ON GENERAL REPRESENTATION OF A DENSITY FUNCTION,
COLUMBIA UNIV NEW YORK INST FOR THE STUDY OF FATIGUE AND RELIABILITY
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To establish analytical forms of the density functions of the resistance of structures and of the applied load from samples of finite size for use in computing the probability of failure in the structural reliability analysis, the methods of the series expansion associated with the gamma distribution and of the asymptotic expansion are introduced while the two known methods, Gram-Charliers series of type A and type C, are reviewed with numerical examples. On the basis of these examples, it may be concluded that all the methods, obviously except for the asymptotic expansion, produce desirable result in the central portion of the distribution and that the simultaneous use of the GramCharlier series of type A and the asymptotic expansion will be successful in many cases, although not always, to cover the entire domain of the variable.