Estimasi Distribusi Mixing dalam Model Mixture Poisson

N Dwidayati

Abstract


Model mixture telah dikenalkan sejak tahun 1986 (Farewell, 1986) dengan menganalisis penderita kanker payudara. Model ini diaplikasikan dalam ruang kerja yang berbeda sesuai dengan fleksibilitas pandangan kompleksnya situasi, walaupun generalisasi teori belum sepenuhnya dikembangkan. Studi klinik yang dilakukan difokuskan pada estimasi proporsi pasien yang sembuh dan distribusi failure time pasien yang tidak sembuh. Pada penelitian ini dikonstruksi estimator konsisten dari distribusi mixing dalam model mixture Poisson melalui inversi Laplace, baik untuk data tak tersensor maunpun tersensor. Berdasar estimasi tersebut ditentukan IMSE dan laju kekonvergenan yang berkorespondensi dengan inverse estimator.

The mixture model has been introduced since 1986 (Farewell, 1986) by analyzing breast cancer patients. This model was applied in different workspaces according to the flexibility of the complex view of the situation, although the generalization of the theory has not been fully developed. Clinical studies undertaken focused on estimating the proportion of patients who recovered and the distribution of patient failure times that did not heal. In this research constructed a consistent estimator of the mixing distribution in the Poisson mixture model through Laplace inversion, both for uncensored and uncensored data. Based on these estimates, the IMSE and the convergence rate correspond to the inverse estimator.


Keywords


mixing distribution. Poisson mixture model, Laplace inversion, IMSE, convergence

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References


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