Negative multinomial distribution: Difference between revisions

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The '''Rohn Emergency Scale'''<ref name="RohnBlackmore">Rohn, Eli and Blackmore, Denis (2009) [http://www.igi-global.com/bookstore/Article.aspx?TitleId=37523 A Unified Localizable Emergency Events Scale], ''International Journal of Information Systems for Crisis Response Management'' (IJISCRAM), Volume 1, Issue 4, October 2009</ref> is a [[scale (social sciences)|scale]] on which the magnitude (intensity)<ref>{{cite web | url = http://www.fema.gov/kids/intense.htm | title = FEMA Intensity Scales | accessdate = 13 September 2010 }}</ref> of an [[emergency]] is measured. It was first proposed in 2006, and explained in more detail in a [[Peer review|peer-reviewed]] paper presented at a 2007 system sciences conference.<ref>Gomez, Elizabeth, Plotnick, Linda , Rohn, Eli, Morgan, John, and Turoff, Murray (2007). [http://www.computer.org/portal/web/csdl/doi/10.1109/HICSS.2007.557 Towards a Unified Public Safety Scale], Hawaii International Conference on System Sciences (HICSS), Waikoloa, Hawaii.</ref> The idea was further refined later that year.<ref>{{cite journal | last1 = Plotnick | first1 = Linda | last2 = Gomez | first2 = Elizabeth | last3 = White | first3 = Connie | last4 = Turoff | first4 = Murray | year = 2007 | id = {{citeseerx|10.1.1.103.5779}} | title = Furthering Development of a Unified Emergency Scale Using Thurstone’s Law of Comparative Judgment: A Progress Report | journal = ISCRAM | date = May 2007 }}</ref> The need for such a scale was ratified in two later independent publications.<ref>Turoff Murray and Hiltz Roxanne (2008). [http://iospress.metapress.com/index/N72872K8Q4712T76.pdf Assessing the health information needs of the emergency preparedness and management community]. ''Inf. Serv. Use'' 28, 3-4 (Aug. 2008), 269-280.</ref><ref>Turoff, M., White, C., Plotnick, L., and Hiltz, S. R., [http://www.iscram.org/dmdocuments/ISCRAM2008/papers/ISCRAM2008_Turoff_etal.pdf Dynamic Emergency Response Management for Large Scale Decision Making in Extreme Events], ''Proceedings of ISCRAM 2008'', Washington D.C. May.</ref> It is the first scale that [[Quantification|quantifies]] any emergency situation based on a [[mathematical model]]. The scale can be tailored for use at any geographic level – city, county, state or continent. It can be used to monitor the development of an ongoing emergency event, as well as forecast the probability and nature of a potential developing emergency and in the planning and execution of a [[National Response Plan]].
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== Existing emergency-related scales ==
Scales relating to natural phenomena that may result in an emergency are numerous. This section provides a review of several notable emergency related scales. They concentrate mainly on weather and environmental scales that provide a common understanding and lexicon with which to understand the level of intensity and impact of a crisis.  Some scales are used before and/or during a crisis to predict the potential intensity and impact of an event and provide an understanding that is useful for preventative and recovery measures.  Other scales are used for post-event classification. Most of these scales are descriptive rather than quantitative, which makes them subjective and ambiguous.
: 1805 [[Beaufort Scale]]<ref>{{cite web | title = The Beaufort Wind Scale | publisher = National Oceanic and Atmospheric Administration, Storm Prediction Center | accessdate = 13 September 2010 | url = http://www.spc.noaa.gov/faq/tornado/beaufort.html }}</ref>
: 1931 [[Modified Mercalli Intensity Scale]]<ref>{{cite web | title = Modified Mercalli Intensity Scale | publisher = U.S. Geological Survey, Earthquake Hazards Program | accessdate = 13 September 2010 | url = http://earthquake.usgs.gov/learn/topics/mercalli.php }}</ref>
: 1935 [[Richter Scale]]<ref>{{cite web | title = The Richter Magnitude Scale | publisher = U.S. Geological Survey, Earthquake Hazards Program | accessdate = 13 September 2010 | url = http://earthquake.usgs.gov/learn/topics/richter.php }}</ref>
: 1969 [[Saffir-Simpson Hurricane Scale]]<ref>{{cite web | title = The Saffir-Simpson Hurricane Wind Scale | publisher = National U.S. Oceanic and Atmospheric Administration - National Hurricane Center | accessdate = 13 September 2010 | url = http://www.nhc.noaa.gov/aboutsshws.shtml }}</ref>
: 1971 [[Fujita scale]]<ref>{{cite web | title = Fujita Tornado Damage Scale | publisher = National Oceanic and Atmospheric Administration | accessdate = 13 September 2010 | url = http://www.spc.noaa.gov/faq/tornado/f-scale.html }}</ref> (superseded by [[Enhanced Fujita Scale]] in 2007<ref>{{cite web | url = http://www.spc.noaa.gov/efscale/ | title = The Enhanced Fujita Scale (EF Scale)  | publisher = National Oceanic and Atmospheric Administration }}</ref>)
: 1982 [[Volcanic explosivity index]]
: 1990 [[International Nuclear Event Scale]]<ref>[http://www.iaea.org/Publications/Factsheets/English/ines.pdf IAEA fact sheet]</ref>
: 1999 [[Air Quality Index]]<ref>{{cite web | title = Air-Quality Index | publisher = The U.S. EPA, NOAA and NPS AIRnow Project | accessdate = 13 September 2010 | url = http://www.airnow.gov }}</ref>
 
