Journal ArticleDOI
A class of new probability distributions for modelling environmental evolution with periodic behaviour
Boyan N. Dimitrov,Z. Khalil +1 more
TLDR
In this paper, a new class of probability distributions is introduced, which accentuates the periodic behaviour of environmental conditions in time and the random occurrence of some events on each period, following the logic of the appearance of random events in the evolution of real-world systems.Abstract:
A new class of probability distributions is introduced. This class accentuates the periodic behaviour of environmental conditions in time and the random occurrence of some events on each period. A constructive approach is used following the logic of the appearance of random events in the evolution of real-world systems. Some physical and probabilistic properties of the new distributions are discussed. Elementary statistical data models are considered and two types of estimations of the attributes of these distributions are offered. Numerical and graphical illustrations with simulated and observed data are used to motivate our suggestions.read more
Citations
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Probability distributions in periodic random environment and their applications
TL;DR: Periodic random environments and mechanisms of their effect on imbedded random variables are discussed, and nonstationary Poisson processes with periodic failure rates appear to be the closest extension of the homogeneous Poisson process to model the number of events imbedding into random environment of p...
Journal ArticleDOI
Sensitivity of extreme events to climate change: The case of autocorrelated time series
Richard W. Katz,Barbara G. Brown +1 more
TL;DR: In this paper, the hazard rate for the maximum of a finite sequence of autocorrelated random variables is determined by means of simulations, and the results imply that the relative sensitivity of extreme events to overall climate change is even greater than the asymptotic theory would predict.
Journal ArticleDOI
Periodic Poisson Processes and Almost-lack-of-memory Distributions
TL;DR: In this paper, a method for verifying the hypothesis on the membership of a sample to the class of almost-lack-of-memory (ALM) distributions is developed.
Journal ArticleDOI
Modeling uncertainty in periodic random environment: applications to environmental studies
TL;DR: It is shown that varying effects are modeled by extended in time Poisson trials with periodically changed components, and with periodicity with a driving non-stationary components, relevant to environmental studies and with constant periodicity in additive models.
On Statistical Hypothesis Testing Via Simulation Method
TL;DR: This paper shows how the present day fast computer could solve non-standard old statistical problems, and proposes a general simulation approach for using this method, which is first used in [3] for a specific case of almost lack of memory distributions.
References
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Journal ArticleDOI
Statistical inference: Some theoretical methods and directions
Donald Fraser,Nancy Reid +1 more
TL;DR: In this article, the authors examine four core methods and principles of statistical inference and discuss implications among them, leading to the consideration of some recent methods of obtaining distributions for inference concerning an interest parameter, free of nuisance parameters.