VGAM (version 0.7-5)

logistic: Logistic Distribution Family Function

Description

Estimates the location and scale parameters of the logistic distribution by maximum likelihood estimation.

Usage

logistic1(llocation="identity", elocation=list(),
          scale.arg=1, method.init=1)
logistic2(llocation="identity", lscale="loge",
          elocation=list(), escale=list(),
          ilocation=NULL, iscale=NULL, method.init=1, zero=NULL)

Value

• An object of class "vglmff" (see vglmff-class). The object is used by modelling functions such as vglm, rrvglm and vgam.

Details

The two-parameter logistic distribution has a density that can be written as $$f(y;l,s) = \frac{\exp[-(y-l)/s]}{ s\left( 1 + \exp[-(y-l)/s] \right)^2}$$ where $s>0$ is the scale parameter, and $l$ is the location parameter. The response $-\infty

logistic1 estimates the location parameter only while logistic2 estimates both parameters. By default, $\eta_1=l$ and $\eta_2=\log(s)$ for logistic2.

References

Johnson, N. L. and Kotz, S. and Balakrishnan, N. (1994) Continuous Univariate Distributions, 2nd edition, Volume 1, New York: Wiley. Chapter 15.

Evans, M., Hastings, N. and Peacock, B. (2000) Statistical Distributions, New York: Wiley-Interscience, Third edition.

Castillo, E., Hadi, A. S., Balakrishnan, N. Sarabia, J. S. (2005) Extreme Value and Related Models with Applications in Engineering and Science, Hoboken, N.J.: Wiley-Interscience, p.130.

deCani, J. S. and Stine, R. A. (1986) A note on Deriving the Information Matrix for a Logistic Distribution, The American Statistician, 40, 220--222.

See Also

rlogis, bilogistic4.

Examples

# location unknown, scale known
n = 500
x = runif(n)
y = rlogis(n, loc=1+5*x, scale=4)
fit = vglm(y ~ x, logistic1(scale=4), trace=TRUE, crit="c")
coef(fit, matrix=TRUE)

# Both location and scale unknown
n = 2000
x = runif(n)
y = rlogis(n, loc=1+5*x, scale=exp(0+1*x))
fit = vglm(y ~ x, logistic2)
coef(fit, matrix=TRUE)
vcov(fit)
summary(fit)