The family of continuous distribution laws which factorize in two positive functions, one depending on the variable only and the other one depending on a scalar parameter exclusively, is concerned. The family has no intersection with the Exponential class and includes Uniform distributions over an interval depending upon the parameter as well as infinitely many other distributions arising, for instance, by truncation. Simple sufficient conditions, regarding the support of random variables with distribution included in the family of factorizable densities and suitable to prove completeness are stated. Completeness of statistics based on sample from densities included in the family is also considered.
Mecatti, F., Cattaneo, C. (2005). On the completeness of the family of factorizable densities. STATISTICA & APPLICAZIONI, 3(2), 25-37.
On the completeness of the family of factorizable densities
MECATTI, FULVIA
;
2005
Abstract
The family of continuous distribution laws which factorize in two positive functions, one depending on the variable only and the other one depending on a scalar parameter exclusively, is concerned. The family has no intersection with the Exponential class and includes Uniform distributions over an interval depending upon the parameter as well as infinitely many other distributions arising, for instance, by truncation. Simple sufficient conditions, regarding the support of random variables with distribution included in the family of factorizable densities and suitable to prove completeness are stated. Completeness of statistics based on sample from densities included in the family is also considered.
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