Wiley, pp. 437--471.
Stephenson, A. G. (2003) Simulating multivariate extreme value distributions of logistic type. Extremes, 6(1), 49--60.
Tawn, J. A. (1988) Bivariate extreme value theory: models and estimation. Biometrika, 75, 397--415.
# NOT RUN {
pbvevd(matrix(rep(0:4,2), ncol=2), dep = 0.7, model = "log")
pbvevd(c(2,2), dep = 0.7, asy = c(0.6,0.8), model = "alog")
pbvevd(c(1,1), dep = 1.7, model = "hr")
margins <- cbind(0, 1, seq(-0.5,0.5,0.1))
rbvevd(11, dep = 1.7, model = "hr", mar1 = margins)
rbvevd(10, dep = 1.2, model = "neglog", mar1 = c(10, 1, 1))
rbvevd(10, alpha = 0.7, beta = 0.52, model = "bilog")
dbvevd(c(0,0), dep = 1.2, asy = c(0.5,0.9), model = "aneglog")
dbvevd(c(0,0), alpha = 0.75, beta = 0.5, model = "ct", log = TRUE)
dbvevd(c(0,0), alpha = 0.7, beta = 1.52, model = "negbilog")
# }
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