Noriaki Setô

Uniformly Minimum Variance Unbiased Estimation for the Inverse Gaussian Distribution

Abstract For the inverse Gaussian distribution, we prove a general result concerning the expectation of a certain class of functions of the complete sufficient statistics. Uniformly minimum variance unbiased estimators of the rth cumulant and of several other parametric functions are obtained as special cases. The variance of the estimator for the case r = 2 is also given.

Umvu estimators of the mode and limits of an interval for the inverse gaussian distribution

For a random variable obeying the inverse Gaussian distribu-tion and its reciprocal, the uniformly minimum variance unbiased (UMVU) estimators of each mode are obtained. The UMVU estimators of the left and right limits of a certain interval which contains an inverse Gaussian variate with an arbitrary given probability are also proposed.

Scalar-Scalar Ladder Model in the Unequal-Mass Case. II : Numerical Studies of the BS Amplitudes

The Bethe-Salpeter amplitudes of the bound states formed by two scalar particles with unequal masses are analyzed in the massive scalar particle exchange ladder model. The norms of the amplitudes are calculated numerically, and it is confirmed that the norm vanishes for the bound state corresponding to the complex eigenvalue of the coupling constant. The behaviour of the Bethe-Salpeter amplitudes in the momentum space is also investigated.

On the Structure of the Continuous Spectra in the Spinor-Spinor Bethe-Salpeter Equation

The Bethe-Salpeter equation for a bound state of a fermion-anti fermion system is analyzed in the ladder approximation of a massless vector particle exchange. For the bound state mass between zero and the threshold, all the continuous spectra of the coupling strength are obtained explicitly. The thresholds of the continuous spectra do not depend on the mass of the bound state, and exhibit the O( 4) symmetry even at the nonvanishing total four-momentum. Besides the positive continuous spectra of Goldstein type, there exist negative ones extending to minus infinity.

Scalar-Scalar Ladder Model in the Unequal-Mass Case. III Numerical Studies of the P-Wave Case

The eigenvalue problem for the p-wave bound states formed with two unequal-mass scalar particles through massive scalar particle exchange is analyzed numerically in the framework of the Bethe-Salpeter ladder model. As in the s-wave case, the eigenvalues of the coupling constant are found to become complex for some mass configurations in some range of the bound state mass. The Bethe-Salpeter amplitudes of the low-lying bound states are also investigated.