## Abstract

This paper deals with parameter estimations when a sample is drawn from a population having a minimum-type distribution function (DF) G(x) = 1 - π^{n} _{i=1} (1 - F_{i}(x,θ_{i})), We propose a simple method to estimate one of the parameters of θ_{i}. The sample size s is randomly subdivided into m equal subsamples, (each subsample of size k); the minimal value τ_{q} is found in each subsample and the estimator θ= Σ^{m} _{q=1} τ_{q}/m is used. It turns out that under certain conditions concerning only the behavior of F_{1} (x,θ_{1}) near x = 0, θ is an asymptotically unbiased (as k → ∞) and consistent (as s/k → ∞) estimator of only one unknown parameter, for example θ_{1}. A numerical example based on simulation of 200 samples with s = 24, 48, 96 is considered for F_{1}(x,θ_{1}) - the exponential function and F_{2}- the Weibull DF. The results of our method are summarized in Tables I-IV from which we deduce the characters of our estimator. We tried to improve our estimator θ_{1} by jackknifing, and show the improvement in a numerical example.

Original language | English |
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Pages (from-to) | 439-462 |

Number of pages | 24 |

Journal | Communications in Statistics - Theory and Methods |

Volume | 10 |

Issue number | 5 |

DOIs | |

State | Published - 1 Jan 1981 |

## Keywords

- Weibull distri-
- bution
- exponential distribution
- jackknifing
- minimum-type Scheme