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Characterizations of Archimedean n -copulas

Włodzimierz Wysocki (2015)

Kybernetika

We present three characterizations of n -dimensional Archimedean copulas: algebraic, differential and diagonal. The first is due to Jouini and Clemen. We formulate it in a more general form, in terms of an n -variable operation derived from a binary operation. The second characterization is in terms of first order partial derivatives of the copula. The last characterization uses diagonal generators, which are “regular” diagonal sections of copulas, enabling one to recover the copulas by means of an...

Characterizations of continuous distributions through inequalities involving the expected values of selected functions

Faranak Goodarzi, Mohammad Amini, Gholam Reza Mohtashami Borzadaran (2017)

Applications of Mathematics

Nanda (2010) and Bhattacharjee et al. (2013) characterized a few distributions with help of the failure rate, mean residual, log-odds rate and aging intensity functions. In this paper, we generalize their results and characterize some distributions through functions used by them and Glaser’s function. Kundu and Ghosh (2016) obtained similar results using reversed hazard rate, expected inactivity time and reversed aging intensity functions. We also, via w ( · ) -function defined by Cacoullos and Papathanasiou...

Characterizations of the exponential distribution based on certain properties of its characteristic function

Simos G. Meintanis, George Iliopoulos (2003)

Kybernetika

Two characterizations of the exponential distribution among distributions with support the nonnegative real axis are presented. The characterizations are based on certain properties of the characteristic function of the exponential random variable. Counterexamples concerning more general possible versions of the characterizations are given.

Characterizing experimental designs by properties of the standard quadratic forms of observations

Czesław Stępniak (2007)

Applicationes Mathematicae

For any orthogonal multi-way classification, the sums of squares appearing in the analysis of variance may be expressed by the standard quadratic forms involving only squares of the marginal and total sums of observations. In this case the forms are independent and nonnegative definite. We characterize all two-way classifications preserving these properties for some and for all of the standard quadratic forms.

Checking proportional rates in the two-sample transformation model

David Kraus (2009)

Kybernetika

Transformation models for two samples of censored data are considered. Main examples are the proportional hazards and proportional odds model. The key assumption of these models is that the ratio of transformation rates (e. g., hazard rates or odds rates) is constant in time. A~method of verification of this proportionality assumption is developed. The proposed procedure is based on the idea of Neyman's smooth test and its data-driven version. The method is suitable for detecting monotonic as well...

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