ON DISCRIMINANT ANALYSIS ASSOCIATED WITH GOMPERTZ DISTRIBUTIONS
Sabreen Gad EL-Hak Ali Ramadan;
Abstract
In Chapter I, some basic concepts of discriminant analysis, generalized likelihood ratio test and the bootstrap method for estimation are introduced. Gompertz distribution and its properties are also introduced. A short review ofliterature is given.
In Chapter II, the identifiability of finite mixtures of Gompertz distributions is proved. A procedure is presented for finding maximum likelihood estimates of the four parameters of a mixture of two Gompertz distributions, using classified and unclassified observations. A nonlinear discriminant function is derived from a mixture of two Gompertz distributions. Based on small sample size, estimation of a nonlinear discriminant function is considered. Throughout simulation experiments, the performance -of the corresponding estimated nonlinear discriminant function is investigated.
In Chapter III, the Bayes estimates of the errors of misclassification corresponding to the nonlinear discriminant function derived from a mixture of two Gompertz populations are obtained. Since the mixture is not unimodal, Lindley's (1980) approximation is used as a suitable approximation •in this case. A comparison between Bayes and maximum likelihood estimates is performed via a Monte Carlo simulation.
In Chapter II, the identifiability of finite mixtures of Gompertz distributions is proved. A procedure is presented for finding maximum likelihood estimates of the four parameters of a mixture of two Gompertz distributions, using classified and unclassified observations. A nonlinear discriminant function is derived from a mixture of two Gompertz distributions. Based on small sample size, estimation of a nonlinear discriminant function is considered. Throughout simulation experiments, the performance -of the corresponding estimated nonlinear discriminant function is investigated.
In Chapter III, the Bayes estimates of the errors of misclassification corresponding to the nonlinear discriminant function derived from a mixture of two Gompertz populations are obtained. Since the mixture is not unimodal, Lindley's (1980) approximation is used as a suitable approximation •in this case. A comparison between Bayes and maximum likelihood estimates is performed via a Monte Carlo simulation.
Other data
| Title | ON DISCRIMINANT ANALYSIS ASSOCIATED WITH GOMPERTZ DISTRIBUTIONS | Other Titles | تحليل التمييز المرتبط بتوزيعات جومبرتز | Authors | Sabreen Gad EL-Hak Ali Ramadan | Issue Date | 2004 |
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