Afaf Hatem Syam

In this paper, we study the concomitants of m?dual generalized order statistics (and consequently m?generalized order statistics) from Huang-Kotz Farlie-Gumble-Morgenstern bivariate distribution (HK-FGM) of the types 1 and 2. Some important information measures are derived and studied for ordinary order statistics and sequential order statistics with a comparison. Specifically, the Shannon entropy, inaccuracy measure, and Fisher information number. Moreover, a comparison between the two types of HK-FGM distribution is carried out.

Suppose F_X is a continuous distribution function (DF) of an RV X. If we kept the withdrawal observations from time to time from F_X, then an observation that is larger than all the drawn observations previously is called a record and its value is called an upper record value or a record value. Let {R_n} be the sequence of the observed record values and let f_X be the probability density function (PDF) of X. Furthermore, we adopt R_0=X. Then, the PDF of R_n The FI is a vital criterion in statistical inference especially in large sample studies in estimation theory. In this paper, we will define the form of the FI for the DF (see Kharazmi and Asadi, 2018). The FI related to the distribution parameters give us feed back how much information about an unknown parameter from a sample and FI is connecting with the efficiency of an estimator and sufficiency of a statistic. When we have an unknown parameter in the DF from which the sample is drawn, and when the sample is sufficiently huge, the Knowing FI helps tracking down limits on the variance of a given estimator of that parameter and to rough the testing appropriation of this estimator. The Fisher information (FI) about the shape-parameter vectors of the Huang-Kotz FGM (HK-FGM) is investigated. We study analytically and numerically the Fisher information matrix (FIM) and Shanon entropy related to the record values and their concomitants for HK-FGM.

In this paper, we study the extropy for concomitants of m−generalized order statistics (m−GOSs) from Huang–Kotz–Farlie–Gumbel–Morgenstern (HK‐FGM) bivariate distribution. Moreover, the cumulative residual extropy (CREX) and negative cumulative extropy (NCEX) are depicted. Furthermore, the empirical technique in conjunction with the concomitant of m−GOS is used to investigate the problem of estimating the CREX and NCEX. The concomitants of order statistics and record values are offered as some applications of these findings.

We introduce the Bairamov-Kotz-Becki-Farlie-Gumble-Morgenstern (BKB-FGM) type bivariategeneralized exponential distribution. Some distributional properties of concomitants of order statistics as well as record values for this family are studied. Recurrence relations between the moments of concomitants are obtained, some of these recurrence relations were not publishes before for Morgenstern type bivariate distributions. Moreover, most of the paper results are extended to arbitrary distributions (see Remark 3.1).