This study extends the joint estimation of revealed and stated preference data literature by accounting for truncation in the revealed preference data. The analytical model and estimation procedure are used to estimate the value of recreational red snapper fishing in the Gulf of Mexico. This recreational red snapper valuation is decomposed into its direct and indirect components. As expected, the value of recreational red snapper fishing using the joint revealed-stated preference model proposed in this analysis is bracketed on the upper limit by the value obtained using the contingent valuation method and on the lower limit by the travel cost method. The results also indicate that the joint model improves the precision of estimated recreational red snapper valuation.

A saddlepoint approximation is derived for the cumulative distribution function of the sample mean of n independent bivariate random vectors. The derivations use Lugannani and Rice's saddlepoint formula and the standard bivariated normal distribution function. The separate versions of the approximation for the discrete cases are also given. A Monte Carlo study shows that the new approximation is very accurate.

Suppose given an absolutely continuous distribution on the plane, and points Pi, · · ·, Pj, Πt, · · ·, Πk chosen independently according to the given distribution. Denoting by Gj the convex hull of {Pi, · · ·, Pj}, and by Γk the convex hull of (Πt, · · ·, Πk}, and writing pjk for the probability that Gj and Γk are disjoint, certain properties of the array {pjk; j, k = 1,2, · · ·} are established, including a recurrence generating the array in terms of {p1n; n = 1,2, · · ·}, and asymptotic results for {pnn; n = 1,2, · · ·}. Some examples are considered.