Estimation of the Poisson Parameter from Truncated Samples and from Censored Samples

Abstract Maximum likelihood estimators of the Poisson parameter applicable to both truncated and censored samples are derived in this paper. Singly and doubly truncated samples as well as singly and doubly censored samples are considered. The estimators obtained are presented in simple algebraic forms and their application to practical problems with the aid of standard Poisson tables is illustrated with numerical examples. Asymptotic variances of estimates for the different cases considered are obtained from second derivatives of the likelihood functions and are simplified to forms which permit ready evaluation. * Preliminary report presented before American Mathematical Society, Auburn, Alabama, November 23, 1951. Abstract published in Bulletin of the American Mathematical Society, 58 (1952), 60