In this note, two characterizations of the exponential distribution are established. Theorem 1: Let a > -1, a ~ O. A positive random variable X has an exponential distribution if and only if E[CX-y)aI X > y] is a finite constant for all y ~ O. Theorem 2: Let Xl ,X2, ..• ,Xn be i.i.d. random variables having a continuous distribution FCx), and XCl)'XC2)' ... 'XCn) their order statistics. Let a >...

A thorough understanding of the joint default behavior of credit-risky securities is essential for credit risk measurement as well as the valuation of multi-name credit derivatives and Collateralized Debt Obligations. In this paper we study a simple and tractable intensity-based model for correlated defaults, in which unpredictable default arrival times are jointly exponentially distributed. Si...

We propose a new higher-dimensional mechanism for solving the hierarchy problem. The weak scale is generated from a large scale of order the Planck scale through an exponential hierarchy. However, this exponential arises not from gauge interactions but from the background metric (which is a slice of AdS5 spacetime). This mechanism relies on the existence of only a single additional dimension. W...

Recent work drawing on data for large and small firms has shown a Pareto distribution of firm size. We mix a Gibrat-type growth process among incumbents with an exponential distribution of firm’s age, to obtain the empirical Pareto distribution. JEL codes: L20, L25

A generalization of the exponential distribution is presented. The generalization always has a decreasing probability density function and yet allows for increasing, decreasing and constant hazard rates. It can be used for modeling lifetime data from reliability and survival studies. One example is discussed to illustrate its applicability.

In this paper we give some recurrence relations satisfied by single and product moments of generalized order statistics from doubly truncated generalized exponential distribution. These relations are deduced for moments of record values and order statistics. Further, using a recurrence relation for single moments we obtain a characterization of generalized exponential distribution.

In this paper explicit expressions and some recurrence relations are derived for marginal and joint moment generating functions of generalized order statistics from Erlang-truncated exponential distribution. The results for k-th record values and order statistics are deduced from the relations derived. Further, a characterizing result of this distribution on using the conditional expectation of...