extremevalues (version 2.3.4)

getLimit: Determine outlier limit

Description

Determine outlier limit. These functions are called by the wrapper function getOutliers

Usage

getExponentialLimit(y, p, N, rho)
getLognormalLimit(y, p, N, rho)
getNormalLimit(y, p, N, rho)
getParetoLimit(y, p, N, rho)
getWeibullLimit(y, p, N, rho)

Value

limit

The y-value above which less then rho observations are expected

R2

R-squared value for the fit

nFit

Number of values used in fit (length(y))

lamda

(exponential only) Estimated location (and spread) parameter for \(f(y)=\lambda\exp(-\lambda y)\)

mu

(lognormal only) Estimated \({\sf E}(\ln(y))\) for lognormal distribution

sigma

(lognormal only) Estimated Var(ln(y)) for lognormal distribution

ym

(pareto only) Estimated location parameter (mode) for pareto distribution

alpha

(pareto only) Estimated spread parameter for pareto distribution

k

(weibull only) estimated power parameter \(k\) for weibull distribution

lambda

(weibull only) estimated scaling parameter \(\lambda\) for weibull distribution

Arguments

y

Vector of one-dimensional nonnegative data

p

Corresponding quantile values

N

Number of observations

rho

Limiting expected value

Author

Mark van der Loo, see www.markvanderloo.eu

Details

The functions fit a model cdf to the observed y and p and returns the y-value above which less than rho values are expected, given N observations. See getOutlierLimit for a complete explanation.

References

M.P.J. van der Loo, Distribution based outlier detection for univariate data. Discussion paper 10003, Statistics Netherlands, The Hague (2010). Available from www.markvanderloo.eu or www.cbs.nl.

Examples

y <- sort(exp(rnorm(100)));
p <- seq(1,100)/100;
II <- seq(10,90)
L <- getExponentialLimit(y[II],p[II],100,1.0);