expexpff1: Exponentiated Exponential Distribution

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

View source: R/family.univariate.R

Description

Estimates the two parameters of the exponentiated exponential distribution by maximizing a profile (concentrated) likelihood.

Usage

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expexpff1(lrate = "loglink", irate = NULL, ishape = 1)

Arguments

lrate

Parameter link function for the (positive) rate parameter. See Links for more choices.

irate

Initial value for the rate parameter. By default, an initial value is chosen internally using ishape.

ishape

Initial value for the shape parameter. If convergence fails try setting a different value for this argument.

Details

See expexpff for details about the exponentiated exponential distribution. This family function uses a different algorithm for fitting the model. Given rate, the MLE of shape can easily be solved in terms of rate. This family function maximizes a profile (concentrated) likelihood with respect to rate. Newton-Raphson is used, which compares with Fisher scoring with expexpff.

Value

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

Warning

The standard errors produced by a summary of the model may be wrong.

Note

This family function works only for intercept-only models, i.e., y ~ 1 where y is the response.

The estimate of shape is attached to the misc slot of the object, which is a list and contains the component shape.

As Newton-Raphson is used, the working weights are sometimes negative, and some adjustment is made to these to make them positive.

Like expexpff, good initial values are needed. Convergence may be slow.

Author(s)

T. W. Yee

References

Gupta, R. D. and Kundu, D. (2001). Exponentiated exponential family: an alternative to gamma and Weibull distributions, Biometrical Journal, 43, 117–130.

See Also

expexpff, CommonVGAMffArguments.

Examples

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# Ball bearings data (number of million revolutions before failure)
edata <- data.frame(bbearings = c(17.88, 28.92, 33.00, 41.52, 42.12, 45.60,
48.80, 51.84, 51.96, 54.12, 55.56, 67.80, 68.64, 68.64,
68.88, 84.12, 93.12, 98.64, 105.12, 105.84, 127.92,
128.04, 173.40))
fit <- vglm(bbearings ~ 1, expexpff1(ishape = 4), trace = TRUE,
            maxit = 250, checkwz = FALSE, data = edata)
coef(fit, matrix = TRUE)
Coef(fit)  # Authors get c(0.0314, 5.2589) with log-lik -112.9763
logLik(fit)
fit@misc$shape  # Estimate of shape


# Failure times of the airconditioning system of an airplane
eedata <- data.frame(acplane = c(23, 261, 87, 7, 120, 14, 62, 47,
225, 71, 246, 21, 42, 20, 5, 12, 120, 11, 3, 14,
71, 11, 14, 11, 16, 90, 1, 16, 52, 95))
fit <- vglm(acplane ~ 1, expexpff1(ishape = 0.8), trace = TRUE,
            maxit = 50, checkwz = FALSE, data = eedata)
coef(fit, matrix = TRUE)
Coef(fit)  # Authors get c(0.0145, 0.8130) with log-lik -152.264
logLik(fit)
fit@misc$shape  # Estimate of shape

