Pareto Distribution

Examples of Pareto Distribution in the following topics:

• Shapes of Sampling Distributions

  • The "shape of a distribution" refers to the shape of a probability distribution.
  • The shape of a distribution will fall somewhere in a continuum where a flat distribution might be considered central; and where types of departure from this include:
  • A normal distribution is usually regarded as having short tails, while a Pareto distribution has long tails.
  • Even in the relatively simple case of a mounded distribution, the distribution may be skewed to the left or skewed to the right (with symmetric corresponding to no skew).
  • Sample distributions, when the sampling statistic is the mean, are generally expected to display a normal distribution.

• Do It Yourself: Plotting Qualitative Frequency Distributions

  • Qualitative frequency distributions can be displayed in bar charts, Pareto charts, and pie charts.
  • Sometimes a relative frequency distribution is desired.
  • A special type of bar graph where the bars are drawn in decreasing order of relative frequency is called a Pareto chart .
  • This pie chart shows the frequency distribution of a bag of Skittles.
  • This graph shows the frequency distribution of a bag of Skittles.

• The Gauss Model

  • The normal (Gaussian) distribution is a commonly used distribution that can be used to display the data in many real life scenarios.
  • In probability theory, the normal (or Gaussian) distribution is a continuous probability distribution, defined by the formula:
  • A random variable with a Gaussian distribution is said to be normally distributed and is called a normal deviate.
  • If $\mu = 0$ and $\sigma = 1$, the distribution is called the standard normal distribution or the unit normal distribution, and a random variable with that distribution is a standard normal deviate.
  • Such variables may be better described by other distributions, such as the log-normal distribution or the Pareto distribution.

• Distribution of Wealth and Income

  • It differs from the income distribution in that it looks at the distribution of asset ownership in a society, rather than the current income of members of that society.
  • There are many ways in which the distribution of wealth can be analyzed.
  • A Pareto distribution is a statistical measure that is often used to model the distribution of wealth, though other mathematical models are also used.
  • As with general wealth distribution, land is also distributed unequally.
  • Various forms of socialism, an economic system in which the state exerts significant control over wealth distribution, attempt to diminish the unequal distribution of wealth and the conflicts that arise from it.

• Definition of Perfect Competition

  • Perfect competition is a market structure that leads to the Pareto-efficient allocation of economic resources.
  • Market structure is determined by the number and size distribution of firms in a market, entry conditions, and the extent of product differentiation.
  • Perfect competition leads to the Pareto-efficient allocation of economic resources.

• Trade Leads to Gains

  • An allocation of resources is Pareto efficient when it is impossible to make any one individual better off without making at least one individual worse off.
  • A distribution in which Individual A has all of the peanut butter and individual B has all of the jelly is not Pareto efficient, because both parties would be better off if they shared their resources.
  • Similarly, an action that makes at least one party better off without making any individual worse off is called a Pareto improvement.
  • It is commonly assumed that outcomes that are not Pareto efficient are to be avoided, and if a Pareto improvement is possible it should always be implemented.
  • One way to look at whether a transaction is a Pareto improvement is to ask whether it increases consumer or producer surplus without decreasing either party's surplus.

• Voluntary Exchange

  • One of the basic concepts described in Chapter I Introduction was "Pareto Efficiency or Pareto Optimality."
  • This improvement is called a Pareto improvement and the result is said to be Pareto superior to the initial alternative.
  • Nor is it possible to assume that the utility or welfare of the group would be maximized by that distribution.
  • Consider a distribution where every member of society is given 1 case of cola and 1 box of tea bags.
  • This exchange ratio is determined by the preferences of the individuals, the relative amount and distribution of cola and tea.

• Introduction to Deadweight Loss

  • Deadweight loss is the decrease in economic efficiency that occurs when a good or service is not priced at its pareto optimal level.
  • Deadweight loss is the decrease in economic efficiency that occurs when a good or service is not priced and produced at its pareto optimal level.
  • In a perfectly competitive market, products are priced at the pareto optimal point.
  • the point on the supply curve where the y-coordinate equals the non-pareto optimal price;
  • the point on the demand curve where the y-coordinate equals the non-pareto optimal price.

• Exploratory Data Analysis (EDA)

  • His reasoning was that the median and quartiles, being functions of the empirical distribution, are defined for all distributions, unlike the mean and standard deviation.
  • Moreover, the quartiles and median are more robust to skewed or heavy-tailed distributions than traditional summaries (the mean and standard deviation).

• Total Quality Management Techniques

  • Six sigma, JIT, Pareto analysis, and the Five Whys technique are all approaches that can be used to improve overall quality.
  • Pareto analysis is a statistical technique used to select a limited number of tasks that produce significant overall effect.
  • It uses the Pareto principle: most problems have a few key causes.
  • Pareto analysis also concludes that 80% of the result can be generated by focusing on 20% of the key work.