A new class of bivariate lifetime distributions

ABSTRACT

This paper introduces a new class of bivariate lifetime distributions. Let {X_i}_{i ⩾ 1} and {Y_i}_{i ⩾ 1} be two independent sequences of independent and identically distributed positive valued random variables. Define T₁ = min (X₁, …, X_M) and T₂ = min (Y₁, …, Y_N), where (M, N) has a discrete bivariate phase-type distribution, independent of {X_i}_{i ⩾ 1} and {Y_i}_{i ⩾ 1}. The joint survival function of (T₁, T₂) is studied.

KEYWORDS:

• Bivariate geometric distribution
• bivariate phase-type distributions
• survival function.

MATHEMATICS SUBJECT CLASSIFICATION:

• 60E05
• 62E15
• 62E17

Acknowledgment

The author thanks the anonymous referees for their helpful comments and suggestions, which were useful in improving the paper.