Characterization of distributions through failure rate and mean residual life functions

2010 ◽  
Vol 80 (9-10) ◽  
pp. 752-755 ◽  
Author(s):  
Asok K. Nanda
Keyword(s):  
Failure Rate ◽  
Residual Life ◽  
Mean Residual Life ◽  
Characterization Of Distributions

The hazard and vitality measures of ageing

1989 ◽  
Vol 26 (03) ◽  
pp. 532-542 ◽  
Author(s):  
Joseph Kupka ◽  
Sonny Loo
Keyword(s):  
Sudden Death ◽  
Failure Rate ◽  
Residual Life ◽  
Ageing Process ◽  
Mean Residual Life ◽  
Absolutely Continuous ◽  
Intrinsic Interest ◽  
Increasing Failure Rate ◽  
Time Period ◽  
The Relationship

A new measure of the ageing process called the vitality measure is introduced. It measures the ‘vitality' of a time period in terms of the increase in average lifespan which results from surviving that time period. Apart from intrinsic interest, the vitality measure clarifies the relationship between the familiar properties of increasing hazard and decreasing mean residual life. The main theorem asserts that increasing hazard is equivalent to the requirement that mean residual life decreases faster than vitality. It is also shown for general (i.e. not necessarily absolutely continuous) distributions that the properties of increasing hazard, increasing failure rate, and increasing probability of ‘sudden death' are all equivalent.

Shock models leading to increasing failure rate and decreasing mean residual life survival

1982 ◽  
Vol 19 (01) ◽  
pp. 158-166 ◽  
Author(s):  
Malay Ghosh ◽  
Nader Ebrahimi
Keyword(s):  
Poisson Process ◽  
Failure Rate ◽  
Residual Life ◽  
Mean Residual Life ◽  
Increasing Failure Rate ◽  
Shock Models

Shock models leading to various univariate and bivariate increasing failure rate (IFR) and decreasing mean residual life (DMRL) distributions are discussed. For proving the IFR properties, shocks are not necessarily assumed to be governed by a Poisson process.

On a characterization of gamma distributions via exponential mixtures

1980 ◽  
Vol 17 (02) ◽  
pp. 574-576
Author(s):  
Manish C. Bhattacharjee
Keyword(s):  
General Result ◽  
Residual Life ◽  
Infinite Divisibility ◽  
Mean Residual Life ◽  
Gamma Distributions ◽  
Mixing Distributions

A new and simpler proof of Morrison's result that within exponential mixtures only IFR gamma mixing produces linearly increasing mean residual life functions is given. A parallel and new characterization of the DFR gamma laws follows as a consequence. The method of proof used suggests a general result on the infinite divisibility of the mixing distributions in exponential mixtures.

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