== Variables common to all emergencies ==
According to the Rohn Emergency Scale, all emergencies can be described by three independent dimensions:
(a) scope;
(b) topographical change (or lack thereof); and
(c) speed of change.
The intersection of the three dimensions provides a detailed scale for defining any emergency,<ref name="RohnBlackmore"/> as depicted on the Emergency Scale Website.<ref>{{cite web | url = http://www.emergencyscale.com/ | title = The Emergency Scale Website | accessdate = 8 March 2011 }}</ref>
 
=== Scope ===
The scope of an emergency in the Rohn scale is represented as a [[continuous variable]] with a lower limit of zero and a theoretical calculable upper limit. The Rohn Emergency Scale use two parameters that form the scope: percent of affected humans out of the entire population, and damages, or loss, as a percentile of a given [[Gross National Product]] (GNP). Where applied to a specific locality, this parameter may be represented by a [[Gross State Product]], [[Gross Regional Product]], or any similar measure of economic activity appropriate to the entity under emergency.
 
=== Topography ===
A topographical change means a measurable and noticeable change in land characteristics, in terms of elevation, slope, orientation, and land coverage. These could be either natural (e.g., trees) or artificial (e.g., houses).
Non-topographical emergencies are situations where the emergency is non-physical in nature.  The [[Wall Street Crash of 1929|collapse of the New York stock market in 1929]] is such an example, and the [[Financial crisis (2007–present)|global liquidity crisis of August 2007]]<ref>{{cite web | url = http://money.cnn.com/2007/08/10/markets/markets_0315/index.htm | title = CNN Money (2007) | accessdate = 13 September 2010 }}</ref> is another example.
The model treats topographical change as a continuum ranging between 0 and 1 that gives the estimated visual fractional change in the environment.
 
=== Speed of change ===
An emergency is typified by a departure from normal state of affairs. The scale uses the change of the number of victims over time and economical losses over time to calculate a rate of change that is of utmost importance to society (e.g., life and a proxy for quality of life).
 
== Emergency scale mathematical model ==
{{refimprove section|talk=talk|date=March 2011}}
The scale is a normalized function whose variables are scope (''S''), topography (''T''), and rate of change (''D''), expressed as
:<math>E = Emergency = f(S,T,D)</math>.
These parameters are defined as follows:
 
=== Scope ===
:<math>\hbox{Scope}=\tfrac{\hbox{RawScope}}{\hbox{MaxScope}}</math>
:where
:<math>\hbox{RawScope}=\left(\tfrac{\hbox{Victims}}{\hbox{Population}} + \tfrac{\hbox{Monetary Losses}}{\hbox{GNP}}\right)^W</math>
:where
:<math>W=\left( \tfrac{\ln(\hbox{Victims})}{\ln(\hbox{Monetary Losses})} \right)^\beta</math>
:''β'' is a coefficient which the model creator calculated to be 1.26 ± 0.03,
:and
:<math>\hbox{MaxScope}=\left(\tfrac{0.7*\hbox{Population}}{\hbox{Population}} + \tfrac{0.5*\hbox{GNP}}{\hbox{GNP}}\right)^V</math>,
:where
:<math>V= \tfrac{\ln(\hbox{Victims})}{\ln(\hbox{Monetary Losses})}</math>
 
The model loosely assumes that a society whose majority of the population (70% in this model) is affected and half of its GNP is drained as a result of a calamity reaches a breaking point of disintegration. Sociologists and economists may come up with a better estimate.
 
=== Topographical change ===
:<math>\tfrac{\hbox{Volume before the event}}{\hbox{Volume after the event}}</math> or zero for non-topographical events.
 
=== Rate of change ===
:<math>\tfrac {d(\hbox{Victims})}{d(\hbox{Time})}</math> and <math>\tfrac {d(\hbox{Losses})}{d(\hbox{Time})}</math>
comprise the rate of change that is of utmost importance to society and therefore incorporated in the model.
 
== Simplified scale for public communications ==
In some instances, it may be preferable to have an integral scale to more simply and dramatically convey the extent of an emergency, with a range, say, from 1 to 10, and 10 representing the direst emergency. This can be obtained from the function above in any number of ways. One of them is the [[ceiling function]]{{clarify|reason=should this perhaps be "maximum"?|date=March 2011}}. Another one is a single number representing the volume under the 3D emergency scale.
 
== References ==
{{reflist|2}}
 
== External links ==
{{Wiktionary|disaster}}
* {{cite web | url = http://memagazine.asme.org/web/LargeScale_Disasters.cfm | title = Large-Scale Disasters as Dynamical Systems | publisher = [[ASME]] }} (provides an alternative measure of general disaster scaling)
 
{{Use dmy dates|date=September 2010}}
 
[[Category:Emergency management]]

Latest revision as of 03:06, 16 October 2014

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