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 ...

2022年6月27日 · Kurtosis is a measure of the tailedness of a distribution. Tailedness is how often outliers occur. Excess kurtosis is the tailedness of a distribution relative to a normal distribution. Distributions with medium kurtosis (medium tails) are mesokurtic. Distributions with low kurtosis (thin tails) are platykurtic.

2024年4月17日 · To calculate kurtosis in statistics, you can follow these steps: Compute the Mean (μ): Calculate the arithmetic mean of the dataset. Compute the Variance (σ2): Calculate the variance of the dataset, which is the average of the squared differences from the mean.

2022年4月24日 · The kurtosis of X is the fourth moment of the standard score: kurt(X) = E[(X − μ σ)4] Kurtosis comes from the Greek word for bulging. Kurtosis is always positive, since we have assumed that σ> 0 (the random variable really is random), and therefore P(X ≠ μ)> 0.

2023年7月24日 · What is the Kurtosis Formula? The term “Kurtosis” refers to the statistical measure that describes the shape of either tail of a distribution, i.e. whether the distribution is heavy-tailed (presence of outliers) or light-tailed (paucity of …

2011年3月5日 · For univariate data Y 1, Y 2, ..., Y N, the formula for kurtosis is: \[ \mbox{kurtosis} = \frac{\sum_{i=1}^{N}(Y_{i} - \bar{Y})^{4}/N} {s^{4}} \] where \(\bar{Y}\) is the mean, s is the standard deviation, and N is the number of data points.

2024年7月31日 · Kurtosis is a statistical measure used to describe the distribution of observed data around the mean. It is used to describe tail risk found in certain investments.

2025年1月7日 · Kurtosis is defined as β 2 = (E(x) 4 / (E(x) 2) 2) − 3, where E is the expected value of x. The kurtosis of a distribution can be classified as leptokurtic, mesokurtic, or platykurtic. Leptokurtic distributions are variable distributions with wide tails and have positive kurtosis.

2025年1月31日 · Kurtosis is defined as a normalized form of the fourth central moment of a distribution.

2023年7月31日 · Kurtosis is a statistical measure used to describe the degree to which scores cluster in the tails or the peak of a frequency distribution. The peak is the tallest part of the distribution, and the tails are the ends of the distribution. There are three types of kurtosis: mesokurtic, leptokurtic, and platykurtic.