Μελέτη της βαθμίδας αποτυχίας για μείξεις κατανομών πιθανότητας
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Keywords
Βαθμίδα αποτυχίας ; Μείξεις κατανομών ; Μονοτονία ; IFR ; DFRAbstract
The failure rate is a fundamental tool in reliability theory and lifetime analysis, as it
describes the instantaneous risk of failure of a system that has survived up to a specific
point in time. This dissertation studies the behaviour of the failure rate for distribution
mixtures, which are used to model heterogeneous populations. Initially, the main properties
of the Exponential, Gamma, Erlang, Weibull and Pareto distributions are presented, together
with the monotonicity of their corresponding failure rates.
The study then examines whether the properties of the individual distributions are
preserved when they are combined into a mixture. The analysis shows that the failure rate
of a mixture may exhibit a different and more complex behaviour than the failure rates
of its components. In particular, a mixture of distributions with increasing failure rates
may have a decreasing or non-monotonic failure rate. Moreover, its initial and asymptotic
behaviour is influenced by the mixture weights, the distribution parameters and the tail
behaviour of the components. The theoretical results are illustrated through numerical
examples and graphical representations, highlighting the important role of heterogeneity
in the overall behaviour of distribution mixtures.
Postgraduate Studies Programme
Εφαρμοσμένη ΣτατιστικήDepartment
Σχολή Χρηματοοικονομικής και Στατιστικής. Τμήμα Στατιστικής και Ασφαλιστικής ΕπιστήμηςNumber of pages
118Language
GreekCollections
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Αναφορά Δημιουργού-Μη Εμπορική Χρήση-Όχι Παράγωγα Έργα 3.0 Ελλάδα
Αναφορά Δημιουργού-Μη Εμπορική Χρήση-Όχι Παράγωγα Έργα 3.0 Ελλάδα