Extreme value distribution

Fig. 10.19 The probability density of the extreme value distribution typical of the MSP scores for random sequena The probability that a random variable with this distribution has a score of at least x is given by 1 - exp[-e -where u is the characteristic value and A is the decay constant. The figure shows the probability density function (which corresponds to the function s first derivative) for u = 0 and A = 1.

Plotting data on hazard paper requires less effort, and at the same time, it succeeds in using all of the failures and gives the same information. Hazard papers are shown here for exponential, Weibull, normal, log normal, and extreme value distributions. 

Large segments contain identical residues, the value (the assessment of the statistical significance based on the extreme value distribution) of the alignment is statistically highly significant, the active site is conserved, and so we tentatively classify it as a "probable mitochondrial NUCLEASE."... 

In the detection of repeats using SMART an algorithm is used that derives similarity thresholds that are dependent on the number of repeats already found in a protein sequence (Andrade et al., 1999b). These thresholds are based on the assumption that suboptimal local alignment scores of a profile/HMM against a random sequence database are well described by an extreme value distribution (EVD). The result of this protocol is that acceptance thresholds for suboptimal alignments are lowered below the optimal scores of nonhomologous sequences. 

Fig. 3. Statistical models a Correlation between the product of sets sizes and the mean of the raw score. The fitted function typically corresponds to an equation of the formula = mxn + p with n = 1. b Correlation between the product of sets sizes and the standard deviation of the raw score. The fitted function typically corresponds to an equation of the formula ya=qxr+ s, with 0.6

R.H. Doremus, Fracture statistics A comparison of the normal, Weibull and type I extreme value distributions, J. Appl. Phys. 54, 193-201 (1983). 

A Weibull distribution has the distribution function P y] = exp - exp(- y]]. It is sometimes also called a Gumbel distribution or a type 1 extreme value distribution in standard form. 

The reliability computations for other distributions, such as exponential, lognormal, gamma, Wei-buU, and extreme value distributions, have also been developed (Kapur and Lamberson 1977). In addition, the reliability analysis has been generalized when the stress and strength variables follow a known stochastic process. The references cited in this subsection also contain simple design examples illustrating the use of the probabihstic approach to design. 

Assuming that the underlying distributions of 8 are type I extreme-value-distributed, the probability of observing the rth worker in claimant status j is... 

The climatic actions may often be described by the Extreme value distributions. The characteristic value of a climatic action is defined in Eurocodes as the upper fractile of the probabilistic distribution for the basic time period corresponding to the 2% probabihty of atmual exceeding. The design value of a climatic action is considered as 0,996% fractile of the probabilistic distribution for structures in the reUabUity class RC2. 

However, to describe a time varying process completely it is not sufficient to have either the distribution of the arbitrary point value or the extreme value distribution or even both. The full description of a time varying process requires some additional modeUing with respect to its correlation structure in time. 

The probability distribution of the maximum value (i.e. the largest extreme) is often approximated by one of the asymptotic extreme value distributions. Hence for structures subjected to a single time-varying action, a random process model is replaced by a random variable model and the principles and methods for time invariant models may he apphed. 

Generalized Extreme Value Distribution (GEVD) Functions for Risk Impact... 

To estimate the parameters of the generalized extreme value distribution (GEVD), we use the PWM method, described in detail in Hosking et al. (1985). The PWM method requires moment estimates, which can be... 

What are the pros and cons of using extreme value distributions to model supply chain risks ... 

Hosking, J., J. Wallis, and E. Wood. 1985. Estimation of generalized extreme value distribution by the method of probabiUly weighted moments. Technometrics. 27(3) 251-261. 

When the phenomenon is known only poorly, the collected data may contain some degree of randomness or even reflect beliefs and bias on the part of the collector. To mitigate this problem, analysts may rely on probability, which relates statistical concepts to stochastic variables by mean of large data sets. An example of the use of one statistical and probabilistic method is the use of extreme value distributions applied to cumulative distribution functions to analyze pitting corrosion as performed by Macdonald and colleagues and shown in Figure 3.5. ... 

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