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Lui [Five confidence intervals of the closed population size in the capturerecapture problem under inverse sampling with replacement. Biom J. 2004;46:474-480] considered five confidence intervals for the closed population size in a two-sample capture-recapture experiment under inverse sampling with replacement in the recapture phase. The results of his Monte Carlo study indicated that the exact confidence intervals and those based on X²-approximation perform very well. In this paper, we consider three other methods of interval estimation including the bootstrap, likelihood ratio and Jeffreys prior approaches. A Monte Carlo simulation is carried out to evaluate the performance of these intervals together with those based on existing methods in terms of the coverage probability, error rates and standardized average length. Our results show that confidence intervals based on Wald statistics, logarithmic transformation, and bootstrap methods are inappropriate, having coverage probabilities less than the desired nominal level. Also, the exact confidence intervals and those based on X²- approximation are not invariant with respect to the proportion of marked individuals in the capture phase, say p. When p is chosen to be small-tomoderate, the likelihood ratio method is preferred, since it gives confidence intervals with shorter length from among all methods that provide the coverage probability close to the desired nominal level. Overall, the Jeffreys method appears to be more robust than other competitors, providing intervals with nearest coverage probabilities to the desired nominal level and with balanced non-coverage rates. [ABSTRACT FROM AUTHOR]

A generalized version of inverted exponential distribution (IED) is considered in this paper. This lifetime distribution is capable of modeling various shapes of failure rates, and hence various shapes of aging criteria. The model can be considered as another useful two-parameter generalization of the IED. Maximum likelihood and Bayes estimates for two parameters of the generalized inverted exponential distribution (GIED) are obtained on the basis of a progressively type-II censored sample. We also showed the existence, uniqueness and finiteness of the maximum likelihood estimates of the parameters of GIED based on progressively type-II censored data. Bayesian estimates are obtained using squared error loss function. These Bayesian estimates are evaluated by applying the Lindley's approximation method and via importance sampling technique. The importance sampling technique is used to compute the Bayes estimates and the associated credible intervals. We further consider the Bayes prediction problem based on the observed samples, and provide the appropriate predictive intervals. Monte Carlo simulations are performed to compare the performances of the proposed methods and a data set has been analyzed for illustrative purposes. [ABSTRACT FROM PUBLISHER]