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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 ...
The kurtosis is here defined to be the standardised fourth moment around the mean. The value of b lies between 0 and 1. [27] The logic behind this coefficient is that a bimodal distribution with light tails will have very low kurtosis, an asymmetric character, or both – all of which increase this coefficient. The formula for a finite sample ...
In probability theory and statistics, the binomial distribution with parameters n and p is the discrete probability distribution of the number of successes in a sequence of n independent experiments, each asking a yes–no question, and each with its own Boolean-valued outcome: success (with probability p) or failure (with probability q = 1 − p).
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 ...
In probability theory ... Based on the formula of ... D'Agostino's K-squared test is a goodness-of-fit normality test based on sample skewness and sample kurtosis.
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
[6]: 115 The excess kurtosis of a distribution is the difference between its kurtosis and the kurtosis of a normal distribution, . [10]: 217 Therefore, the excess kurtosis of the geometric distribution is +.
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.