Tail distribution bounds play a major role in the estimation of failure probabilities in performance and reliability analysis of systems. They are usually estimated using the Markov and Chebyshev’s inequalities, which represent tail distribution bounds for a random variable in terms of its mean or variance. This paper presents the formal verification of Markov’s and Chebyshev’s inequalities for...

Generalizing Cox, Ingersoll, and Ross (1979), this paper defines the stochastic duration of a bond in a general multi-factor diffusion model as the time to maturity of the zero-coupon bond with the same relative volatility as the bond. Important general properties of the stochastic duration measure are derived analytically, and the stochastic duration is studied in detail in various well-known ...

We consider the classical coupon collector’s problem in which each new coupon collected is type i with probability pi; P i1⁄41 n pi1⁄41. We derive some formulas concerning N, the number of coupons needed to have a complete set of at least one of each type, that are computationally useful when n is not too large. We also present efficient simulation procedures for determining P(N . k), as well a...

In this report an entropy bound on the memory size is given for a compression method of leaf-labeled trees. The compression converts the tree into a Directed Acyclic Graph (DAG) by merging isomorphic subtrees. I. COUPON COLLECTOR’S PROBLEM WITH ARBITRARY COUPON PROBABILITIES Given a set of C coupons, where δ = |C| denotes the number of coupons. At each draw po denotes the probability for gettin...

European options on coupon bonds are studied in a quantum field theory model of forward interest rates. Swaptions are briefly reviewed. An approximation scheme for the coupon bond option price is developed based on the fact that the volatility of the forward interest rates is a small quantity. The field theory for the forward interest rates is Gaussian, but when the payoff function for the coup...

In our model, we have assumed that all consumers are coupon users. As we show here, our results do not change qualitatively if we introduce coupon non-users. Assume that there is a fraction, 1 − γ, of consumers who do not use coupons. They are uniformly distributed on the interval [−L,L] as well, but they can have different price sensitivity than the coupon users have. Specifically, we assume t...

The growth and popularity of online shopping platforms have attracted numerous vendors to invest in this shopping channel. Coupon proneness is one key price-related personality influencing trust in online retailing environment. This study seeks to examine the moderating effect of personality trait (coupon proneness) on trust in satisfaction-repurchase intention link. The research model was empi...

Pr[|X −E[X]| ≥ a] = Pr[(x−E[x]) ≥ a] ≤ E[(x−E[x]) 2] a2 = Var[X] a2 1.3 Example: Coupon Collector Xi : # boxes bought when you have exactly i− 1 different coupons, and after buying these boxes, you have i different coupons. Let X = ∑ i∈nXi: # boxes one bought until at least one of every type of coupon is obtained. Let pi be the probability of obtaining a new coupon when we have exactly i−1 diff...