normalp (version 0.7.2.1)

estimatep: Estimation of p

Description

The estimatep function estimates the shape parameter \(p\) from a vector of observations.

Usage

estimatep(x, mu, p=2, method=c("inverse","direct"))

Value

An estimate of \(p\) from a sample of observations.

Arguments

x

Vector of observations.

mu

An estimate of the location parameter.

p

Starting value of the shape parameter.

method

Method used to estimate \(p\) from a sample.

Author

Angelo M. Mineo

Details

The used algorithm is based on a method proposed by A.M. Mineo (1994), which uses a particular index of kurtosis, called \(VI\)

$$VI=\frac{\sqrt{\Gamma(1/p)\Gamma(3/p)}}{\Gamma(2/p)}.$$

With method the user can choice between an inverse interpolation (faster) or a direct solution of the equation

$$\hat{VI}=\frac{\sqrt{\Gamma(1/p)\Gamma(3/p)}}{\Gamma(2/p)}.$$

References

Mineo, A.M. (1994) Un nuovo metodo di stima di p per una corretta valutazione dei parametri di intensita e di scala di una curva normale di ordine p, Atti della XXXVII Riunione Scientifica della Societa Italiana di Statistica, San Remo, Vol. 2, pp. 147-154.

Examples

x<-rnormp(300,mu=1,sigmap=2,p=4)
p<-estimatep(x,mu=1,p=2)
p