Example output

Loading required package: stats4
Loading required package: splines
Applying Greenstadt modification to 23 matrices
VGLM    linear loop  1 :  loglikelihood = -142.86097
Applying Greenstadt modification to 19 matrices
VGLM    linear loop  2 :  loglikelihood = -138.55752
Applying Greenstadt modification to 18 matrices
VGLM    linear loop  3 :  loglikelihood = -134.61146
Applying Greenstadt modification to 18 matrices
VGLM    linear loop  4 :  loglikelihood = -131.02887
Applying Greenstadt modification to 18 matrices
VGLM    linear loop  5 :  loglikelihood = -127.81272
Applying Greenstadt modification to 18 matrices
VGLM    linear loop  6 :  loglikelihood = -124.96291
Applying Greenstadt modification to 18 matrices
VGLM    linear loop  7 :  loglikelihood = -122.47572
Applying Greenstadt modification to 17 matrices
VGLM    linear loop  8 :  loglikelihood = -120.34414
Applying Greenstadt modification to 17 matrices
VGLM    linear loop  9 :  loglikelihood = -118.55463
Applying Greenstadt modification to 18 matrices
VGLM    linear loop  10 :  loglikelihood = -117.08958
Applying Greenstadt modification to 18 matrices
VGLM    linear loop  11 :  loglikelihood = -115.9242
Applying Greenstadt modification to 18 matrices
VGLM    linear loop  12 :  loglikelihood = -115.02504
Applying Greenstadt modification to 18 matrices
VGLM    linear loop  13 :  loglikelihood = -114.35458
Applying Greenstadt modification to 19 matrices
VGLM    linear loop  14 :  loglikelihood = -113.87332
Applying Greenstadt modification to 20 matrices
VGLM    linear loop  15 :  loglikelihood = -113.5415
Applying Greenstadt modification to 23 matrices
VGLM    linear loop  16 :  loglikelihood = -113.32227
Applying Greenstadt modification to 23 matrices
VGLM    linear loop  17 :  loglikelihood = -113.18287
Applying Greenstadt modification to 23 matrices
VGLM    linear loop  18 :  loglikelihood = -113.09699
Applying Greenstadt modification to 23 matrices
VGLM    linear loop  19 :  loglikelihood = -113.04553
Applying Greenstadt modification to 23 matrices
VGLM    linear loop  20 :  loglikelihood = -113.01541
Applying Greenstadt modification to 23 matrices
VGLM    linear loop  21 :  loglikelihood = -112.99811
Applying Greenstadt modification to 23 matrices
VGLM    linear loop  22 :  loglikelihood = -112.98834
Applying Greenstadt modification to 23 matrices
VGLM    linear loop  23 :  loglikelihood = -112.98288
Applying Greenstadt modification to 23 matrices
VGLM    linear loop  24 :  loglikelihood = -112.97986
Applying Greenstadt modification to 23 matrices
VGLM    linear loop  25 :  loglikelihood = -112.9782
Applying Greenstadt modification to 23 matrices
VGLM    linear loop  26 :  loglikelihood = -112.9773
Applying Greenstadt modification to 23 matrices
VGLM    linear loop  27 :  loglikelihood = -112.9768
Applying Greenstadt modification to 23 matrices
VGLM    linear loop  28 :  loglikelihood = -112.97654
Applying Greenstadt modification to 23 matrices
VGLM    linear loop  29 :  loglikelihood = -112.97639
Applying Greenstadt modification to 23 matrices
VGLM    linear loop  30 :  loglikelihood = -112.97631
Applying Greenstadt modification to 23 matrices
VGLM    linear loop  31 :  loglikelihood = -112.97627
Applying Greenstadt modification to 23 matrices
VGLM    linear loop  32 :  loglikelihood = -112.97625
Applying Greenstadt modification to 23 matrices
VGLM    linear loop  33 :  loglikelihood = -112.97624
Applying Greenstadt modification to 23 matrices
VGLM    linear loop  34 :  loglikelihood = -112.97623
Applying Greenstadt modification to 23 matrices
VGLM    linear loop  35 :  loglikelihood = -112.97623
Applying Greenstadt modification to 23 matrices
VGLM    linear loop  36 :  loglikelihood = -112.97622
            loge(rate)
(Intercept)   -3.43239
      rate 
0.03230964 
[1] -112.9762
