# expexpff1: Exponentiated Exponential Distribution In VGAM: Vector Generalized Linear and Additive Models

## Description

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

## Usage

 `1` ```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.

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.

`expexpff`, `CommonVGAMffArguments`.

## Examples

 ``` 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23``` ```# 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
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
 -112.9762
 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
 -152.2006
 0.8095687
```

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