Characterizations of probability distributions via bivariate regression of record values

Characterizations of Probability Distributions via Bivariate Regression of Record Values

Bairamov et al. (2005) characterize the exponential distribution in terms of the regression of a function of a record value with its adjacent record values as covariates. We extend these results to the case of nonadjacent covariates. We also consider a more general setting involving monotone transformations. As special cases, we present characterizations involving weighted arithmetic, geometric...

Asymptotic Efficiencies of the MLE Based on Bivariate Record Values from Bivariate Normal Distribution

Abstract. Maximum likelihood (ML) estimation based on bivariate record data is considered as the general inference problem. Assume that the process of observing k records is repeated m times, independently. The asymptotic properties including consistency and asymptotic normality of the Maximum Likelihood (ML) estimates of parameters of the underlying distribution is then established, when m is ...

A Characterization of Continuous Distributions via Regression on Pairs of Record Values

Let X1, X2, . . . be independent copies of a random variable X whose distribution function is denoted by F. There have been many studies on characterizations of F via linear regression relations of one order statistic on one or two other order statistics. See Wesolowski & Ahsanullah (1997) for references and the most complete results. Similarly, the regression of one record value on another has...

Characterizations of Distributions by Expected Values of Lower Record Statistics with Spacing

On characterizations based on regression of linear combinations of record values

We characterize the exponential distribution in terms of the regression of a record value with two non-adjacent record values as covariates. We also study characterizations based on the regression of linear combinations of record values. AMS (2000) Subject Classification. 62G30, 62E10.