[1] 5.288181
Applying Greenstadt modification to 30 matrices
VGLM    linear loop  1 :  loglikelihood = -229.62305
Applying Greenstadt modification to 29 matrices
VGLM    linear loop  2 :  loglikelihood = -223.12728
Applying Greenstadt modification to 29 matrices
VGLM    linear loop  3 :  loglikelihood = -216.82414
Applying Greenstadt modification to 29 matrices
VGLM    linear loop  4 :  loglikelihood = -210.72536
Applying Greenstadt modification to 29 matrices
VGLM    linear loop  5 :  loglikelihood = -204.84383
Applying Greenstadt modification to 29 matrices
VGLM    linear loop  6 :  loglikelihood = -199.19363
Applying Greenstadt modification to 30 matrices
VGLM    linear loop  7 :  loglikelihood = -193.79011
Applying Greenstadt modification to 30 matrices
VGLM    linear loop  8 :  loglikelihood = -188.64997
Applying Greenstadt modification to 30 matrices
VGLM    linear loop  9 :  loglikelihood = -183.79108
Applying Greenstadt modification to 30 matrices
VGLM    linear loop  10 :  loglikelihood = -179.2324
Applying Greenstadt modification to 30 matrices
VGLM    linear loop  11 :  loglikelihood = -174.99364
Applying Greenstadt modification to 30 matrices
VGLM    linear loop  12 :  loglikelihood = -171.0948
Applying Greenstadt modification to 30 matrices
VGLM    linear loop  13 :  loglikelihood = -167.55531
Applying Greenstadt modification to 30 matrices
VGLM    linear loop  14 :  loglikelihood = -164.39285
Applying Greenstadt modification to 30 matrices
VGLM    linear loop  15 :  loglikelihood = -161.62175
Applying Greenstadt modification to 30 matrices
VGLM    linear loop  16 :  loglikelihood = -159.25086
Applying Greenstadt modification to 30 matrices
VGLM    linear loop  17 :  loglikelihood = -157.28105
Applying Greenstadt modification to 30 matrices
VGLM    linear loop  18 :  loglikelihood = -155.70247
Applying Greenstadt modification to 30 matrices
VGLM    linear loop  19 :  loglikelihood = -154.4922
Applying Greenstadt modification to 30 matrices
VGLM    linear loop  20 :  loglikelihood = -153.61294
Applying Greenstadt modification to 30 matrices
VGLM    linear loop  21 :  loglikelihood = -153.01404
Applying Greenstadt modification to 30 matrices
VGLM    linear loop  22 :  loglikelihood = -152.6357
Applying Greenstadt modification to 30 matrices
VGLM    linear loop  23 :  loglikelihood = -152.41607
Applying Greenstadt modification to 27 matrices
VGLM    linear loop  24 :  loglikelihood = -152.29971
Applying Greenstadt modification to 20 matrices
VGLM    linear loop  25 :  loglikelihood = -152.24343
Applying Greenstadt modification to 18 matrices
VGLM    linear loop  26 :  loglikelihood = -152.21827
Applying Greenstadt modification to 18 matrices
VGLM    linear loop  27 :  loglikelihood = -152.20765
Applying Greenstadt modification to 18 matrices
VGLM    linear loop  28 :  loglikelihood = -152.20337
Applying Greenstadt modification to 17 matrices
VGLM    linear loop  29 :  loglikelihood = -152.20168
Applying Greenstadt modification to 17 matrices
VGLM    linear loop  30 :  loglikelihood = -152.20104
Applying Greenstadt modification to 17 matrices
VGLM    linear loop  31 :  loglikelihood = -152.20079
Applying Greenstadt modification to 17 matrices
VGLM    linear loop  32 :  loglikelihood = -152.2007
Applying Greenstadt modification to 16 matrices
VGLM    linear loop  33 :  loglikelihood = -152.20066
Applying Greenstadt modification to 16 matrices
VGLM    linear loop  34 :  loglikelihood = -152.20065
Applying Greenstadt modification to 16 matrices
VGLM    linear loop  35 :  loglikelihood = -152.20065
Applying Greenstadt modification to 16 matrices
VGLM    linear loop  36 :  loglikelihood = -152.20064
            loge(rate)
(Intercept)  -4.230272
      rate 
0.01454843 
[1] -152.2006
[1] 0.8095687

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