distrib_sk {genlogis} | R Documentation |
The Generalized logistic distribution with skewness
Description
Density, distribution function, quantile function and random generation a generalized logistic distribution with skewness.
Usage
pgenlog_sk(
q,
a = sqrt(2/pi),
b = 0.5,
p = 2,
mu = 0,
skew = 0.5,
lower.tail = TRUE
)
dgenlog_sk(x, a = sqrt(2/pi), b = 0.5, p = 2, mu = 0, skew = 0.5)
qgenlog_sk(
k,
a = sqrt(2/pi),
b = 0.5,
p = 2,
mu = 0,
skew = 0.5,
lower.tail = TRUE
)
rgenlog_sk(n, a = sqrt(2/pi), b = 0.5, p = 2, mu = 0, skew = 0.5)
Arguments
a , b , p |
parameters |
mu |
mu parameter |
skew |
skewness parameter limited to the interval (-1, 1) |
lower.tail |
logical; if TRUE (default), probabilities are |
x , q |
vector of quantiles. |
k |
vector of probabilities. |
n |
number of observations. If length(n) > 1, the length is taken to be the number required |
Details
The used distribution for this package is given by:
f(x) = 2*((a + b*(1+p)*(abs(x-mu)^p))*exp(-(x-mu)*(a+b*(abs(x-mu)^p))))/
((exp(-(x-mu)*(a + b* (abs(x-mu)^p)))+1)^2) *
((exp(-(skew*(x-mu))*(a+b*(abs(skew*(x-mu))^p)))+1)^(-1))
The default values for a, b, p and mu
produces a function with mean 0 and variance close to 1.
*Restrictions:
If p
equals to 0, b
or a
must be 0 otherwise there is identifiability problem.
The distribution is not defined for a
and b
equal to 0 simultaneously.
Value
dgenlog_sk
gives the density, pgenlog_sk
gives the distribution function,
qgenlog_sk
gives the quantile function, and rgenlog_sk
generates random deviates.
The length of the result is determined by n
for rgenlog_sk
, and is the maximum of the lengths
of the numerical arguments for the other functions.
References
Rathie, P. N. and Swamee, P. K (2006) On a new invertible generalized logistic distribution approximation to normal distribution, Technical Research Report in Statistics, 07/2006, Dept. of Statistics, Univ. of Brasilia, Brasilia, Brazil.
Azzalini, A. (1985) A class of distributions which includes the normal ones. Scandinavian Journal of Statistics.
Examples
pgenlog_sk(0.5)
curve(dgenlog_sk(x), xlim = c(-3,3))
rgenlog_sk(100)
qgenlog_sk(0.95)