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

Generic function for the computation of the Kolmogorov(-Smirnov) minimum distance estimator.

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 | ```
ksEstimator(x, distribution, ...)
## S4 method for signature 'numeric,Binom'
ksEstimator(x, distribution, param, eps = .Machine$double.eps^0.5)
## S4 method for signature 'numeric,Pois'
ksEstimator(x, distribution, param, eps = .Machine$double.eps^0.5)
## S4 method for signature 'numeric,Norm'
ksEstimator(x, distribution, param, eps = .Machine$double.eps^0.5)
## S4 method for signature 'numeric,Lnorm'
ksEstimator(x, distribution, param, eps = .Machine$double.eps^0.5)
## S4 method for signature 'numeric,Gumbel'
ksEstimator(x, distribution, param, eps = .Machine$double.eps^0.5)
## S4 method for signature 'numeric,Exp'
ksEstimator(x, distribution, param, eps = .Machine$double.eps^0.5)
## S4 method for signature 'numeric,Gammad'
ksEstimator(x, distribution, param, eps = .Machine$double.eps^0.5)
``` |

`x` |
sample |

`distribution` |
object of class |

`...` |
additional parameters |

`param` |
name of the unknown parameter. If missing all parameters of the corresponding distribution are estimated. |

`eps` |
the desired accuracy (convergence tolerance). |

In case of discrete distributions the Kolmogorov distance is computed and
the parameters which lead to the minimum distance are returned. In case of
absolutely continuous distributions `ks.test`

is called and the parameters
which minimize the corresponding test statistic are returned.

The Kolmogorov minimum distance estimator is computed. Returns a list
with components named like the parameters of `distribution`

.

- x = "numeric", distribution = "Binom"
Binomial distributions.

- x = "numeric", distribution = "Pois"
Poisson distributions.

- x = "numeric", distribution = "Norm"
Normal distributions.

- x = "numeric", distribution = "Lnorm"
Lognormal distributions.

- x = "numeric", distribution = "Gumbel"
Gumbel distributions.

- x = "numeric", distribution = "Exp"
Exponential distributions.

- x = "numeric", distribution = "Gamma"
Gamma distributions.

Matthias Kohl Matthias.Kohl@stamats.de

Rieder, H. (1994) *Robust Asymptotic Statistics*. New York: Springer.

Kohl, M. (2005) *Numerical Contributions to the Asymptotic Theory of Robustness*.
Bayreuth: Dissertation.

1 2 3 4 5 6 7 8 | ```
x <- rnorm(100, mean = 1, sd = 2)
ksEstimator(x=x, distribution = Norm()) # estimate mean and sd
ksEstimator(x=x, distribution = Norm(mean = 1), param = "sd") # estimate sd
ksEstimator(x=x, distribution = Norm(sd = 2), param = "mean") # estimate mean
mean(x)
median(x)
sd(x)
mad(x)
``` |

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