## Abstract

This paper deals with parameter estimation for a minimum-type distribution function - G(x) = 1 - exp[- x/θ_{1} - θ_{2} x^{α}]. A ^{2}Two modifications of the least-squares method (LSM) proposed by Bain and Antle are investigated and compared by means of the Monte Carlo study. The first one is an estimation of θ_{1}, θ_{2}, a by solving the set of three equations defining the stationary point of the sum of squares. It is shown that the solution reduces to solving only one equation for the parameter a. It is demonstrated that there is a rather high probability of not obtaining a solution in the parameter space Ω = {θ_{1} >0, θ_{2} > 0, α>0\}. The performance of LSM can be improved considerably when only two parameters - θ_{2} and α - are unknown. We investigate this using an independent method for obtaining an estimate for θ_{1}.

Original language | English |
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Pages (from-to) | 463-487 |

Number of pages | 25 |

Journal | Communications in Statistics - Theory and Methods |

Volume | 10 |

Issue number | 5 |

DOIs | |

State | Published - 1 Jan 1981 |

## Keywords

- Weibull distribution
- estimators
- exponential distribution
- least souare
- minimum-tune Scheme

## ASJC Scopus subject areas

- Statistics and Probability