extremevalues (version 2.1)

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)

Arguments

y

Vector of one-dimensional nonnegative data

p

Corresponding quantile values

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

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);