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Thus, the mean time between peaks, including the residence time or mean time before the very first peak, is the inverse of the frequency of exceedance N −1 (y max). If the number of peaks exceeding y max grows as a Poisson process, then the probability that at time t there has not yet been any peak exceeding y max is e −N(y max)t. [6] Its ...
An estimate of the uncertainty in the first and second case can be obtained with the binomial probability distribution using for example the probability of exceedance Pe (i.e. the chance that the event X is larger than a reference value Xr of X) and the probability of non-exceedance Pn (i.e. the chance that the event X is smaller than or equal ...
The theoretical return period between occurrences is the inverse of the average frequency of occurrence. For example, a 10-year flood has a 1/10 = 0.1 or 10% chance of being exceeded in any one year and a 50-year flood has a 0.02 or 2% chance of being exceeded in any one year.
The bPOE is the probability of a tail with known mean value . The figure shows the bPOE at threshold x {\displaystyle x} (marked in red) as the blue shaded area. Therefore, by definition, bPOE is equal to one minus the confidence level at which the Conditional Value at Risk (CVaR) is equal to x {\displaystyle x} .
Template documentation. Use one of the following depending on the transcluding article. ... {Probability distributions|discrete-finite}} {{Probability distributions ...
Some maps released by the USGS are shown with peak ground acceleration with a 10% probability of exceedance in 50 years, measured in Metre per second squared.For parts of the US, the National Seismic Hazard Mapping Project in 2008 resulted in seismic hazard maps showing peak acceleration (as a percentage of gravity) with a 2% probability of exceedance in 50 years.
Cumulative distribution function for the exponential distribution Cumulative distribution function for the normal distribution. In probability theory and statistics, the cumulative distribution function (CDF) of a real-valued random variable, or just distribution function of , evaluated at , is the probability that will take a value less than or equal to .
Probability of precipitation (PoP) is a commonly used term referring to the likelihood of precipitation falling in a particular area over a defined period of time, which is commonly a day, half day, or hour. The PoP measure is meaningless unless it is associated with an interval of time.