### Abstract

Normal mixture distribution (NM) is arguably the most important mixture models, and also the most challenging technically. It has been successfully applied in many fields where the application is still expending. In this paper, we provide a tutorial exposition on expectation–maximization (EM) algorithm and Gibbs sampler for parameter estimation of unconditional finite Normal mixture distribution. Both methods are extremely useful for solving difficult computation problems especially in Normal mixture distribution case. Practical issues that arise in the use of EM algorithm and Gibb sampler are discussed, as well as variants of algorithm and programming that help to deal with these challenges. The purpose of this paper is to provide a good conceptual explanation of the statistical estimation methods with illustrative example so the reader can have a grasp of some of the basic principles and techniques.

Original language | English |
---|---|

Pages (from-to) | 3687-3701 |

Number of pages | 15 |

Journal | Global Journal of Pure and Applied Mathematics |

Volume | 11 |

Issue number | 5 |

Publication status | Published - 2015 |

### Fingerprint

### Keywords

- EM algorithm
- Gibbs sampler
- Normal mixture distribution

### ASJC Scopus subject areas

- Mathematics(all)
- Applied Mathematics

### Cite this

*Global Journal of Pure and Applied Mathematics*,

*11*(5), 3687-3701.

**Statistical estimation methods for unconditional finite normal mixture distribution.** / Kamaruzzaman, Zetty Ain; Isa, Zaidi.

Research output: Contribution to journal › Article

*Global Journal of Pure and Applied Mathematics*, vol. 11, no. 5, pp. 3687-3701.

}

TY - JOUR

T1 - Statistical estimation methods for unconditional finite normal mixture distribution

AU - Kamaruzzaman, Zetty Ain

AU - Isa, Zaidi

PY - 2015

Y1 - 2015

N2 - Normal mixture distribution (NM) is arguably the most important mixture models, and also the most challenging technically. It has been successfully applied in many fields where the application is still expending. In this paper, we provide a tutorial exposition on expectation–maximization (EM) algorithm and Gibbs sampler for parameter estimation of unconditional finite Normal mixture distribution. Both methods are extremely useful for solving difficult computation problems especially in Normal mixture distribution case. Practical issues that arise in the use of EM algorithm and Gibb sampler are discussed, as well as variants of algorithm and programming that help to deal with these challenges. The purpose of this paper is to provide a good conceptual explanation of the statistical estimation methods with illustrative example so the reader can have a grasp of some of the basic principles and techniques.

AB - Normal mixture distribution (NM) is arguably the most important mixture models, and also the most challenging technically. It has been successfully applied in many fields where the application is still expending. In this paper, we provide a tutorial exposition on expectation–maximization (EM) algorithm and Gibbs sampler for parameter estimation of unconditional finite Normal mixture distribution. Both methods are extremely useful for solving difficult computation problems especially in Normal mixture distribution case. Practical issues that arise in the use of EM algorithm and Gibb sampler are discussed, as well as variants of algorithm and programming that help to deal with these challenges. The purpose of this paper is to provide a good conceptual explanation of the statistical estimation methods with illustrative example so the reader can have a grasp of some of the basic principles and techniques.

KW - EM algorithm

KW - Gibbs sampler

KW - Normal mixture distribution

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UR - http://www.scopus.com/inward/citedby.url?scp=84946085950&partnerID=8YFLogxK

M3 - Article

VL - 11

SP - 3687

EP - 3701

JO - Global Journal of Pure and Applied Mathematics

JF - Global Journal of Pure and Applied Mathematics

SN - 0973-1768

IS - 5

ER -