ufitstab.skew {alphastable} R Documentation

## ufitstab.skew

### Description

using the EM algorithm, it estimates the parameters of skew stable distribution.

### Usage

ufitstab.skew(y, alpha0, beta0, sigma0, mu0, param)

### Arguments

 y vector of observations alpha0 initial value of tail index parameter to start the EM algorithm beta0 initial value of skewness parameter to start the EM algorithm sigma0 initial value of scale parameter to start the EM algorithm mu0 initial value of location parameter to start the EM algorithm param kind of parameterization; must be 0 or 1 for S_0 and S_1 parameterizations, respectively

### Details

For any skew stable distribution we give a new representation by the following. Suppose Y~ S_{0}(alpha, beta, sigma, mu), P~ S_{1}(alpha/2,1,(cos(pi*alpha/4))^(2/alpha),0), and V~ S_{1}(alpha,1,1,0). Then, Y=eta*(2P)^(1/2)*N+theta*V+ mu-lambda, where eta=sigma*(1-|beta|)^(1/alpha), theta=sigma*sign(beta)*|beta|^(1/alpha), lambda=sigma*beta*tan(pi*alpha/2), and N~N(0,1) follows a skew stable distribution. All random variables N, P, and V are mutually independent.

### Value

 alpha estimated value of the tail index parameter beta estimated value of the skewness parameter sigma estimated value of the scale parameter mu estimated value of the location parameter

### Note

Daily price returns of Abbey National shares between 31/7/91 and 8/10/91 (including n=50 business days). By assuming that p_{t} denotes the price at t-th day, the price return at t-th day is defined as (p_{t-1}-p_{t})/p_{t-1}; for t=2,...,n, see Buckle (1995). We note that the EM algorithm is robust with respect to the initial values.

### References

Buckle, D. J. (1995). Bayesian inference for stable distributions, Journal of the American Statistical Association, 90(430), 605-613.

### Examples

# For example, We use the daily price returns of Abbey National shares. Using the initial
# values as alpha_{0}=0.8, beta_{0}=0, sigma_{0}=0.25, and mu_{0}=0.25.
price<-c(296,296,300,302,300,304,303,299,293,294,294,293,295,287,288,297,
305,307,304,303,304,304,309,309,309,307,306,304,300,296,301,298,
295,295,293,292,307,297,294,293,306,303,301,303,308,305,302,301,
297,299)
x<-c()
n<-length(price)
for(i in 2:n){x[i]<-(price[i-1]-price[i])/price[i-1]}
library("stabledist")
ufitstab.skew(x[2:n],0.8,0,0.25,0.25,1)


[Package alphastable version 0.2.1 Index]