slash: Slash Distribution Family Function

Description Usage Arguments Details Value Note Author(s) References See Also Examples

View source: R/family.aunivariate.R

Description

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

Usage

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slash(lmu = "identitylink", lsigma = "loglink",
      imu = NULL, isigma = NULL, gprobs.y = ppoints(8), 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.

imu, isigma

Initial values. A NULL means an initial value is chosen internally. See CommonVGAMffArguments for more information.

gprobs.y

Used to compute the initial values for mu. This argument is fed into the probs argument of quantile to construct a grid, which is used to evaluate the log-likelihood. This must have values between 0 and 1.

nsimEIM, zero

See CommonVGAMffArguments for 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, simulate.vlm.

Examples

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## 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)

Example output

Loading required package: stats4
Loading required package: splines
VGLM    linear loop  1 :  loglikelihood = -4979.4228
VGLM    linear loop  2 :  loglikelihood = -4944.1548
VGLM    linear loop  3 :  loglikelihood = -4850.9323
VGLM    linear loop  4 :  loglikelihood = -4833.9557
VGLM    linear loop  5 :  loglikelihood = -4821.8525
VGLM    linear loop  6 :  loglikelihood = -4819.3752
VGLM    linear loop  7 :  loglikelihood = -4818.9378
VGLM    linear loop  8 :  loglikelihood = -4818.8661
VGLM    linear loop  9 :  loglikelihood = -4818.8523
VGLM    linear loop  10 :  loglikelihood = -4818.8497
VGLM    linear loop  11 :  loglikelihood = -4818.8491
VGLM    linear loop  12 :  loglikelihood = -4818.849
VGLM    linear loop  13 :  loglikelihood = -4818.849
VGLM    linear loop  14 :  loglikelihood = -4818.849
                  mu loglink(sigma)
(Intercept) 7.120096       2.014675
      mu    sigma 
7.120096 7.498290 

Call:
vglm(formula = y ~ 1, family = slash, data = sdata, trace = TRUE)

Coefficients: 
              Estimate Std. Error z value Pr(>|z|)    
(Intercept):1  7.12010    0.54183   13.14   <2e-16 ***
(Intercept):2  2.01467    0.04071   49.49   <2e-16 ***
---
Signif. codes:  0***0.001**0.01*0.05.’ 0.1 ‘ ’ 1

Names of linear predictors: mu, loglink(sigma)

Log-likelihood: -4818.849 on 1998 degrees of freedom

Number of Fisher scoring iterations: 14 

No Hauck-Donner effect found in any of the estimates

VGAM documentation built on Jan. 16, 2021, 5:21 p.m.