extremevalues (version 2.3.4)

fitFunctions: Fit model distributions

Description

Fit model distribution to a set of observations.

Usage

fitNormal(y, p)
fitLognormal(y, p)
fitPareto(y, p)
fitExponential(y, p)
fitWeibull(y, p)

Value

R2

R-squared value for the fit

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

Author

Mark van der Loo, see www.markvanderloo.eu

Details

The function sorts the values of y and uses (log)linear regression to fit the values between the pmin and pmax quantile to the cdf of a model distribution.

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 = 10^rnorm(50);
L <- getOutliers(y,rho=0.5);