Please use this identifier to cite or link to this item: http://hdl.handle.net/10397/21223
Title: Determination of embedded distributions
Authors: Shao, Q
Ip, WC
Wong, H 
Keywords: Δ- discriminant
Burr type III distribution
Burr type XII distribution
Embedded model problem
Gamma distribution
Inverse Gaussian distribution
Left-censored observations
Lognormal distribution
Pareto distribution
Right-censored observations
Weibull distribution
Issue Date: 2004
Publisher: Elsevier Science Bv
Source: Computational statistics and data analysis, 2004, v. 46, no. 2, p. 317-334 How to cite?
Journal: Computational Statistics and Data Analysis 
Abstract: Maximum likelihood estimates may not exist for some distributions. One way to deal with this problem is to derive the so-called embedded distributions. In computer programming, it is important to know whether or not the maximum likelihood estimates for the original distribution exists, that is, whether or not an embedded distribution occurs. This paper provides a criterion for this purpose. The criterion, which we term the "Δ-discriminant", is derived by evaluating the difference of the log-likelihood functions between the original distribution and the corresponding embedded distribution around the point of the maximum likelihood estimates for the embedded distribution. As applications, we provide the Δ-discriminants for some commonly used distributions in the presence of both left-censored and right-censored observations. Some published data sets are used to illustrate our results. Crown
URI: http://hdl.handle.net/10397/21223
ISSN: 0167-9473
DOI: 10.1016/S0167-9473(03)00171-3
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