Monotonic Estimators for the Survival Function of Quality Adjusted Lifetime

ABSTRACT

The simple weighted estimator of the survival function of quality adjusted lifetime is a consistent estimator and a proper survival function. It is considerably less efficient than many estimators that are not monotonic and therefore are not proper survival functions. The non monotonic estimators can be modified to be monotonic, but additional work is required to determine the effect of the modification on their consistency and efficiency. As a prelude to the main results, we introduce a new non monotonic estimator and study the positive and negative mass jump points of three estimators. This article proposes several classes of monotonic estimators for the survival function of quality adjusted life. All proposed estimators are shown to be consistent. Two proposed estimators are nearly as efficient as their non monotonic counterparts, when the sample size is large.

Keywords:

• Consistency
• Linear programming
• Quality Adjusted Lifetime
• Survival Function

Mathematics Subject Classification:

• Primary 62N01
• Secondary 62N02

Notes

*Source: Almanassra (2003), Table 4.5.

The columns MSIM, MZHAO, MWANG, MMZHAO, MMWANG are the MSE of the SW-estimator, ZT-estimator, W-estimator, MZT-estimator, and MW-estimator, respectively. Each entry comes from 1000 simulations.

* Source: Almanassra (2003), Table 4.6.

The columns BSIM, BZHAO, BWANG, BMZHAO, BMWANG are the biases of the SW-estimator, ZT-estimator, W-estimator, MZT-estimator, and MW-estimator, respectively. Each entry comes from 1000 simulations.

*Source: Almanassra (2003), Table 4.11.

The columns MSIM, MZHAO, MWANG, MMZHAO, MMWANG are the MSE of the SW-estimator, ZT-estimator, W-estimator, MZT-estimator, and MW-estimator, respectively. Each entry comes from 1000 simulations.

*Source: Almanassra (2003), Table 4.12.

The columns BSIM, BZHAO, BWANG, BMZHAO, BMWANG are the biases of the SW-estimator, ZT-estimator, W-estimator, MZT-estimator, and MW-estimator, respectively. Each entry comes from 1000 simulations with sample size 50.

*Source: Almanassra (2003), Table 2.5.

*Source: Almanassra (2003), Table 2.6.