When only a small sample is available, it is well known that the empirical distribution contains scarce information about the shape of the hazard function as well as about the far-right tail of the “parent” probability density. So, the probabilistic analysis of the mechanisms that lead to the involved random variable can be a decisive factor to identify the appropriate distribution model. In this context, three recurrent degradation mechanisms (“simple degradation”, “stress-strength”, and “latent-defensive-attempts”) which lead exactly to the inverse Weibull survival time are identified and mathematically formulated. They are derived as first passage time distributions. Then, the proposed mechanism approach, applied to the proper identification of this relatively unknown survival model, is illustrated by means of two real world examples.

GENERATIVE MECHANISMS OF A SURVIVAL TIME: THE CASE OF THE INVERSE WEIBULL MODEL / Erto, Pasquale; Lepore, Antonio; Palumbo, Biagio. - In: JOURNAL OF STATISTICS: ADVANCES IN THEORY AND APPLICATIONS. - ISSN 0975-1262. - 15:2(2016), pp. 113-130. [http://dx.doi.org/10.18642/jsata_7100121675]

### GENERATIVE MECHANISMS OF A SURVIVAL TIME: THE CASE OF THE INVERSE WEIBULL MODEL

#### Abstract

When only a small sample is available, it is well known that the empirical distribution contains scarce information about the shape of the hazard function as well as about the far-right tail of the “parent” probability density. So, the probabilistic analysis of the mechanisms that lead to the involved random variable can be a decisive factor to identify the appropriate distribution model. In this context, three recurrent degradation mechanisms (“simple degradation”, “stress-strength”, and “latent-defensive-attempts”) which lead exactly to the inverse Weibull survival time are identified and mathematically formulated. They are derived as first passage time distributions. Then, the proposed mechanism approach, applied to the proper identification of this relatively unknown survival model, is illustrated by means of two real world examples.
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2016
GENERATIVE MECHANISMS OF A SURVIVAL TIME: THE CASE OF THE INVERSE WEIBULL MODEL / Erto, Pasquale; Lepore, Antonio; Palumbo, Biagio. - In: JOURNAL OF STATISTICS: ADVANCES IN THEORY AND APPLICATIONS. - ISSN 0975-1262. - 15:2(2016), pp. 113-130. [http://dx.doi.org/10.18642/jsata_7100121675]
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Utilizza questo identificativo per citare o creare un link a questo documento: `https://hdl.handle.net/11588/636070`
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