Given a set of observations from a population, the first question that arises in our mind is about the nature of the parent population. A vague idea is provided by the frequency polygon (or frequency curve) but the information is totally inadequate and unreliable, because the sample observations may not cover the entire range of the parent distribution. Moreover, an unusually high frequency in one class, arising out of sheer chance, may completely distort the shape of the frequency curve.
Consequently, to determine the frequency curve, we resort to the technique of curve fitting to the given data. The failure of the normal distribution to fit many distributions which are observed in practice for continuous variables necessitated the development of generalized system of frequency curves. Since a trial and error approach is clearly undesirable, an elastic system of frequency curves must be evolved, which should incorporate, of not all, at least the most common of the distributions. Pearsonian system of frequency curves is one of the most important approaches in this direction, in which we decide about the shape of the curve on the basis of a criterion k calculated from the sample observations.
Karl Pearson’s first memoir dealing with generalized frequency curves appeared in 1895. In this paper and the subsequent two papers published in 1908 and 1916, karl pearson developed a set of frequency curves which could be obtained by assigning values to the parameters in a certain first order differential equation.
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