## Abstract

Let X_{(1)} ≤ … ≤ X_{(n)} be the order statistics of a sample of size n from the left truncated k-parameter exponential family of distributions with unknown truncation parameter. The densities of this family are of the form f(x:θ,γ_{1}) = a(x) exp{θ «u(x) }/b (θ,γ_{1}), c < γ_{1} < x < d, θ = (θ_{1},…,θ_{k}), u(x) = (u_{1}(x),…, U_{k}(x)). Let Z = (Z_{1},…, Z_{k}) where and g_{n} be a vector valued function. The existence of a statistic of the form Z* = Z - g_{n}(X_{(1)} with distribution independent of X_{(1)} and depending on θ is characterized. The case k=l is shown to be of particular interest and an application in this case to uniformly most powerful unbiased tests is presented. Right and two-sided truncation models are also discussed.

Original language | English |
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Pages (from-to) | 2161-2172 |

Number of pages | 12 |

Journal | Communications in Statistics - Theory and Methods |

Volume | 13 |

Issue number | 17 |

DOIs | |

State | Published - 1 Jan 1984 |

## Keywords

- Truncated exponential family
- uniformly most powerful unbiased tests

## ASJC Scopus subject areas

- Statistics and Probability