Slash Distribution Family Function
Estimates the two parameters of the slash distribution by maximum likelihood estimation.
slash(lmu = "identitylink", lsigma = "loglink",
imu = NULL, isigma = NULL, gprobs.y = ppoints(8), nsimEIM = 250,
zero = NULL, smallno = .Machine$double.eps*1000)lmu, lsigma |
Parameter link functions applied to the mu
and sigma parameters, respectively.
See |
imu, isigma |
Initial values.
A |
gprobs.y |
Used to compute the initial values for |
nsimEIM, zero |
See |
smallno |
Small positive number, used to test for the singularity. |
The standard slash distribution is the distribution of the ratio of a standard normal variable to an independent standard uniform(0,1) variable. It is mainly of use in simulation studies. One of its properties is that it has heavy tails, similar to those of the Cauchy.
The general slash distribution can be obtained by replacing the univariate normal variable by a general normal N(mu,sigma) random variable. It has a density that can be written as
f(y) = 1/(2*sigma*sqrt(2*pi)) if y=mu = 1-exp(-(((x-mu)/sigma)^2)/2))/(sqrt(2*pi)*sigma*((x-mu)/sigma)^2) if y!=mu
where mu and sigma are the mean and standard deviation of the univariate normal distribution respectively.
An object of class "vglmff" (see vglmff-class).
The object is used by modelling functions such as vglm,
and vgam.
Fisher scoring using simulation is used. Convergence is often quite slow. Numerical problems may occur.
T. W. Yee and C. S. Chee
Johnson, N. L. and Kotz, S. and Balakrishnan, N. (1994). Continuous Univariate Distributions, 2nd edition, Volume 1, New York: Wiley.
Kafadar, K. (1982). A Biweight Approach to the One-Sample Problem Journal of the American Statistical Association, 77, 416–424.
## Not run: sdata <- data.frame(y = rslash(n = 1000, mu = 4, sigma = exp(2))) fit <- vglm(y ~ 1, slash, data = sdata, trace = TRUE) coef(fit, matrix = TRUE) Coef(fit) summary(fit) ## End(Not run)
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