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I am given that the amount of loss has a two-point mixture cdf, (55% and 45% weightage) which both follow a Gamma distribution. An insurance imposes an ordinary deductible of d and max. covered loss is u.

How can i determine the value of d such that 20% of the losses do not result in a payment?

What are the steps I should take to approach this question? (the Value of the parameters are assumed to be known)

appreciate any help!

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  • $\begingroup$ Ummm, compute the value where the CDF is 0.2 ? $\endgroup$
    – user1566
    Commented Nov 8, 2014 at 16:35
  • $\begingroup$ @barrycarter The question concerns how to compute that value. It comes down to finding the inverse CDF of a mixture distribution (which has to be done numerically in general). $\endgroup$
    – whuber ♦
    Commented Nov 8, 2014 at 17:10
  • $\begingroup$ @whuber what do you mean by finding the inverse CDF of the mixture distribution? I was given the hint of taking F(x) - (some value)= 0 but i cant figure out what is the "some value" $\endgroup$
    – user1234
    Commented Nov 8, 2014 at 17:24
  • $\begingroup$ It is sometimes called the quantile function. If you're unsure of what a mixture distribution is, then visit en.wikipedia.org/wiki/…. $\endgroup$
    – whuber ♦
    Commented Nov 8, 2014 at 17:36

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