Density, distribution function, quantile function and random generation a generalized logistic distribution.
pgenlog(q, a = sqrt(2/pi), b = 0.5, p = 2, mu = 0, lower.tail = TRUE)dgenlog(x, a = sqrt(2/pi), b = 0.5, p = 2, mu = 0)
qgenlog(k, a = sqrt(2/pi), b = 0.5, p = 2, mu = 0, lower.tail = TRUE)
rgenlog(n, a = sqrt(2/pi), b = 0.5, p = 2, mu = 0)
dgenlog gives the density, pgenlog gives the distribution function,
qgenlog gives the quantile function, and rgenlog generates random deviates.
The length of the result is determined by n for rgenlog, and is the maximum of the lengths
of the numerical arguments for the other functions.
parameters \(\ge 0\), with restrictions.*
mu parameter
logical; if TRUE (default), probabilities are \(P[X \le x]\) otherwise, \(P[X > x]\).
vector of quantiles.
vector of probabilities.
number of observations. If length(n) > 1, the length is taken to be the number required
The used distribution for this package is given by: $$f(x) = ((a + b*(1+p)*(|x-mu|^p))*exp(-(x-mu)*(a+b*(|x-mu|^p)))) / ((exp(-(x-mu)*(a + b* (|x-mu|^p)))+1)^2)$$
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.
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.
pgenlog(0.5)
curve(dgenlog(x), xlim = c(-3,3))
rgenlog(100)
qgenlog(0.95)
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