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kurtosis

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Kurtosis - Wikipedia
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. en.wikipedia.org
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Kurtosis: Definition, Types, and Importance - Investopedia
Kurtosis is a measure of the combined weight of a distribution's tails relative to the center of the distribution curve referred to as the mean. www.investopedia.com
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Kurtosis - Corporate Finance Institute
Kurtosis is a statistical measure that defines how heavily the tails of a distribution differ from the tails of a normal distribution. corporatefinanceinstitute.com
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kurtosis
kurtosis Statistics. (kɜːˈtəʊsɪs) [mod.L., f. Gr. κύρτωσις a bulging, convexity, f. κυρτός bulging, convex.] A shape characteristic of a frequency distribution that reflects the sharpness of the peak (for a unimodal distribution) and the shortness of the tails, and is generally measured by the quant... Oxford English Dictionary
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Kurtosis - an overview | ScienceDirect Topics
Kurtosis is defined as a measure of the dispersion of a distribution relative to its mean, particularly focusing on the concentration of data around the mean ... www.sciencedirect.com
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What Is Kurtosis? | Definition, Examples & Formula - Scribbr
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 ... www.scribbr.com
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Rationale for describing kurtosis as "peakedness"? Planned maintenance ...
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Kurtosis as Peakedness, 1905 – 2014. R.I.P - PMC - PubMed Central
Kurtosis somehow measures “peakedness” (flatness, pointiness or modality) of a distribution is remarkably persistent, despite attempts by statisticians to set ... pmc.ncbi.nlm.nih.gov
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Kurtosis -- from Wolfram MathWorld
Kurtosis is defined as a normalized form of the fourth central moment mu_4 of a distribution. There are several flavors of kurtosis. mathworld.wolfram.com
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Kurtosis: Definition, Leptokurtic & Platykurtic - Statistics By Jim
Kurtosis is a statistic that measures the extent to which a distribution contains outliers. It assesses the propensity of a distribution to have extreme values ... statisticsbyjim.com
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Kurtosis: Definition, Leptokurtic, Platykurtic - Statistics How To
Excess kurtosis is a way to measure the deviation of tails in any given probability distribution from that of a normal distribution. www.statisticshowto.com
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Kurtosis - an overview | ScienceDirect Topics
Kurtosis is a measure that describes how heavily the tails of a distribution differ from the tails of a normal distribution. www.sciencedirect.com
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Kurtosis Excess -- from Wolfram MathWorld
Jan 23, 2024The "kurtosis excess" (Kenney and Keeping 1951, p. 27) is defined in terms of the usual kurtosis by gamma_2 = beta_2-3 (1) = (mu_4)/(mu_2^2)-3. (2) It is commonly denoted gamma_2 (Abramowitz and Stegun 1972, p. 928) or b_2. Kurtosis excess is commonly used because gamma_2 of a normal distribution is equal to 0, while the kurtosis proper is equal to 3.
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Kurtosis risk
Kurtosis risk is commonly referred to as "fat tail" risk. Ignoring kurtosis risk will cause any model to understate the risk of variables with high kurtosis. wikipedia.org
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Is excess kurtosis for a mixture of two normal distributions with the same means and different variances always positive? For a mixture of two normal distributions with the same mean the excess kurtosis is stated to b...
You forgot to mention $p_1 + p_2 = 1$ which follows from the web site you linked. I will use $s,t$ for $\sigma_1, \sigma_2$ and $p,q$ for $p_1, p_2 = 1-p_1$ to simplify notation. Sufficient to show that $$ps^4 + qt^4 \geq \left(ps^2 + qt^2\right)^2.$$ Note that $$ \begin{split} 0 &\leq \left(s^2 - t...
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