Ghosh, J. K. ; Roy, K. K.
(1972)
*Families of densities with non-constant carriers which have finite dimensional sufficient statistics*
Sankhya Series A, 34
.
pp. 205-226.
ISSN 0581-572X

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Official URL: http://sankhya.isical.ac.in/search/34a3/34a3026.ht...

## Abstract

Let X_{1},X_{2},....,X_{n} be independently and identically distributed random variables with common density function f_{θ}(x). Let the carrier X_{θ} = {x: f_{θ}(x) > 0} of the density f_{θ} (x) be an open interval (a(θ), b(θ)). If a(θ), b(θ) are continuous and monotonic in opposite sense and if there is a continuous real-valued statistic which is sufficient for the given family of densities for a sample of size n ≥ 2, then we prove f_{θ}(x) has the following form f_{θ}(x) = g(θ).h(x). In our second theorem we have the same conclusion where a(θ), b(θ) are constinuous and monotonic in the same sense and there is a continuous statistic taking values in R^{2}, which is sufficient for a sample of size n ≥ 3. In the last section we investigate cases when a(θ), b(θ) are monotonic and the sufficient statistic is k-dimensional, k ≥ 2.

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ID Code: | 22663 |

Deposited On: | 24 Nov 2010 08:03 |

Last Modified: | 02 Jun 2011 07:27 |

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