On some properties of equilibrium distributions of order n

In the present paper we derive some identities connecting the failure rate functions and moments of residual life of the nth order equilibrium distribution and the baseline distribution. These identities are used to characterize the generalized Pareto model, mixture of exponentials and gamma distribution by relationships between various reliability characteristics. An approach using the characteristic functions is also discussed with illustrations.

[1]  Jorge Navarro,et al.  How to obtain bathtub-shaped failure rate models from normal mixtures , 2004 .

[2]  N. L. Johnson,et al.  Continuous Univariate Distributions. , 1995 .

[3]  DISTRIBUTIONAL CHARACTERIZATIONS THROUGH SCALING RELATIONS , 2007 .

[4]  Ramesh C. Gupta,et al.  The role of weighted distributions in stochastic modeling , 1990 .

[5]  A. Pakes.  Length Biasing and Laws Equivalent to the Log-Normal , 1996 .

[7]  B. Abraham,et al.  On characterizing mixtures of some life distributions , 2001 .

[8]  Properties of moments for s-order equilibrium distributions , 1996 .

[9]  A. Pakes,et al.  Characterizations using weighted distributions , 2003 .

[10]  M. R. Mahmoud,et al.  On Characterizations of a Mixture of Exponential Distributions , 1985, IEEE Transactions on Reliability.

[11]  Harshinder Singh,et al.  Aspects of positive ageing , 1986 .

[12]  C. Chatfield.  Continuous Univariate Distributions, Vol. 1 , 1995 .

[13]  Ramesh C. Gupta,et al.  ROLE OF EQUILIBRIUM DISTRIBUTION IN RELIABILITY STUDIES , 2007, Probability in the Engineering and Informational Sciences.

[14]  On the characterization of survival distributions in reliability by properties of their renewal densities , 1979 .

[15]  Adriana Hornikova,et al.  Stochastic Ageing and Dependence for Reliability , 2007, Technometrics.

[16]  F. Pellerey,et al.  New partial orderings and applications , 1993 .

[17]  N. Nair,et al.  Characterization of discrete models by distribution based on their partial sums , 1989 .

[18]  J. Navarro,et al.  Characterizations from Relationships Between Failure Rate Functions and Conditional Moments , 2004 .