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.

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