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E[X ^ u]
Policy Limit Insurer Expected Lost E[Y^L]
E[X ^ u] / E[X ^ b]
ILF
E[(X-d)+] = E[X] - E[X ^ d]
Ordinary Deductible Insurer Expected Loss E[Y^L]
E[X ^ d] / E[X]
LER
E[(X-d)+] + d*S(d)
Franchise Deductible E[Y^L]
E[Y^L]/S(d)
E[Y^P]
u/alpha + d
Max loss covered formula (m)
alpha(1+r) [ E[X ^ m/(1+r)] - E[X ^ d/(1+r)] ]
Ultimate Formula E[Y^L]
(n+r-1 choose n) (beta/(1+beta)^n * (1/(1+beta))^r
Negative Binomial PDF
a + b/n
Pn/Pn-1
Poisson
a = 0, b= +
Negative Binomial
a = + , b= +
Binomial
a= -, b= +
Binomial
mu > sigma²
Negative Binomial
mu < sigma²
(1/(1-Po) * Pn
Zero Truncated P^Tn
(1-P^m)/(1-Po) * Pn
Zero Modified P^Mn