THE RISK OF EXTREME EVENTS   

 9.  MISUSING STATISTICS

             This is a vast subject that could easily occupy an entire semester.  
             For our purposes in this class, it is important to understand that
             data distributions  and data variability  affect the interpretation of
             representative values.

             Common Data Distributions:  uniform, normal, and skewed

             Common Representative Values:  mean, median, and mode

A.  INTRODUCTION

        Extreme events are here defined as the occurrences of destructive
        geologic phenomena such as earthquakes, volcanic eruptions, and
        floods.   Obviously, the ability to predict such events is important to
        humans who live in areas that are prone to such disasters.

        Unfortunately, geologic processes always involve some degree of random
        randomness  and so cannot be predicted with absolute certainty.  
        Instead, forecasts are made based on the probability  that an event
        will occur within a given time period.                        

B.  IMPORTANT CONCEPTS

        1.  RANDOMNESS

             In this context, random events are those that occur
             without any specific pattern to their sequence through
             time (e.g., the sequence of numbers rolled using dice).  

             Another way of thinking about randomness is that the
             probability of a truly random event occurring does not  
             in any way depend on what occurred previously.  This
             is true when rolling dice: the probability of rolling a six
             on any given roll does not depend on what number was 
             rolled previously.  Note that a truly random event has a
             uniform probability distribution.  

        2.  RECURRENCE INTERVALS

              Recurrence intervals are the average  time period
              between events of the same magnitude, usually
              expressed in terms of years.

        3.  MAGNITUDE AND FREQUENCY

             The greater the magnitude of an event, the larger
              is its recurrence interval.

C.  QUANTIFYING RISKS

         1.  RANDOM EVENTS

              a.  One Year Risks

                   The probability that a random event will occur during 
                   any given one year  depends only on the recurrence 
                   interval of that event (in years):

                   Risk or Probability  =   1 / (Recurrence Interval)

              b.  Cumulative Risks 

                   The probability that a random event will occur during
                   any given time period  depends upon the time period of
                   interest and the recurrence interval of that event (in yrs):

                   Risk or Probability  =  1 - [1 - (1 / R.I.)]ⁿ

          2.  NON-RANDOM EVENTS 

               The probability of non-random events can be also be
               calculated using other statistical methods if (and only
               if) their frequency distributions are known. 

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