Interval Estimation from the Likelihood Function

Summary During the last few years, several authors have devoted attention to both old and new methods of making inferences from likelihood functions. In this paper we study the properties of interval estimates which are obtained by drawing a horizontal line across the graph of the likelihood function. An exact evaluation is reported for one case of positive and one of negative binomial sampling, with parameter θ. The attained confidence coefficient α(θ) is graphed over 0 ⩽ θ ⩽ 1 for these two cases. A brief look is taken at intervals obtained when the random variable is continuous.