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Dragon King

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Dragon King - Produktinformation

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However, when calling DKs outliers there is an important proviso: In standard statistics outliers are typically erroneous values and are discarded, or statistical methods are chosen that are somehow insensitive to outliers.

Contrarily, DKs are outliers that are highly informative, and should be the focus of much statistical attention. Thus a first step is identifying DKs in historical data.

Existing tests are either based on the asymptotic properties of the empirical distribution function EDF [13] or on an assumption about the underlying cumulative distribution function CDF of the data.

It turns out that testing for outliers relative to an exponential distribution is very general. The latter follows from the Pickands—Balkema—de Haan theorem of extreme value theory which states that a wide range of distributions asymptotically above high thresholds have exponential or power law tails.

As an aside, this is one explanation why power law tails are so common when studying extremes. To finish the point, since the natural logarithm of a power law tail is exponential, one can take the logarithm of power law data and then test for outliers relative to an exponential tail.

There are many test statistics and techniques for testing for outliers in an exponential sample. An inward test sequentially tests the largest point, then the second largest, and so on, until the first test that is not rejected i.

The number of rejected tests identifies the number of outliers. At each step the p-value for the test statistic must be computed and, if lower than some level, the test rejected.

This test has many desirable properties: It does not require that the number of outliers be specified, it is not prone to under masking and over swamping estimation of the number outliers, it is easy to implement, and the test is independent of the value of the parameter of the exponential tail.

Some examples of where dragon kings have been detected as outliers include: [7] [13]. How one models and predicts dragon kings depends on the underlying mechanism.

However, the common approach will require continuous monitoring of the focal system and comparing measurements with a non-linear or complex dynamic model.

It has been proposed that the more homogeneous the system, and the stronger its interactions, the more predictable it will be.

For instance, in non-linear systems with phase transitions at a critical point, it is well known that a window of predictability occurs in the neighborhood of the critical point due to precursory signs: the system recovers more slowly from perturbations, autocorrelation changes, variance increases, spatial coherence increases, etc.

For the phenomena of unsustainable growth e. In systems that are discrete scale invariant such a model is power law growth, decorated with a log-periodic function.

This has been applied to many problems, [3] for instance: rupture in materials, [24] [28] earthquakes, [29] and the growth and burst of bubbles in financial markets [12] [30] [31] [32] [33].

An interesting dynamic to consider, that may reveal the development of a block-buster success, is epidemic phenomena : e. Given a model and data, one can obtain a statistical model estimate.

This model estimate can then be used to compute interesting quantities such as the conditional probability of the occurrence of a dragon king event in a future time interval, and the most probable occurrence time.

When doing statistical modeling of extremes, and using complex or nonlinear dynamic models, there is bound to be substantial uncertainty.

Thus, one should be diligent in uncertainty quantification: not only considering the randomness present in the fitted stochastic model, but also the uncertainty of its estimated parameters e.

One can then use the estimated probabilities and their associated uncertainties to inform decisions. In the simplest case, one performs a binary classification : predicting that a dragon king will occur in a future interval if its probability of occurrence is high enough, with sufficient certainty.

For instance, one may take a specific action if a dragon king is predicted to occur. For instance, if the cost of a miss is very large relative to the cost of a false alarm, the optimal decision will detect dragon kings more frequently than they occur.

One should also study the true positive rate of the prediction. The smaller this value is, the weaker the test, and the closer one is to black swan territory.

In practice the selection of the optimal decision, and the computation of its properties must be done by cross validation with historical data if available , or on simulated data if one knows how to simulate the dragon kings.

In a dynamic setting the dataset will grow over time, and the model estimate, and its estimated probabilities will evolve. In this dynamic setting, the test will likely be weak most of the time e.

Dragon kings form special kinds of events leading to extreme risks which can also be opportunities. That extreme risks are important should be self-evident.

Natural disasters provide many examples e. In general such statistics arrive in the presence of heavy-tailed distributions , and the presence of dragon kings will augment the already oversized impact of extreme events.

Despite the importance of extreme events, due to ignorance, misaligned incentives, and cognitive biases, there is often a failure to adequately anticipate them.

Technically speaking, this leads to poorly specified models where distributions that are not heavy-tailed enough, and under-appreciate both serial and multivariate dependence of extreme events.

Some examples of such failures in risk assessment include the use of Gaussian models in finance Black—Scholes , the Gaussian copula, LTCM , the use of Gaussian processes and linear wave theory failing to predict the occurrence of rogue waves , the failure of economic models in general to predict the financial crisis of — , and the under-appreciation of external events, cascades, and nonlinear effects in probabilistic risk assessment , leading to not anticipating the Fukushima Daiichi nuclear disaster in Such high impact failures emphasize the importance of the study of extremes.

The dragon king concept raises many questions about how one can deal with risk. Of course, if possible, exposure to large risks should be avoided often referred to as the "black swan approach".

However, in many developments, exposure to risk is a necessity, and a trade-off between risk and return needs to be navigated.

In an adaptive system, where prediction of dragon kings is successful, one can act to defend the system or even profit. How to design such resilient systems , as well as their real time risk monitoring systems, [39] is an important and interdisciplinary problem where dragon kings must be considered.

On another note, when it comes to the quantification of risk in a given system whether it be a bank, an insurance company, a dike, a bridge, or a socio-economic system , risk needs to be accounted for over a period, such as annually.

Typically one is interested in statistics such as the annual probability of loss or damage in excess of some value value at risk , other tail risk measures , and return periods.

To provide such risk characterizations, the dynamic dragon kings must be reasoned about in terms of annual frequency and severity statistics.

These frequency and severity statistics can then be brought together in a model such as a compound Poisson process.

If not, one may only construct scenarios. However, in any case, given the uncertainty present, a range of scenarios should be considered.

Due to the shortage of data for extreme events, the principle of parsimony , and theoretical results from extreme value theory about universal tail models, one typically relies on a generalized Pareto distribution GPD tail model.

However such a model excludes DKs. Thus, when one has sufficient reason to believe that DKs are present, or if one simply wants to consider a scenario, one may e.

From Wikipedia, the free encyclopedia. Redirected from Dragon King Theory. Event that is both extremely large in impact and of unique origins.

Sornette, Predictability of catastrophic events: material rupture, earthquakes, turbulence, financial crashes and human birth, Proc.

Extreme events in nature and society. A simple test for deviations from the power law". Carlson , and James S. B1 : — Bibcode : PhyA..

Miltenberger, and C. Nonlinear dynamics and chaos: with applications to physics, biology, chemistry, and engineering.

The Dragon King survived until modern times and moved to the United States , living in the small town of Blue Valley , Nebraska , with his daughter Cindy Burman, who herself became the supervillain Shiv.

They went up against the war criminal with the help of Pat's old teammate the Shining Knight. Sir Justin was on the quest to find the missing Holy Grail.

It was revealed that the Dragon King was responsible for the death of Firebrand all those years ago. He died during the battle, though the body was never located.

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