ProphetesAI is thinking...
kurtosis
MindMap
Loading...
Sources
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
prophetes.ai
Rationale for describing kurtosis as "peakedness"? Planned maintenance ...
Subscribe. Subscribe to this blog
ttykuu.blogspot.com
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.
mathworld.wolfram.com
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
en.wikipedia.org
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 $$ \begin{split} 0 &\leq \left(s^2 - t...
prophetes.ai
Kurtosis of Normal Distribution I have a basic question about kurtosis and specific distributions. > **Definition:** Let $Y$ be a random variable. $\mu_Y$ and $\sigma_Y$ denote $Y$'s mean and standard deviation respe...
Let $X=\frac{Y-\mu_Y}{\sigma_Y}$. Then $E(\frac{(Y-\mu_Y)^4}{\sigma_Y^4})=E(X^4)=3$, since $X$ is standard normal.
prophetes.ai
Kurtosis of sum of Independent Random Variables Suppose that $X$ and $Y$ are independent random variables with different expected values and variances. Suppose we define kurtosis as $$Kurt(X)=\frac{E[(X- \mu)^4]}{E[(...
Suppose that $X$ and $Y$ are independent, then $$\text{Kurt} (X+Y) = \frac{E\left[\left(X+Y-\left(\mu _X+\mu _y\right)\right){}^4\right]}{E\left[\left(X+Y-\left(\mu _X+\mu _Y\right)\right){}^2\right]^2} = \frac{\left.\left.E\left[(X-\mu _X+Y-\mu _y\right.\right){}^4\right]}{\text{Var}(X+Y)^2} = \fra...
prophetes.ai
Distribution without Kurtosis I am doing work on predicting stock price volatility with ARCH Models. One thing struck me. It was mentioned that the Model only had a Kurtosis under certain restrictions. How is it possi...
Then $E[X^4] = \infty$ so the kurtosis of $X$ is undefined. The related Cauchy distribution is a classic example that doesn't even have an expectation, let alone kurtosis.
prophetes.ai
Why is Kurtosis of ND 3? 3 seems to be an important number when it comes to kurtosis. I see that it is often removed from the value entirely and this seems to be due to its being the kurtosis of the normal distributio...
For a standard normal distribution with $E(X) = 0$. $$\mu_2 = \frac{1}{\sqrt{2 \pi}}\int_{-\infty}^{\infty}x^2e^{-x^2/2} \, dx = 1,$$ and integrating by parts with $u = x^3$ and $dv = xe^{-x^2/2}dx$, $$\mu_4 = \frac{1}{\sqrt{2 \pi}}\int_{-\infty}^{\infty}x^4e^{-x^2/2} \, dx = -\left.\frac{1}{\sqrt{2...
prophetes.ai
Python Scipy stats.kurtosis()用法及代码示例 - 纯净天空
Python Scipy stats.kurtosis ()用法及代码示例. scipy.stats.kurtosis (array, axis=0, fisher=True, bias=True) 函数计算数据集的峰度 (Fisher或Pearson)。. 它是第四个中心矩除以方差的平方。. 它是"tailedness"的量度，即real-valued随机变量的概率分布形状的描述符。. 简而言之，这可以说是 ...
vimsky.com
pandas.DataFrame.kurtosis — pandas 2.2.0 documentation
Parameters: axis{index (0), columns (1)} Axis for the function to be applied on. For Series this parameter is unused and defaults to 0. For DataFrames, specifying axis=None will apply the aggregation across both axes. New in version 2.0.0. skipnabool, default True. Exclude NA/null values when computing the result.
pandas.pydata.org
1.3.5.11. Measures of Skewness and Kurtosis - NIST
Measures of Skewness and Kurtosis. A fundamental task in many statistical analyses is to characterize the location and variability of a data set. A further characterization of the data includes skewness and kurtosis. Skewness is a measure of symmetry, or more precisely, the lack of symmetry. A distribution, or data set, is symmetric if it looks ...
www.itl.nist.gov
Correlation between MR Diffusion Kurtosis Imaging Parameters and Serum ...
Abstract: The purpose of this study was to investigate the correlation and significance of diffusion kurtosis imaging (DKI) parameters and serum microRNA (miR)-181c, miR-120 levels in patients with acute cerebral infarction. A total of 155 patients with acute cerebral infarction were selected as observation group and 100 healthy people were selected as control group.
www.yxkxyghx.org
www.yxkxyghx.org
Skewness and kurtosis of sum of lognormals Below is an equation $f(x)$ that is the sum of two lognormal waveforms. All of the coefficients are known, and by integration, the area under the curve is simply $P_1 + P_2$....
Long story short: I worked out the solution. Disregarding the measurement baseline B and shared delay D above, we have the following pdf: $$ f_X(x) = \frac {1} {P_1 + P_2} \left ( \frac {P_1 } {S_1x \sqrt { 2 \pi}} e ^ {-(\ln(x)-M_1) ^2 / (2S_1^2)} + \frac {P_2 } {S_2x \sqrt { 2 \pi}} e ^ {-(\ln(x)-...
prophetes.ai
generalized normal distribution with additional kurtosis parameter I am looking for a generalized normal distribution with mean $\mu$ and variance $\sigma^2$ but with an additional parameter for the kurtosis to add fa...
I think Pearson type VII distribution might be what your are looking for. You will need to reparametrize it, but wikipedia page has the necessary formulas.
prophetes.ai