A Pseudo-Pareto Distribution and Concomitants of Its Order Statistics

• Published in: Methodology and computing in applied probability Vol. 18; no. 4; pp. 1043 - 1064
• Main Authors: Gebizlioglu, Omer L., Yörübulut, Serap
• Format: Journal Article
• Language: English
• Published: New York Springer US 01-12-2016; Springer Nature B.V
• Subjects: Bonds; Business and Management; Displays; Economics; Electrical Engineering; Graph theory; Illustrations; Life Sciences; Mathematical analysis; Mathematical models; Mathematics and Statistics; Pareto optimality; Pareto optimum; Probability; Reliability analysis; Risk analysis; Statistics; Studies; Concomitants; 91G70; Hazard function; Pseudo-Pareto distribution; 62H10; Complementing cumulative distribution function; 62E15; Order statistics; Defaultable bonds; 60E05
• ISSN: 1387-5841; 1573-7713
• DOI: 10.1007/s11009-016-9500-0

Pareto distributions are very flexible probability models with various forms and kinds. In this paper, a new bivariate Pseudo-Pareto distribution and its properties are presented and discussed. Main variables, order statistics and concomitants of this distribution are studied and their importance for risk and reliability analysis is explained. Joint and marginal distributions, complementing cumulative distributions and hazard functions of the variables are derived. Numerical illustrations, graphical displays and interpretations for the obtained distributions and derived functions are provided. An implementation example on defaultable bonds is performed.