### Abstract

There are few studies on the mixture of discrete distributions, where most of the studies introduced a mixture of negative binomial, Poisson and binomial distributions. Recently, a sequence of studies on the mixture discrete distributions were published, but still very few. This paper introduced the new idea of mixture of discrete Weibull models. These models can be obtained by combining two or more discrete Weibull distributions using a mixing parameter. These models contain five or more parameters because each discrete Weibull contains two shape parameters q and β where 0<q<1 and β>0 and a mixing parameter w>0. In this paper, the distribution function, hazard (failure rate) function and second failure rate, called pseudo -hazard function of the mixture of discrete Weibull distribution were found using different values for the shape parameters and the mixing parameters. The distribution functions, hazard (failure rate) functions and pseudo- hazard functions were plotted depending on the data tables. It was found that the hazard (failure rate) functions and the pseudo-hazard functions can be increasing, decreasing or constant depending on the value of the shape parameter β, similar to the continuous Weibull distribution. Different values of the mixing parameter and the shape parameter were considered.

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

Pages (from-to) | 580-586 |

Number of pages | 7 |

Journal | Australian Journal of Basic and Applied Sciences |

Volume | 5 |

Issue number | 3 |

Publication status | Published - Mar 2011 |

### Fingerprint

### Keywords

- Discrete weibull
- Hazard
- Mixture weibull
- Pseudo-hazard

### ASJC Scopus subject areas

- General

### Cite this

*Australian Journal of Basic and Applied Sciences*,

*5*(3), 580-586.

**Mixture of discrete weibull model.** / Al-Wakeel, A. A.; Razali, Ahmad Mahir.

Research output: Contribution to journal › Article

*Australian Journal of Basic and Applied Sciences*, vol. 5, no. 3, pp. 580-586.

}

TY - JOUR

T1 - Mixture of discrete weibull model

AU - Al-Wakeel, A. A.

AU - Razali, Ahmad Mahir

PY - 2011/3

Y1 - 2011/3

N2 - There are few studies on the mixture of discrete distributions, where most of the studies introduced a mixture of negative binomial, Poisson and binomial distributions. Recently, a sequence of studies on the mixture discrete distributions were published, but still very few. This paper introduced the new idea of mixture of discrete Weibull models. These models can be obtained by combining two or more discrete Weibull distributions using a mixing parameter. These models contain five or more parameters because each discrete Weibull contains two shape parameters q and β where 00 and a mixing parameter w>0. In this paper, the distribution function, hazard (failure rate) function and second failure rate, called pseudo -hazard function of the mixture of discrete Weibull distribution were found using different values for the shape parameters and the mixing parameters. The distribution functions, hazard (failure rate) functions and pseudo- hazard functions were plotted depending on the data tables. It was found that the hazard (failure rate) functions and the pseudo-hazard functions can be increasing, decreasing or constant depending on the value of the shape parameter β, similar to the continuous Weibull distribution. Different values of the mixing parameter and the shape parameter were considered.

AB - There are few studies on the mixture of discrete distributions, where most of the studies introduced a mixture of negative binomial, Poisson and binomial distributions. Recently, a sequence of studies on the mixture discrete distributions were published, but still very few. This paper introduced the new idea of mixture of discrete Weibull models. These models can be obtained by combining two or more discrete Weibull distributions using a mixing parameter. These models contain five or more parameters because each discrete Weibull contains two shape parameters q and β where 00 and a mixing parameter w>0. In this paper, the distribution function, hazard (failure rate) function and second failure rate, called pseudo -hazard function of the mixture of discrete Weibull distribution were found using different values for the shape parameters and the mixing parameters. The distribution functions, hazard (failure rate) functions and pseudo- hazard functions were plotted depending on the data tables. It was found that the hazard (failure rate) functions and the pseudo-hazard functions can be increasing, decreasing or constant depending on the value of the shape parameter β, similar to the continuous Weibull distribution. Different values of the mixing parameter and the shape parameter were considered.

KW - Discrete weibull

KW - Hazard

KW - Mixture weibull

KW - Pseudo-hazard

UR - http://www.scopus.com/inward/record.url?scp=79955125567&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=79955125567&partnerID=8YFLogxK

M3 - Article

VL - 5

SP - 580

EP - 586

JO - Australian Journal of Basic and Applied Sciences

JF - Australian Journal of Basic and Applied Sciences

SN - 1991-8178

IS - 3

ER -