Heavy-tailed distributionIn probability theory, heavy-tailed distributions are probability distributions whose tails are not exponentially bounded: that is, they have heavier tails than the exponential distribution. In many applications it is the right tail of the distribution that is of interest, but a distribution may have a heavy left tail, or both tails may be heavy. There are three important subclasses of heavy-tailed distributions: the fat-tailed distributions, the long-tailed distributions, and the subexponential distributions.
Zipf's lawZipf's law (zɪf, ts͡ɪpf) is an empirical law that often holds, approximately, when a list of measured values is sorted in decreasing order. It states that the value of the nth entry is inversely proportional to n. The best known instance of Zipf's law applies to the frequency table of words in a text or corpus of natural language: Namely, it is usually found that the most common word occurs approximately twice as often as the next common one, three times as often as the third most common, and so on.
Pareto principleThe Pareto principle states that for many outcomes, roughly 80% of consequences come from 20% of causes (the "vital few"). Other names for this principle are the 80/20 rule, the law of the vital few, or the principle of factor sparsity. Management consultant Joseph M. Juran developed the concept in the context of quality control and improvement after reading the works of Italian sociologist and economist Vilfredo Pareto, who wrote about the 80/20 connection while teaching at the University of Lausanne.
Power lawIn statistics, a power law is a functional relationship between two quantities, where a relative change in one quantity results in a relative change in the other quantity proportional to a power of the change, independent of the initial size of those quantities: one quantity varies as a power of another. For instance, considering the area of a square in terms of the length of its side, if the length is doubled, the area is multiplied by a factor of four.
Stable distributionIn probability theory, a distribution is said to be stable if a linear combination of two independent random variables with this distribution has the same distribution, up to location and scale parameters. A random variable is said to be stable if its distribution is stable. The stable distribution family is also sometimes referred to as the Lévy alpha-stable distribution, after Paul Lévy, the first mathematician to have studied it. Of the four parameters defining the family, most attention has been focused on the stability parameter, (see panel).
Pareto distributionThe Pareto distribution, named after the Italian civil engineer, economist, and sociologist Vilfredo Pareto, is a power-law probability distribution that is used in description of social, quality control, scientific, geophysical, actuarial, and many other types of observable phenomena; the principle originally applied to describing the distribution of wealth in a society, fitting the trend that a large portion of wealth is held by a small fraction of the population.
Log-normal distributionIn probability theory, a log-normal (or lognormal) distribution is a continuous probability distribution of a random variable whose logarithm is normally distributed. Thus, if the random variable X is log-normally distributed, then Y = ln(X) has a normal distribution. Equivalently, if Y has a normal distribution, then the exponential function of Y, X = exp(Y), has a log-normal distribution. A random variable which is log-normally distributed takes only positive real values.
BusinessBusiness is the practice of making one's living or making money by producing or buying and selling products (such as goods and services). It is also "any activity or enterprise entered into for profit." Having a business name does not separate the business entity from the owner, which means that the owner of the business is responsible and liable for debts incurred by the business. If the business acquires debts, the creditors can go after the owner's personal possessions.
