Title
The bivariate probability distributions with periodic failure rate via hyperbolic differential equation
Document Type
Article
Publication Date
3-1-1999
Publication Title
Dynamics of Continuous, Discrete and Impulsive Systems 5; Series A: Mathematical Analysis
Abstract
The bivariate random vectors with almost lack of memory property is a new area of investigation in applied studies. It has been shown that they possess a periodic (with respect to both arguments) failure rate, and have a specific form for its probability distribution. We discuss the question how complete a periodic bivariate failure rate function will characterize this class of probability distributions. It is shown that bivariate failure rates (positive functions with integrable square on the first quadrant) and marginal distributions along the coordinate axes uniquely determine a two-dimensional random vector under some minimal restrictions. More details are given for the case of periodic bivariate failure rates. It is proven that the latter characterize bivariate distributions with almost lack of memory property. As a special case, the bivariate exponential distribution with constant failure rate is discussed. Some possible applications are briefly comment. components is derived.
First Page
81
Last Page
92
ISSN
1201-3390
Rights
© 1999 Watam Press
Recommended Citation
Dimitrov, Boyan N.; Chukova, Stefanka; and Green, David Jr., "The bivariate probability distributions with periodic failure rate via hyperbolic differential equation" (1999). Mathematics Publications. 47.
https://digitalcommons.kettering.edu/mathematics_facultypubs/47