ufitstab.sym.mix {alphastable}

ufitstab.sym.mix

Description

estimates the parameters of a k-component mixture of symmetric stable distributions, Teimouri et al. (2018) <doi.org/10.1080/03610918.2017.1288244>. Having k and given the vector of initial values of entire parameter space, it uses some type of the EM algorithm (ECME) to estimate the parameters of mixture of symmetric stable distributions.

Usage

ufitstab.sym.mix(yy, k, omega0, alpha0, sigma0, mu0)

Arguments

yy

vector of observations

k

number of components

omega0

vector of initial values for weights

alpha0

vector of initial values for tail indices

sigma0

vector of initial values for scale parameters

mu0

vector of initial values for location parameters

Value

omega-bar

a k-component vector of estimated values for the weight vector

alpha-bar

a k-component vector of estimated values for the tail index vector

sigma-bar

a k-component vector of estimated values for the scale vector

mu-bar

a k-component vector of estimated values for the location vector

membership

a k by n matrix whose entries are 1 and 0; for i-th row, if j-th column is one; then i-th observation belongs to the j-th component

Note

The set of data, used here, is the velocities of 82 distant galaxies, diverging from our own galaxy, called here galaxy. These data are available at https://people.maths.bris.ac.uk/mapjg/mixdata. We note that ufitstab.sym.mix() is robust with respect to the initial values.

Author(s)

Mahdi Teimouri, Adel Mohammadpour, and Saralees Nadarajah

References

Teimouri, M., Rezakhah, S., and Mohammadpour, A. (2018). EM algorithm for symmetric stable mixture model, Communications in Statistics-Simulation and Computation, 47(2), 582-604.

Examples

# In what follows, we apply the EM algorithm to estimate the parameters of the
# mixture of symmetric stable distributions. For this, the initial values for
# fitting a three-component mixture of symmetric stable distribution to the
# galaxy data are: (0.1,0.35,0.55) for weight vector, (1.2,1.2,1.2) for tail
# index vector, (1,1,1) for scale vector, and (8,20,22) for the location vector.
galaxy<-c(9.172,9.350,9.483,9.558,9.775,10.227,10.406,16.084,16.170,18.419,
          18.552,18.600,18.927,19.052,19.070,19.330,19.343,19.349,19.440,
          19.473,19.529,19.541,19.547,19.663,19.846,19.856,19.863,19.914,
          19.918,19.973,19.989,20.166,20.175,20.179,20.196,20.215,20.221,
          20.415,20.629,20.795,20.821,20.846,20.875,20.986,21.137,21.492,
          21.701,21.814,21.921,21.960,22.185,22.209,22.242,22.249,22.314,
          22.374,22.495,22.746,22.747,22.888,22.914,23.206,23.241,23.263,
          23.484,23.538,23.542,23.666,23.706,23.711,24.129,24.285,24.289,
          24.366,24.717,24.990,25.633,26.960,26.995,32.065,32.789,34.279)
library("stabledist")
ufitstab.sym.mix(galaxy,3,c(0.1,0.35,0.55),c(1.2,1.2,1.2),c(1,1,1),c(8,20,22))