Abstract:  Firstly, the maximum likelihood estimate and asymptotic confidence interval
of the unkown parameter for the Topp-Leone distribution are obtained under Type-I left
censored samples, furthermore, the asymptotic confidence interval of reliability function
is obtained based on monotonicity. Secondly, under different loss functions, the Bayesian
estimates of the unkown parameter and reliability function are obtained, and the expected
mean square errors of Bayesian estimates are calculated. Monte-Carlo method is used to
calculate the mean values and relative errors of the estimates. Finally, an example of life
data is analyzed by using the statistical method in this paper.

Key words:  Topp-Leone distribution, Type-I left censored samples, Maximum likelihood
estimate, Bayesian estimate