Concomitants Of Record Values Research Articles

Fisher Information and Shannon’s Entropy for Record Values and Their Concomitants under Iterated FGM Family

Let {(Xi ,Yi), i ≥ 1} be independent and identically distributed random variables (RVs) from a continuous bivariate distribution. If {Rn,n ≥ 1} is the sequence of upper record values in the sequence {Xi}, then the RV Yi, which corresponds to Rn is called the concomitant of the nth record, denoted by R[n]. We study the Shannon entropy (SHANE) of R[n] and (Rn,R[n]) under iterated Farlie-Gumbel-Morgenstern (IFGM) family. In addition, we find the Kullback-Leibler distance (K-L) between R[n] and Rn. Moreover, we study the Fisher information matrix (FIM) for record values and their concomitants about the shape-parameter vector of the IFGM family. Also, we study the relative efficiency matrix of that vector-estimator of the shape-parameter vector whose covariance matrix is equal to Cramer-Rao lower bound, based on record ´ values and their concomitants. In addition, the Fisher information number (FIN) of R[n] is derived. Finally, we evaluate the FI about the mean of exponential distribution in the concomitants of record values.

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In this article we have derived the best linear unbiased estimators (BLUE’s) of the parameters µ2 and involved σ2 in the Morgenstern type bivariate exponential distribution (MTBED) by concomitants of record values. Efficiency comparisons are also made on the proposed estimators with that of competing unbiased estimators for µ2 and σ2 involved in MTBED.

Notes on Entropy for Concomitants of Record Values in Farlie-Gumbel-Morgenstern (FGM) Family

Let {(Xi , Yi), i ≥ 1} be a sequence of bivariate random variables from a continuous distribution. If {Rn, n ≥ 1} is the sequence of record values in the sequence of X’s, then the Y which corresponds with the nth record will be called the concomitant of the nth-record, denoted by R[n] . In FGM family, we determine the amount of information contained in R[n] and compare it with amount of information given in Rn. Also, we show that the Kullback-Leibler distance among the concomitants of record values is distribution-free. Finally, we provide some numerical results of mutual information and Pearson correlation coefficient for measuring the amount of dependency between Rn and R[n] in the copula model of FGM family.

Characterizations of bivariate distributions using concomitants of record values

In this paper, we consider a family of bivariate distributions which is a generalization of the Morgenstern family of bivariate distributions. We have derived some properties of concomitants of record values which characterize this generalized class of distributions. The role of concomitants of record values in the unique determination of the parent bivariate distribution has been established. We have also derived properties of concomitants of record values which characterize each of the following families viz Morgenstern family, bivariate Pareto family and a generalized Gumbel’s family of bivariate distributions. Some applications of the characterization results are discussed and important conclusions based on the characterization results are drawn.

Estimation of parameters of bivariate normal distribution using concomitants of record values

In this paper, we discuss the concomitants of record values arising from the well-known bivariate normal distribution BVND(µ1, µ2,σ1,σ2, ρ). We have obtained the best linear unbiased estimators of µ2 and σ2 when ρ is known and derived some unbiased linear estimators of ρ when µ2 and σ2 are known, based on the concomitants of first n record values. The variances of these estimators have been obtained.

Concomitants of Record Values Arising from Morgenstern Type Bivariate Logistic Distribution and Some of their Applications in Parameter Estimation

In this paper we have obtained the joint probability density function of concomitants of two record values and hence obtained an explicit expression for the product moment of concomitants of two record values arising from Morgenstern family of distributions. Appling this expression for the product moments of concomitants of record values we have derived the best linear unbiased estimators based on concomitants of record values of some parameters involved in Morgenstern type bivariate logistic distribution which is a subfamily of the Morgenstern family of distributions. The efficiencies of these estimators based on the first n concomitants of record values for n≤10 are also obtained.