ON FOUR-PARAMETER ODD GENERALIZED EXPONENTIAL-PARETO DISTRIBUTION: ITS PROPERTIES AND APPLICATIONS

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ON FOUR-PARAMETER ODD GENERALIZED EXPONENTIAL-PARETO DISTRIBUTION: ITS PROPERTIES AND APPLICATIONS

 

CHAPTER ONE

INTRODUCTION

1.1    Background of the study

The Pareto distribution is a widely known distribution in applied sciences as well as in Economics. It was introduced in order to explain the distribution of income in the society (Pareto, 1896). It was first proposed by a Professor of Economics, Vilfredo Pareto (1843-1923). The distribution was found while studying various distributions for modeling income in Switzerland. The various forms of the Pareto distribution are versatile and can usually be used to model uncertainties. Since that time its applicability spans diverse areas of human endeavour comprising Biology, Physics, Actuarial Science, Geography, etc. Pareto made several important contributions to Economics, mostly in the study of income distribution and in the analysis of individuals choices.

Pareto found out that income approximately follows a Pareto distribution, which is considered as power law probability distribution. The Pareto principle was named after him and noted that 80% of the land in Italy was owned by 20% of the popula-tion. One of Pareto’s equations attained special importance and argument. He was captivated by problems of power and wealth. How do people get it? How is it spread around society? How do those who have it use it? The gap between rich and poor has always been part of the human condition, but Pareto resolved to measure it. He collected piles of data on wealth and income through different centuries, across different countries: the tax records of Basel, Switzerland, from 1454 and from Augs-burg, Germany, in 1471, 1498 and 1512; contemporary rental income from Paris; personal income from Britain, Prussia, Saxony, Ireland, Italy, and Peru. What he discovered or thought he discovered was striking. When he plotted the data on a graph sheet, with income on one axis, and number of people with that income on the other, he observed similar scenario nearly everywhere in every era. Society was not a “social pyramid” with the percentage of rich to poor sloping gently from one class to the next. Instead it was more of a “social arrow” the bottom was very fat indicating where the mass of men live, and at the top was very thin indicating where the wealthy elite reside. Nor was this effect by chance; the data did not remotely fit a bell curve, as one would anticipate if wealth were randomly distributed. “It is a social law”, he wrote: something “in the nature of man”. At the bottom of the Wealth curve, he wrote, Men and Women starve and children die young. This reason makes Pareto to develop model for distribution of wealth.

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ON FOUR-PARAMETER ODD GENERALIZED EXPONENTIAL-PARETO DISTRIBUTION: ITS PROPERTIES AND APPLICATIONS