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The statistical study of record values in a sequence of iid continuous random variables was first formulated by Chandler (1952). For an extensive study in this area one can refer to the works of Arnold et al. (1998) and Ahsanullah (1988, 1995). Dzuibdziela and Kopocinski (1976) have generalized the concept of record values of Chandler (1952) by random variables of a more generalized nature and we may call them as generalized record values or k-th record values. In this chapter we mainly focus on the study of generalized record values from Gompertz distribution. The Gompertz distribution was introduced by Gompertz (1825). This distribution plays an important role in modelling human mortality and fitting actuarial tables. Ahuja and Nash (1967) have shown that Gompertz distribution is related by a simple transformation to certain distributions in the Pearson system of distribution. It can be viewed as extensions of the exponential distributions. More recent survey of Gompertz distribution and its applications can be found in Al-Hussaini et al. (2000) and Marshall and Olkin (2007). Let {Xn, n > 1} be a sequence of iid random variables with cumulative distribution function (cdf) F(x) = P(X 6 x) and probability density function (pdf) f (x). For a fixed positive integer k, Journal of Statistical Theory and Applications, Vol. 13, No. 1 (March 2014), 38-45

On Characterization of Gompertz Distribution by Properties of Generalized Record Values