This paper gives maximum likelihood estimators of parameters of truncated and censored exponential distributions, asymptotic variances of the estimators, and asymptotic confidence intervals for the parameters. Applications to bombing accuracy studies and to life testing are pointed out. As regards bombing accuracy the parameter estimated is the reciprocal of the variance in a normal bivariate distribution having circular symmetry. The reciprocal is estimated because there is no maximum likelihood estimator of the variance and any estimator of the variance is badly biased (see Section 2). Results of a synthetic sampling experiment are given to provide information on rapidity of convergence of the distributions of the estimators to their asymptotic distributions.
Walter L. Deemer Jr. David F. Votaw Jr. "Estimation of Parameters of Truncated or Censored Exponential Distributions." Ann. Math. Statist. 26 (3) 498 - 504, September, 1955. https://doi.org/10.1214/aoms/1177728494