Unexpected Extra Expense Calculation for Each 1-Year Period

Exponential Decay Function

y=A * e^(c*x)

Loss in Period

Cumulative frequency for each of 500 LuckLand households in 50 years

Area under the curve from 0 to 1 =

Average loss above a threshold B

Integral of y from 0 to 1

= 1/c * ( B - A - B*ln(B/A) )

= A * 1/c * e^(c) - A * 1/c *e^0

= A/c * ( e^(c) - 1)

Average Loss Above B =

Area under the curve from 0.55 to 1 =

= A/C *( (e^c - e^(0.55*c) )

In each year, 45% of the households have expenses less than a dollar (truncated to $0).

Area under the curve from 0.2 to 0.55 =

= A/C *( (e^(0.55*c) - e^(0.2*c) )

"In another 35% of the households, extra expenses are less than $733 and the average is $104.57."

Area under the curve from 0.1 to 0.2 =

= A/C *( (e^(0.2*c) - e^(0.1*c) )

"In another 10% of the households, the average expense is $2,340.39."

Area under the curve from 0 to 0.10 =

= A/C *( (e^(0.1*c) - 1) )

"But in the last 10% of the households, the average extra expense is $17,293.29."

"And over 50 years, each household is likely to have at least

one extra expense of $27,000 to $40,000."

Integrals

http://en.wikipedia.org/wiki/List_of_integrals_of_exponential_functions