# summaryMLE: Summary the Maximum-Likelihood Estimation with the Inverse... In ihs: Inverse Hyperbolic Sine Distribution

## Description

Summary the maximum-likelihood estimation including standard errors and t-values.

## Usage

 ```1 2 3 4``` ```## S3 method for class 'MLE' summary(object, ...) ## S3 method for class 'mult.MLE' summary(object, ...) ```

## Arguments

 `object` object of class `'MLE'` or of class `'mult.MLE'`, usually a result from maximum-likelihood estimation. `...` currently not used.

## Value

`summary.MLE` returns an object of class `'summary.MLE'` with the following components:

 `parameters` names of parameters used in the estimation procedure. `type` type of maximisation. `iterations` number of iterations. `code` code of success. `message` a short message describing the code. `loglik` the loglik value in the maximum. `estimate` numeric matrix, the first column contains the parameter estimates, the second the standard errors, third t-values and fourth corresponding probabilities. `fixed` logical vector, which parameters are treated as constants. `NActivePar` number of free parameters. `constraints` information about the constrained optimization. Passed directly further from `maxim`-object. `NULL` if unconstrained maximization.

`summary.mult.MLE` returns a list of class `'summary.mult.MLE'` with components of class `'summary.MLE'`.

## Author(s)

Carter Davis, carterdavis@byu.edu

the `maxLik` CRAN package

## Examples

 ``` 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24``` ```### Showing how to fit a simple vector of data to the inverse ### hyperbolic sine distribution. require(graphics) require(stats) set.seed(123456) x = rnorm(100) X.f = X ~ x start = list(mu = 0, sigma = 2, lambda = 0, k = 1) result = ihs.mle(X.f = X.f, start = start) sumResult = summary(result) print(result) coef(result) print(sumResult) ### Comparing the fit xvals = seq(-5, 5, by = 0.05) coefs = coef(result) mu = coefs sigma = coefs lambda = coefs k = coefs plot(xvals, dnorm(xvals), type = "l", col = "blue") lines(xvals, dihs(xvals, mu = mu, sigma = sigma, lambda = lambda, k = k), col = "red") ```

### Example output ```Loading required package: maxLik

Please cite the 'maxLik' package as:
Henningsen, Arne and Toomet, Ott (2011). maxLik: A package for maximum likelihood estimation in R. Computational Statistics 26(3), 443-458. DOI 10.1007/s00180-010-0217-1.

If you have questions, suggestions, or comments regarding the 'maxLik' package, please use a forum or 'tracker' at maxLik's R-Forge site:
https://r-forge.r-project.org/projects/maxlik/
Warning messages:
1: In log(k) : NaNs produced
2: In log(k) : NaNs produced
Maximum Likelihood estimation
BFGS maximization, 73 iterations
Return code 0: successful convergence
Log-Likelihood: -140.6543 (4 free parameter(s))
Estimate(s): 0.01679615 0.9893086 -0.7061181 14.32567
  0.01679615  0.98930857 -0.70611810 14.32567428
--------------------------------------------
Maximum Likelihood estimation
BFGS maximization, 73 iterations
Return code 0: successful convergence
Log-Likelihood: -140.6543
4 free parameters
Estimates:
Parameters Estimate Std. error t value   Pr(> t)
1         mu   0.0168    0.09897  0.1697 8.652e-01
2      sigma   0.9893    0.07119 13.8977 6.541e-44
3     lambda  -0.7061    3.00496 -0.2350 8.142e-01
4          k  14.3257    4.19566  3.4144 6.392e-04
--------------------------------------------
```

ihs documentation built on May 2, 2019, 3:50 p.m.