slash {VGAM} | R Documentation

## Slash Distribution Family Function

### Description

Estimates the two parameters of the slash distribution by maximum likelihood estimation.

### Usage

    slash (lmu="identity", lsigma="loge", emu=list(), esigma=list(),
           imu=NULL, isigma=NULL, iprobs = c(0.1, 0.9), nsimEIM=250,
           zero=NULL, smallno = .Machine$double.eps*1000)

### Arguments

`lmu, lsigma` | Parameter link functions applied to the mu and sigma parameters, respectively. See `Links` for more choices.
`emu, esigma` | List. Extra argument for each of the link functions. See `earg` in `Links` for general information.
`imu, isigma` | Initial values. A `NULL` means an initial value is chosen internally. See `CommonVGAMffArguments` for more information.
`iprobs` | Used to compute the initial values for `mu`. This argument is fed into the `probs` argument of `quantile`, and then a grid between these two points is used to evaluate the log-likelihood. This argument must be of length two and have values between 0 and 1.
`nsimEIM, zero` | See `CommonVGAMffArguments` for more information.
`smallno` | Small positive number, used to test for the singularity.

### Details

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.

### Value

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

### Note

Fisher scoring using simulation is used. Convergence is often quite slow. Numerical problems may occur.

### Author(s)

T. W. Yee and C. S. Chee

### References

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.

### See Also

`rslash`.

### Examples

    y = rslash(n=1000, mu=4, sigma=exp(2))
    fit = vglm(y ~ 1, slash, trace=TRUE)
    coef(fit, matrix=TRUE)
    Coef(fit)
    summary(fit)

[Package VGAM version 0.7-9 Index]