ON THE ‘BEST’ VALUES OF THE CONSTANTS IN FREQUENCY DISTRIBUTIONS

by the method of moments. This method of moments has been extended by Thiele, Pearson, Lapps and others to obtain the constants involved in various stew frequency curves and series. It is an undoubtedly utile and accurate method;, but the question of whether it gives the ' best' values of the constants has not been very fully studied. It is perfectly true that if we deal with individual observations then the method of moments gives, with a somewhat arbitrary definition of what is to be a maximum, the 'best' values for a and x in the above equation to the Gaussian. Pearson* has shown that the method of moments agrees with the method of least squares in the case where the distribution is given by a high order parabola, and accordingly the method of moments is likely to give a very good result, when an expansion by Maclaurin's Theorem would closely give a frequency function. But the method of least squares itself can now-a-days hardly be spoken of as more than a utile and accurate method of fit, indeed its utility, owing to the cumbersome nature of the equations whioh frequently arise, is often far less than that of the method of moments.