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By Erkus E., Duman O.

During this paper, utilizing the concept that ofA-statistical convergence that is a regular(non-matrix) summability technique, we receive a common Korovkin variety approximation theorem which matters the matter of approximating a functionality f through a series {Lnf } of optimistic linear operators.

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The distinguishing feature of the multiple failure modes setting is that each individual has a lifetime T and a mode of failure C, so we require a joint model for T and C. 2) for failure modes j = 1, . , K. The analysis of multiple modes of failure is of considerable importance, and it turns out to be closely related to the analysis of ordinary univariate lifetime data, Chapter 9 is devoted to this topic. 6 SOME COMMENTS ON MODEL SELECTION AND STATISTICAL ANALYSIS A number of factors enter into the process of modeling and analyzing lifetime distributions.

When there are time-varying covariates, it is lsually essential to think about models in terms of their hazard functions. We cannot discus S a lifetime's relationship to covariates without considering the covariate "history," that is, the values the covariates take over time; a generally useful approach is to consider the hazard function at time t conditional on previous covarinte values. Subtle issues arise in connection with the modeling and interpretation of time-vat ying covariate effects. 4, where regression models are discussed.

We make one additional preliminary remark. Models are presented here without the inclusion of a so-called threshold parameter, ot guarantee time. Briefly, this is a Mile y > 0 before which it is assumed that an individual cannot die. Occasionally a situation calls for the inclusion of such a parameter. The distributions considered can all be extended to inclucle a threshold parameter by replacing the lifetime t by = t — 'y, with t' satisfying the restriction t' > O. f. (t) = X exp(—Xt), with t > O.

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