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+ Combining Random Variables
+ Combining Random Variables

Coupling for τ-dependent sequences and applications
Coupling for τ-dependent sequences and applications

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... When α = 2 we have w0α−1 = 1, w1α−1 = −1, and wkα−1 = 0 for k > 1, so that (1.4) reduces to the classical condition (1.3), i.e., the one-sided first derivative. In either case (α = 2 or 1 < α < 2), the boundary term enforces a no-flux condition at the point y = 0 in the state space. The connection bet ...
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... • emerging of new challenges associated with massive highly dimensional data far exceeding traditional assumptions on which traditional methods of statistics have been based. In this introduction we give two examples that illustrate the power of modern computers and computing software both in analys ...
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... reduced (Kendall et al. 1997, Bailey et al. 2004b). Further, the presence of non-random (e.g., Markovian) temporary emigration can substantially bias estimates of capture probability and survival (Kendall and Nichols 1995). Recent decades have seen rapid advances in the statistical analysis of mark- ...
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... (Ist arrival to Ist counter, 2nd arrival to 2nd counter, , mth to mth , (m +1)st arrival to Ist counter, ), then the new subqueues form Erlang-m processes. Interestingly, we can also derive the key Poisson properties (15-5) and (15-25) by starting from a simple axiomatic approach as shown below: ...
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... P (X1 = k)/P (X1 > k) → 0 as k → ∞. Eisenberg, Stengle and Strang (1993) go beyond the study of ρn and also discuss the distribution of Wn ; Brands, Steutel and Wilms (1994) and Kirschenhofer and Prodinger (1996) obtained rates of convergence in the geometric case. For the asymptotics of the maximum ...
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... randomization and replication. But in environmental and ecological work, observations also fall in the non experimental, non- replicated, and nonrandom categories. The problems of model specification and data interpretation then acquire special importance and great concern. The theory of weighted dis ...
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Probability

Probability is the measure of the likeliness that an event will occur. Probability is quantified as a number between 0 and 1 (where 0 indicates impossibility and 1 indicates certainty). The higher the probability of an event, the more certain we are that the event will occur. A simple example is the toss of a fair (unbiased) coin. Since the two outcomes are equally probable, the probability of ""heads"" equals the probability of ""tails"", so the probability is 1/2 (or 50%) chance of either ""heads"" or ""tails"".These concepts have been given an axiomatic mathematical formalization in probability theory (see probability axioms), which is used widely in such areas of study as mathematics, statistics, finance, gambling, science (in particular physics), artificial intelligence/machine learning, computer science, game theory, and philosophy to, for example, draw inferences about the expected frequency of events. Probability theory is also used to describe the underlying mechanics and regularities of complex systems.
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