Furthermore, the coefficient of variation , which is the ratio of the standard deviation to the mean,
is
n
n n
⋅
⋅
=
⋅
σ
μ
σ
μ
. This is smaller than
σ
μ
, the coefficient of variation for each individual X i .
5
The coefficient of variation is useful for comparing variability between positive distributions with
different expected values. So, given n independent policyholders, as n becomes very large, the
insurer’s risk, as measured by the coefficient of variation, tends to zero.
Furthermore, the coefficient of variation , which is the ratio of the standard deviation to the mean,isnn n⋅⋅=⋅σμσμ. This is smaller thanσμ, the coefficient of variation for each individual X i .5The coefficient of variation is useful for comparing variability between positive distributions withdifferent expected values. So, given n independent policyholders, as n becomes very large, theinsurer’s risk, as measured by the coefficient of variation, tends to zero.
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