Likelihood-Weighted Confidence Intervals for the Difference of Two Binomial Proportions

Two new methods for computing confidence intervals for the difference δ = p₁ — p₂ between two binomial proportions (p₁, p₂) are proposed. Both the Mid-P and Max-P likelihood weighted intervals are constructed by mapping the tail probabilities from the two-dimensional (p₁, p₂)-space into a one-dimensional function of δ based on the likelihood weights. This procedure may be regarded as a natural extension of the CLOPPER-PEARSON (1934) interval to the two-sample case where the weighted tail probability is α/2 at each end on the δ scale. The probability computation is based on the exact distribution rather than a large sample approximation. Extensive computation was carried out to evaluate the coverage probability and expected width of the likelihood-weighted intervals, and of several other methods. The likelihood-weighted intervals compare very favorably with the standard asymptotic interval and with intervals proposed by HAUCK and ANDERSON (1986), COX and SNELL (1989), SANTNER and SNELL (1980), SANTNER and YAMAGAMI (1993), and PESKUN (1993). In particular, the Mid-P likelihood-weighted interval provides a good balance between accurate coverage probability and short interval width in both small and large samples. The Mid-P interval is also comparable to COE and TAMHANE'S (1993) interval, which has the best performance in small samples.     

Parameter estimates from mark-recapture experiments on two populations subject to migration and death

A model is developed for a triple catch marking experiment on two areas with migration between the two areas and death or emigration occurring. Estimates of the parameters of the model are derived. Some of these estimates are shown to be suitable even under certain restrictions on migration (e.g. animals may be restricted to a single transfer in the course of the experiment). Variances of the estimates were not derived but some rules were developed, based on computer simulations, to guide the experimenter in planning experiments and in judging the precision of his estimates.     

Bivariate Modified Power Series Distribution Some Properties,Estimation and Applications

The class of bivariate modified power series probability distribution (BMPSD) has been defined by P(X = x, Y=y) =a(x, y) (g(?₁ ?₂))^x (h(?₁, ?₂))^xwhere a(x,y) is a sub-set of the Cartesian product of the set of non-negative integers and g(?₁, ?₂), h(?₁ ?₂) and f(?₁, (?₁, ?₂) are positive finite and successively differentiable functions of ?₁and ?₂. It includes a very large number of well known probability distributions. The recurrence relations for central moments and factorial moments have been determined. Also, the M.L. estimators for ?₁ and ?₂ and their asymptotic biases and variances are obtained. Some important properties are discussed. The results of an BMPSD have been applied to derive the corresponding results for the bivariate generalized negative bino-mial distribution and the bivariate Lagrangian Poisson distribution.