Zeroes expenditure represent a difficulty in the analysis of household survey data. Zero expenditures are the result of two phenomena: nonconsumption and infrequency of purchase. Distinguishing between these types of zeroes is difficult in the kinds of data of interest to agricultural economists. This paper proposes a novel approach that yields less biased estimates of latent expenditure when t...

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Many authors have studied methods of generalising Steiner quasigroups by using certain cycle systems. The usual aims have been to preserve the law (xy)y = x, by using the standard construction, or to preserve the law xy = yx, by using the opposite vertex construction. In this paper we seek to generalise the law (xy)y = x to laws of the form ( ... (xy)y . . . )y = x and (y( ... (y(yx)) ... ) = x...

Engel structures on M×S and M×I are studied in this paper, where M is a 3–dimensional manifold. We suppose that these structures have characteristic line fields parallel to the fibres, S or I . It is proved that they are characterized by contact structures on the cross section M , the twisting numbers, and Legendrian foliations on both ends M × ∂I in the case of M × I . AMS Classification 57R25...