splitt {dng} | R Documentation |
Split-t distribution
Description
Density, distribution function, quantile function and random generation for the normal distribution for the split student-t distribution.
Usage
dsplitt(x, mu, df, phi, lmd, logarithm)
psplitt(q, mu, df, phi, lmd)
qsplitt(p, mu, df, phi, lmd)
rsplitt(n, mu, df, phi, lmd)
Arguments
x |
vector of quantiles. |
mu |
vector of location parameter. (The mode of the density) |
df |
degrees of freedom (> 0, can be non-integer). df = Inf is also allowed. |
phi |
vector of scale parameters (>0). |
lmd |
vector of skewness parameters (>0). If is 1, reduced to the symmetric student t distribution. |
logarithm |
logical; if TRUE, probabilities p are given as log(p). |
q |
vector of quantiles. |
p |
vector of probability. |
n |
number of observations. If length(n) > 1, the length is taken to be the number required. |
Details
The random variable y follows a split-t distribution with \nu
>0
degrees of freedom, y~t(\mu
, \phi
, \lambda
, \nu
),
if its density function is of the form
C K(\mu, \phi, \nu,)I(y\leq\mu) + C K(\mu, \lambda \phi,
\nu)I(y>\mu),
where,
K(\mu, \phi, \nu,) =[\nu/(\nu+(y-\mu)^2 /\phi
^2)]^{(\nu+1)/2}
is the kernel of a student t
density with variance
\phi ^2\nu/(\nu-2)
and
c = 2[(1+\lambda)\phi (\sqrt \nu)
Beta(\nu/2,1/2)]^{-1}
is the normalization constant.
Value
dsplitt
gives the density; psplitt
gives the percentile;
qsplitt
gives the quantile; and rsplitt
gives the random
variables. Invalid arguments will result in return value NaN, with a warning.
The numerical arguments other than n are recycled to the length of the result. Only the first elements of the logical arguments are used.
Functions
-
psplitt
: Percentile for the split-t distribution. -
qsplitt
: Quantile for the split-t distribution. -
rsplitt
: Randon variables from the split-t distribution.
Author(s)
Feng Li, Jiayue Zeng
References
Li, F., Villani, M., & Kohn, R. (2010). Flexible modeling of conditional distributions using smooth mixtures of asymmetric student t densities. Journal of Statistical Planning & Inference, 140(12), 3638-3654.
See Also
splitt_mean()
,
splitt_var()
,splitt_skewness()
and
splitt_kurtosis()
for numerical characteristics of the
Split-t distribution.
Examples
n <- 3
mu <- c(0,1,2)
df <- rep(10,3)
phi <- c(0.5,1,2)
lmd <- c(1,2,3)
q0 <- rsplitt(n, mu, df, phi, lmd)
d0 <- dsplitt(q0, mu, df, phi, lmd, logarithm = FALSE)
p0 <- psplitt(q0, mu, df, phi, lmd)
q1 <- qsplitt(p0,mu, df, phi, lmd)
all.equal(q0, q1)