logit-logistic {lmfor} | R Documentation |
Density, distribution function, quantile function and random generation for the four-parameter logit-logistic distribution.
dll(x, mu, sigma, xi=0, lambda=1, log = FALSE)
pll(q, mu, sigma, xi=0, lambda=1, lower.tail=TRUE, log.p=FALSE)
qll(p, mu, sigma, xi=0, lambda=1, lower.tail=TRUE, log.p=FALSE)
rll(n, mu, sigma, xi=0, lambda=1)
x , q |
vector of quantiles |
p |
vector of probabilitiies |
n |
number of observations. If |
mu , sigma , xi , lambda |
parameters of the distribution, |
log , log.p |
logical; if TRUE, probabilities p are given as log(p) |
lower.tail |
logical; if TRUE (default), probabilities are |
The logit-logistic cdf and pdf are
F(d|\xi,\lambda,\mu,\sigma) =
\frac{1}{1+e^{(\frac{\mu}{\sigma})}
(\frac{d-\xi}{\xi+\lambda-d})^{-\frac{1}{\sigma}}}
f(d|\xi,\lambda,\mu,\sigma) =
\frac{\lambda}{\sigma}\frac{1}{(d-\xi)(\xi+\lambda-d)}
\frac{1}{e^{-\frac{\mu}{\sigma}}(\frac{d-\xi}{\xi+\lambda-d})^{\frac{1}{\sigma}}+e^{\frac{\mu}{\sigma}}(\frac{d-\xi}{\xi+\lambda-d})^{-\frac{1}{\sigma}}+2}
Parameter \xi
is the minimum, \lambda>0
the width of range (max-min), \mu
controls the skewness and \sigma
the curtosis.
dll
gives the density, pll
gives the distribution function, qll
gives the quantile function, and rll
generates random deviates.
Invalid arguments will result in return value NaN
.
The length of the result is determined by n
for rll
, and is the maximum of the lengths of the numerical arguments for the other functions.
The numerical arguments other than n
are recycled to the length of the result. Only the first elements of the logical arguments are used.
Lauri Mehtatalo <lauri.mehtatalo@uef.fi>
Mingliang Wang and Keith Rennolls, 2005. Tree diameter distribution modelling: introducing the logit-logistic distribution. Canadian Journal of Forest Research, 35(6): 1305-1313, doi:10.1139/x05-057.
Mehtatalo, Lauri and Lappi, Juha 2020. Biometry for Forestry and Environmental Data: with examples in R. New York: Chapman and Hall/CRC. 426 p. doi:10.1201/9780429173462
data(spati)
d<-spati$d[spati$plot==22]
hist(d,freq=FALSE)
d0<-seq(0,60,0.1)
lines(d0,dll(d0,0.630,0.573,3.561,35.2))