Definition & Meaning | English word KURTOSIS

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Definitions of KURTOSIS

1. (statistics) A measure of "heaviness of the tails" of a probability distribution, defined as the fourth cumulant divided by the square of the variance of the probability distribution.
2. (statistics) Excess kurtosis: the difference between a given distribution's kurtosis and the kurtosis of a normal distribution.

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Examples of Using KURTOSIS in a Sentence

• Various methods exist for quantifying kurtosis in theoretical distributions, and corresponding techniques allow estimation based on sample data from a population.
• For skewness and kurtosis, alternative definitions exist, which are based on the third and fourth cumulant respectively.
• Allowing the modelling process to allow for empirical characteristics in stock returns such as auto-regression, asymmetric volatility, skewness, and kurtosis is important.
• As with variance, skewness, and kurtosis, these are higher-order statistics, involving non-linear combinations of the data, and can be used for description or estimation of further shape parameters.
• Applications that don't involve sorting would be in finding the mean, standard deviation, skewness and kurtosis of a statistical distribution, and in finding the integral and global maxima and minima of difficult deterministic functions.
• Given an equal (50/50) mixture of two normal distributions with the same standard deviation and different means (homoscedastic), the overall distribution will exhibit low kurtosis relative to a single normal distribution – the means of the subpopulations fall on the shoulders of the overall distribution.
• Abnormalities like kurtosis, fatter tails and higher peaks, or skewness on the distribution can be problematic for the ratio, as standard deviation doesn't have the same effectiveness when these problems exist.
• Apart from serving as an alternative for the mean and the truncated mean, it also forms the basis for robust measures of skewness and kurtosis, and even a normality test.
• The ARCH (Engle, 1982) and GARCH (Bollerslev, 1986) models aim to more accurately describe the phenomenon of volatility clustering and related effects such as kurtosis.
• Rohatgi and Szekely claimed that the skewness and kurtosis of a unimodal distribution are related by the inequality:.
• However, it was not known how to construct probability distributions in which the skewness (standardized third cumulant) and kurtosis (standardized fourth cumulant) could be adjusted equally freely.
• In the same way that the bispectrum identifies contributions to a signal's skewness as a function of frequency triples, the trispectrum identifies contributions to a signal's kurtosis as a function of frequency quadruplets.
• Data quality can be assessed in several ways, using different types of analysis: frequency counts, descriptive statistics (mean, standard deviation, median), normality (skewness, kurtosis, frequency histograms), normal imputation is needed.
• by replacing estimators that are optimal under the assumption of a normal distribution with estimators that are optimal for, or at least derived for, other distributions; for example, using the t-distribution with low degrees of freedom (high kurtosis) or with a mixture of two or more distributions.
• 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.
• The shape of a distribution may be considered either descriptively, using terms such as "J-shaped", or numerically, using quantitative measures such as skewness and kurtosis.
• The sample extrema can be used for a simple normality test, specifically of kurtosis: one computes the t-statistic of the sample maximum and minimum (subtracts sample mean and divides by the sample standard deviation), and if they are unusually large for the sample size (as per the three sigma rule and table therein, or more precisely a Student's t-distribution), then the kurtosis of the sample distribution deviates significantly from that of the normal distribution.
• Statistics = Min, Max, Quartiles, Mean, St Dev, Missing, Medium, Sum, Variance, Skewness, Kurtosis, chi square.
• Allowing the modeling process to allow for empirical characteristics in stock returns such as autoregression, asymmetric volatility, skewness, and kurtosis is important.
• MathProf was considered one of the most prominent contributors to the study of casino Blackjack and the related subjects of bankroll management, risk of ruin, kurtosis and skewness, cut card effects, large deviations, and others.

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