ufitstab.sym.mix {alphastable} | R Documentation |

## 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 |

`alpha-bar` |
a |

`sigma-bar` |
a |

`mu-bar` |
a |

`membership` |
a |

### 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))
```

*alphastable*version 0.2.1 Index]