Search results
Results from the WOW.Com Content Network
In probability theory and statistics, kurtosis (from Greek: κυρτός, kyrtos or kurtos, meaning "curved, arching") refers to the degree of “tailedness” in the probability distribution of a real-valued random variable. Similar to skewness, kurtosis provides insight into specific characteristics of a distribution. Various methods exist ...
In statistics, the concept of the shape of a probability distribution arises in questions of finding an appropriate distribution to use to model the statistical properties of a population, given a sample from that population.
(Equivalently, as in the next section, excess kurtosis is the fourth cumulant divided by the square of the second cumulant.) [4] [5] If a distribution has heavy tails, the kurtosis will be high (sometimes called leptokurtic); conversely, light-tailed distributions (for example, bounded distributions such as the uniform) have low kurtosis ...
The Dirac delta function, although not strictly a probability distribution, is a limiting form of many continuous probability functions. It represents a discrete probability distribution concentrated at 0 — a degenerate distribution — it is a Distribution (mathematics) in the generalized function sense; but the notation treats it as if it ...
The normal probability plot is a graphical technique to identify substantive departures from normality. This includes identifying outliers, skewness, kurtosis, a need for transformations, and mixtures. Normal probability plots are made of raw data, residuals from model fits, and estimated parameters. A normal probability plot
A fat-tailed distribution is a probability distribution that exhibits a large skewness or kurtosis, relative to that of either a normal distribution or an exponential distribution. [when defined as?] In common usage, the terms fat-tailed and heavy-tailed are sometimes synonymous; fat-tailed is sometimes also defined as a subset of heavy-tailed ...
The probability distribution of the ... 115 The excess kurtosis of a distribution is the difference between its kurtosis and the kurtosis of a normal ...
where b 2 is the kurtosis and b 1 is the square of the skewness. Equality holds only for the two point Bernoulli distribution or the sum of two different Dirac delta functions. These are the most extreme cases of bimodality possible. The kurtosis in both these cases is 1. Since they are both symmetrical their skewness is 0 and the difference is 1.