Hellin's law states that if the twinning rate is w, then the triplet rate is w2, the quad... more Hellin's law states that if the twinning rate is w, then the triplet rate is w2, the quadruplet rate is w3, and so forth. The opinion of today is that Hellin's law holds only approximately. In this study the inaccuracy of Hellin's law is studied and the discrepancies are explained mathematically. In our earlier studies we built linear models for the twinning rate. Because most of the mothers are younger than 40 years of age and because in this age interval the twinning rate depends linearly on age, linear regression methods have been applied. Hellin's law suggests using the square-root transformation of the triplet rate r. Statistical arguments speak in favor of using the arcsin square root of r transformation. We discuss both transformations. Despite the fact that Hellin's law is only approximate, the arcsin transformation proves valuable. The transformed triplet rate can be modeled in a way similar to the twinning rate. We consider secular data from Finland for 1881-1990 and from Sweden since 1751. Using Hellin's law, we compare the triplet rates and the twinning rates and study the time trends of the observed twinning and triplet rates. The data are standardized. Our theoretical results are applied to multiple maternity data for Finland. Using maternal age as the regressor, we build a linear model for the twinning rate and for the arcsin-transformed triplet rate. This analysis shows a decreasing linear time trend in the triplet series for the period 1881-1950 but not in the twinning series. The triplet rate has an increasing trend after 1960, which seems to be mainly caused by artificial induction of ovulation.
Aldur W. Eriksson, the noted twin scholar and human geneticist, passed away on Friday, April 3, 2... more Aldur W. Eriksson, the noted twin scholar and human geneticist, passed away on Friday, April 3, 2015, at the age of 88. He had a full, highly productive and accomplished life. He is survived by his wife Maj-Britt and their son Staffan and his family. His death leaves a void, not only among relatives and friends, but among the many who had known him and in the scientific community, particularly that of twin researchers worldwide.
Let X be the pre- and Y be the post-transfer income. In earlier studies we have considered the cl... more Let X be the pre- and Y be the post-transfer income. In earlier studies we have considered the class of transfer policies where Y=h(X) is the post-transfer income and h(x) is non-negative, monotone increasing and continuous. We modify this class, allowing h(x) to be discontinuous. If h(x) is discontinuous, then it can have only a countable number of finite positive steps. If there exists an optimal policy which Lorenz dominates all policies in the class, then it must be continuous. We present necessary and sufficient conditions under which a given Lorenz curve L ¯(p) can be generated by a member of the class. These conditions are equivalent to the condition that the transformed variable stochastically dominates the initial variable.
Hellin's law states that if the twinning rate is w, then the triplet rate is w2, the quad... more Hellin's law states that if the twinning rate is w, then the triplet rate is w2, the quadruplet rate is w3, and so forth. The opinion of today is that Hellin's law holds only approximately. In this study the inaccuracy of Hellin's law is studied and the discrepancies are explained mathematically. In our earlier studies we built linear models for the twinning rate. Because most of the mothers are younger than 40 years of age and because in this age interval the twinning rate depends linearly on age, linear regression methods have been applied. Hellin's law suggests using the square-root transformation of the triplet rate r. Statistical arguments speak in favor of using the arcsin square root of r transformation. We discuss both transformations. Despite the fact that Hellin's law is only approximate, the arcsin transformation proves valuable. The transformed triplet rate can be modeled in a way similar to the twinning rate. We consider secular data from Finland for 1881-1990 and from Sweden since 1751. Using Hellin's law, we compare the triplet rates and the twinning rates and study the time trends of the observed twinning and triplet rates. The data are standardized. Our theoretical results are applied to multiple maternity data for Finland. Using maternal age as the regressor, we build a linear model for the twinning rate and for the arcsin-transformed triplet rate. This analysis shows a decreasing linear time trend in the triplet series for the period 1881-1950 but not in the twinning series. The triplet rate has an increasing trend after 1960, which seems to be mainly caused by artificial induction of ovulation.
Aldur W. Eriksson, the noted twin scholar and human geneticist, passed away on Friday, April 3, 2... more Aldur W. Eriksson, the noted twin scholar and human geneticist, passed away on Friday, April 3, 2015, at the age of 88. He had a full, highly productive and accomplished life. He is survived by his wife Maj-Britt and their son Staffan and his family. His death leaves a void, not only among relatives and friends, but among the many who had known him and in the scientific community, particularly that of twin researchers worldwide.
Let X be the pre- and Y be the post-transfer income. In earlier studies we have considered the cl... more Let X be the pre- and Y be the post-transfer income. In earlier studies we have considered the class of transfer policies where Y=h(X) is the post-transfer income and h(x) is non-negative, monotone increasing and continuous. We modify this class, allowing h(x) to be discontinuous. If h(x) is discontinuous, then it can have only a countable number of finite positive steps. If there exists an optimal policy which Lorenz dominates all policies in the class, then it must be continuous. We present necessary and sufficient conditions under which a given Lorenz curve L ¯(p) can be generated by a member of the class. These conditions are equivalent to the condition that the transformed variable stochastically dominates the initial variable.
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Papers by Johan Fellman