expgeometric: Exponential Geometric Distribution Family Function

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

View source: R/family.others.R

Description

Estimates the two parameters of the exponential geometric distribution by maximum likelihood estimation.

Usage

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expgeometric(lscale = "loglink", lshape = "logitlink",
             iscale = NULL,   ishape = NULL,
             tol12 = 1e-05, zero = 1, nsimEIM = 400)

Arguments

lscale, lshape

Link function for the two parameters. See Links for more choices.

iscale, ishape

Numeric. Optional initial values for the scale and shape parameters.

tol12

Numeric. Tolerance for testing whether a parameter has value 1 or 2.

zero, nsimEIM

See CommonVGAMffArguments.

Details

The exponential geometric distribution has density function

(1/c) * (1 - s) * e^(-y/c) * (1 - s * e^(-y/c))^(-2)

where y > 0, c > 0 and 0 < s < 1. The mean, (c * (s - 1)/ s) * log(1 - s) is returned as the fitted values. Note the median is c * log(2 - s). Simulated Fisher scoring is implemented.

Value

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

Note

We define scale as the reciprocal of the scale parameter used by Adamidis and Loukas (1998).

Author(s)

J. G. Lauder and T. W. Yee

References

Adamidis, K., Loukas, S. (1998). A lifetime distribution with decreasing failure rate. Statistics and Probability Letters, 39, 35–42.

See Also

dexpgeom, exponential, geometric.

Examples

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## Not run: 
Scale <- exp(2); shape = logitlink(-1, inverse = TRUE);
edata <- data.frame(y = rexpgeom(n = 2000, scale = Scale, shape = shape))
fit <- vglm(y ~ 1, expgeometric, edata, trace = TRUE)
c(with(edata, mean(y)), head(fitted(fit), 1))
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 = -5672.17283
VGLM    linear loop  2 :  loglikelihood = -5670.44506
VGLM    linear loop  3 :  loglikelihood = -5670.43414
VGLM    linear loop  4 :  loglikelihood = -5670.43413
[1] 6.310734 6.303428
            loglink(scale) logitlink(shape)
(Intercept)       2.051906       -0.6861986
    scale     shape 
7.7827217 0.3348793 

Call:
vglm(formula = y ~ 1, family = expgeometric, data = edata, trace = TRUE)

Pearson residuals:
                     Min      1Q  Median     3Q   Max
loglink(scale)   -0.8181 -0.6203 -0.3332 0.2120 7.666
logitlink(shape) -1.1289 -0.8385 -0.1682 0.7299 6.922

Coefficients: 
              Estimate Std. Error z value Pr(>|z|)    
(Intercept):1   2.0519     0.0513  39.997  < 2e-16 ***
(Intercept):2  -0.6862     0.2408  -2.849  0.00438 ** 
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

Names of linear predictors: loglink(scale), logitlink(shape)

Log-likelihood: -5670.434 on 3998 degrees of freedom

Number of Fisher scoring iterations: 4 

No Hauck-Donner effect found in any of the estimates

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