Statistical Inference on Residual Life by Jong-Hyeon Jeong

Author:Jong-Hyeon Jeong
Language: eng
Format: epub
Publisher: Springer New York, New York, NY

which has the first derivative with respect to as

(4.16)

Example 4.2 (Exponential Distribution).

To obtain a closed form of the analytic results, suppose the cause-specific distribution for type 1 events follows an exponential with a rate parameter λ 1, so that the cause-specific hazard and survival function are given by h 1(x, λ 1) = λ 1 and , respectively. Then the score function in (4.16) simplifies to

(4.17)

Setting the score function (4.17) to 0 and solving it for λ 1 gives the maximum likelihood estimator of λ 1 as

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