Left-Censored Samples from Skewed Distributions: Statistical Inference and Applications

Abstract

Left‑censored data occur frequently in many areas. At present, researchers pay attention to skewed censored distributions more frequently. This paper deals with statistical inference of type I multiply left‑censored Weibull and exponential distributions. It suggests a computational procedure for calculation of maximum likelihood estimates of the parameters. The expected Fisher information matrix for estimation of variances of estimated parameters is introduced. The estimates are then used for construction of confidence intervals for the expectation using the maximum likelihood method. Asymptotic tests for comparison of distributions (expectations respectively) of two independent left‑censored Weibull samples are proposed. Furthermore, asymptotic tests for assessing suitability of reduction of the Weibull distribution to the exponential distribution are introduced. Finally, the left‑censored exponential distribution is briefly described. Methods derived in this paper are illustrated on elemental carbon measurements, and can be applied in analysis of real environmental and/or chemical data.