Estimation of parameters of the Gompertz distribution using the least ...

146 J.-W. Wu et al. / Appl. Math. Comput. 158 (2004) 133–147
than ML estimates in c ¼ 2:0, k ¼ 0:01; (e) for m ¼ 10, n ¼ 30, the estimates
obtained by Method 1, Methods 5–7 and Methods 9–11 are better than ML
estimates in c ¼ 2:0, k ¼ 0:02; (f) for m ¼ 30, n ¼ 10, the performance of
UWLS and WLS estimates is better than ML estimates in c ¼ 0:1, k ¼ 0:01 and
c ¼ 0:01, k ¼ 0:02, respectively; (g) for m ¼ 30, n ¼ 10, the UWLS estimates
obtained by Method 3 and the WLS estimates obtained by Method 7 and
Method 9 are better than ML estimates in c ¼ 0:01, 0.1, 2.0, k ¼ 0:01; (h) for
m ¼ 30, n ¼ 30, the WLS estimates obtained by Method 8 are better than ML
estimates in c ¼ 0:01, 0.1, 2.0, k ¼ 0:01; (i) for m ¼ 30, n ¼ 30, generally the
UWLS and WLS estimates are better than ML estimates in c ¼ 0:01, k ¼ 0:01;
(j) for m ¼ 30, n ¼ 30, the WLS estimates obtained by Methods 6–10 are better
than ML estimates in c ¼ 2:0, k ¼ 0:01 and (k) for m ¼ 30, n ¼ 30, the WLS
estimates obtained by Methods 6–9 are better than ML estimates in c ¼ 0:1,
2.0, k ¼ 0:02. In addition, from the above results, it is suggested that Method 9
is useful for estimating c and k under the first failured-censored data.
4. Concluding remarks
In summary, least squares methods often provide simple and fairly effective
ways of obtaining estimates with complete data and the first failured-censored
data. The procedures described were based on transform of F ðxÞ, which is the
Gompertz cumulative distribution function. Results from simulation studies
illustrate the performance of the WLS estimates is acceptable.
Acknowledgement
This research was partially supported by the National Science Council,
ROC (Plan No. NSC 89-2118-M-032-013).
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