On the left-censored samples from exponential and weibull distribution: Theory and application

Left-censored samples with one or more detection limits are very frequent in many application areas. The normal or log-normal distributions are usually used. However, the interest in statistical analyses of censored data with asymmetric distributions which cannot be easily transformed into symmetric ones (e.g. normal distribution) has increased in many application areas recently. This contribution is focused on type I left-censored samples from exponential and Weibull distribution. The statistical inference is based on the maximum likelihood method and the analytic form of the expected Fisher information matrix is presented. Properties of the unknown parameter estimates are examined using simulations and a special attention is paid to small sample sizes. Various asymptotic tests for comparison of two independent left-censored samples will be presented. Finally, use of the described methods will be demonstrated on real environmental data.