Question: (Lotka's law and least squares) Lotka's law describes the frequency of publication by authors in a given field. It states that X aY = b, where X is the number of publications, Y the relative frequency of authors with X publications, and a and b are constants (with b > 0) that depend on the specific field. Assume that we have data points (Xi, Yi), i = 1, . . . , m, and seek to estimate the constants a and b.
1. Show how to find the values of a, b according to a linear leastsquares criterion. Make sure to define the least-squares problem involved precisely.
2. Is the solution always unique? Formulate a condition on the data points that guarantees unicity.