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A new variety of Ranked Set Sampling (RSS), namely Induced Generalized Record Ranked Set Sampling (IGRRSS), is introduced. In the proposed methodology, ranking is implemented by considering generalized (k) record values on the auxiliary variable X from each sequence of units. The selected units are further screened for measuring the variable of primary interest Y. Further, we propose estimators based on IGRRSS for the unknown parameters associated with the variable Y when the parent bivariate distribution belongs to the Morgenstern family of distributions. The proposed sampling scheme is utilized to collect primary data on the usable timber volume Y based on the ranking of units by generalized (2) record values on tree height X of acacia trees. Accordingly, Morgenstern type bivariate logistic distribution has been modelled for the distribution of the population random vector (X, Y) and estimated the average usable timber volume of the population.

In this paper, we have obtained the marginal and joint distributions of concomitants of k -record values for the Morgenstern family of distributions (MFD) and hence obtained the moments and product moments of concomitants of k -record values. Applying this results we have derived the best linear unbiased estimators of some parameters involved in Morgenstern type bivariate logistic distribution which belongs to MFD based on concomitants of k -record values.

In this paper we have suggested some improved estimator of parameters of Morgenstern type bivariate logistic distribution (MTBLD) using ranked set sampling. We have shown the superiority of the proposed estimators over Chacko and Thomas (2009) estimators.

In this paper, we propose a new three-parameter lifetime distribution for modeling symmetric real-life data sets. A simple-type Copula-based construction is presented to derive many bivariate- and multivariate-type distributions. The failure rate function of the new model can be “monotonically asymmetric increasing”, “increasing-constant”, “monotonically asymmetric decreasing” and “upside-down-constant” shaped. We investigate some of mathematical symmetric/asymmetric properties such as the ordinary moments, moment generating function, conditional moment, residual life and reversed residual functions. Bonferroni and Lorenz curves and mean deviations are discussed. The maximum likelihood method is used to estimate the model parameters. Finally, we illustrate the importance of the new model by the study of real data applications to show the flexibility and potentiality of the new model. The kernel density estimation and box plots are used for exploring the symmetry of the used data.