More interesting assumptions for the insurance risk problem are that the number of claims N t) is a Poisson process and the sizes of the claims V1, V2,… are independent, identically distributed positive random variables.
Let be a sequence of identically distributed positive strongly mixing random variable with and,,.
Let be a sequence of identically distributed positive strongly mixing random variable with and, and as mentioned above.
Negative numbers can be factored nearly identically to how positive numbers are factored.
Lemma 1: Let G ( p 1, …, p n ) ≜ E [ f ( ∑ k = 1 n p k w k ) ], where f : ℝ → ℝ with f(x) > 0 ∀x > 0, and { w i } i = 1 n are independent and identically distributed (i.i.d) positive random variables.
Suppose that is a sequence of positive independent and identically distributed (i.i.d).i.d
Let be a sequence of positive independent and identically distributed random variables with common Pareto-type distribution function as, where represents a slowly varying function at infinity.
If we denote the cumulative number of FTP mentioning the topic at time t by N t, the growth of attention can be described by N t = ( 1 + χ t ) N t − 1, where the χ t are assumed to be small, positive, independent and identically distributed random variables with mean μ and variance σ 2. For small χ s, the equation can be approximated as: N t ≃ ∏ s = 1 t e χ s N 0 = e ∑ s = 1 t χ s N 0. (1).
Preparation of negative homogenates and positive dilutions were prepared identically to those previously described for the TeSeE™ ELISA.
CMPA's earlier studies found that the broadcast networks gave almost identically negative coverage to George W. Bush (37% positive), Bill Clinton (34% positive) and Ronald Reagan (37% positive) during their first seven months in office.
