Saddlepoint Approximation for Bivariate Cumulative Distribution Function

We identify the expression for the variable that was not defined in Wang (1990) to approximate the bivariate distributions.

Application

Construct confidence interval by inverting joint distribution of the estimators (MSPBB).

Method

Wang (1990) derived the saddlepoint approximation for bivariate distributions using the saddlepoint approximation for distribution (Lugannani & Rice, 1980) and standard bivariate normal distribution. We used complex analysis to derive the expression for the variable that was not defined in Wang (1990) to approximate the bivariate distributions.

Software

  • PhD dissertation Chapter I, section 1.3 supplement.

Paper

  • PhD dissertation Chapter I, section 1.3.