Question

You are the forecaster responsible for hurricane warnings on the southeast corner of the United States in September. Anyone that has lived in North Carolina for a while knows what is it is like at that time of the year, for example. The cost of issuing a warning like a hurricane involves people taking shelter, business stopping, the areas's economy paused - a moderate cost of C dollars. You also know the preventable loss should a hurricane come and the area be unprepared: property damage, lives lost -an extremely high loss of L dollars. Your weather forecast indicates hurricane with a probability of p.

(a) Should you issue a warning? Use expectations to create a decision rule for whether issuing or not a warning. Explain your rule.
(b) For what kind of extreme weather warnings is the decision more likely to be "do not warn" than "warn"? Explain.

Answer 1

A)

C ≤ LP issue warning

C > LP do not issue warning

B )

For ' do not warm ' the condition will be that C is moderate while L is extremely high

Explanation:

Assuming Y is an indicator that represents if a warning is issued or not

probability of occurrence of Hurricane = p

where; C = cost of issuing a warning

L = cost incurred for not issuing warning

A) Determine if you should issue a warning or not

In this scenario there are about four possible cases

1. 'do not warn' , ' Hurricane did not occur ' : ( 1-y) ( 1-p)
2. ' do not warn ' , ' Hurricane occurred ' : ( 1-y ) p
3. ' warn' , ' Hurricane did not occur' : y ( 1-p)
4. ' warn', ' Hurricane occurred' : y (p)

hence the expected cost ( E ) = L ( 1 - Y )p + Cy

when warning is issued = Y ( 1 )

expected cost ( E ) = C

assuming warning is not issued then Y = 0

hence expected cost ( E ) = LP

Hence the decision rule will be :

C ≤ LP issue warning

C > LP do not issue warning

B) For ' do not warm ' the condition will be that C is moderate while L is extremely high ( as seen in the question ) because this will make C/L to be very small. from the condition C > LP and this simply means that the probability of the Hurricane occurring is very small