Parameter Estimation for the Two-Sided BS and IG Distributions

This book considers two independent problems: one in
Statistics and another in Probability Theory. The
statistical problem considered here consists of
classical point estimation and asymptotic analysis.
The probability problem consists of limit theorems
(mainly the weak law of large numbers).

Point estimation based on a new family of the two-
sided Birnbaum-Saunders and inverse Gaussian lifetime
distributions is investigated. The method of moments
of parameters estimation and Asymptotic
statistical properties of the proposed estimators
are developed. A Monte Carlo simulation study
is conducted to appraise the performance of the
proposed strategies for given sample sizes.

Weak laws of large numbers for an array of dependent
random variables satisfying a new notion of uniform
integrability are obtained. The results extend and
sharpen the previously known results in this field.