Isograph and LaSiPiKa Distribution: The Comparative Morphology of Income Inequalities and Intelligible Parameters of 53 LIS Countries 1967-2020

The isograph methodology is developed here with associated distributions, indicators of inequality, additional results, and is implemented on 53 LIS countries (with an annex covering 655 LIS country-year samples). The gb2 and other classical distributions (FC, Dagum, SinghMaddala) are presented along with new proposals, including gb2 subfamilies with p=1/q and p=q, the LaSi distribution to fit the quasi-linear isograph cases of level lambda and slope sigma, and finally the LaSiPiKa that completes LaSi with a polarization term of intensity pi and location kappa. This latest proposal fits better the cases of distributions with sharp flexible profiles in the isograph and provides independent intelligible parameters. The analysis is systematized to 655 samples to show the invariant patterns and significant changes. More complicated distributional shapes can be fitted with hand-tailored additional terms. Working with isograph and LaSiPiKa distributions is a way to diversify and deepen inequality analyses with a larger conceptualization of "morphology of inequality," not reduced to a Gini (or the like) measure.