# Questions tagged [chi-squared-distribution]

The distribution of sum-of-squares of k independent standard normal random variables. For the test, use the [chi-squared-test] tag. Use also for related distributions.

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### Suspicious about 2 ways to compute a variance : weighted sum of $\chi^2$ distrbution gives the same results than Moschopoulos distribution

In an astrophysics context, I am using sherical harmonics from Legendre decomposition. I take the definition of $a_{lm}$ following a normal distribution with mean equal to zero and take also the ...
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### Properties of $\chi^2(1)$ multiplied by a real value "$a$"

Is it true that the $\chi^2$ distribution with $k=1$ (noted $\chi^2(1)$) multiplied by a real value $a$ is equal to $\chi^2(a)$ ? If not, is there a particular distribution for $a\cdot\chi^2(1)$? If ...
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### How do I determine the distribution of an additional sample $x_{n+1}$ given sample mean, variance $\bar x, s^2$ of a normally distributed $x$?

Suppose I draw $n$ samples $x_1...x_n$ of a random variable $x$, which is normally distributed with an unknown mean $\mu$ and variance $\sigma^2$. From those samples, I compute a sample mean $\bar x$ ...
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### What is the distribution of [constant X chi square]?

I know that (n-1)*S^2 / sigma^2 ~ chi_square(df=n-1). ※ S^2 = sigma(Xi-X_bar)/(n-1) However, if n and sigma are known, what is the distribution of S^2? As far as I think, S^2/sigma^2 = Z^2 (Z ~ N(0,1))...
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### Interpretation of Chi square distribution with 1/2 degrees of freedom

How do I interpret the Chi square ditsribution with 1/2 degrees of freedom? I know that with for instance n degrees of freedom the interpretation is that this is the number of squared standard normal ...
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### Equation 10.2 from The Elements of Statistical Learning. Median of a chi-squared distribution

I'm reading about AdaBoost in the The Elements of Statistical Learning and I don't understand the equation 10.2. Below is an excerpt from the book. The power of AdaBoost to dramatically increase the ...
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### Distribution of $\mathbf{v}^{\top} \Sigma^{- 1} \mathbf{v}$, when $\mathbf{v}$ is a multivariate normal with covariance $\Sigma$? [duplicate]

What is the distribution of the quadratic form $\mathbf{v}^{\top} \Sigma^{-1} \mathbf{v}$, when $\mathbf{v}$ is a multivariate normal with covariance $\Sigma$ and zero means? I suspect this is related ...
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### Moments (mean and skewness) of an AR(1) process with Chi2 or Gamma innovation distribution

A bit of context I am looking for a lag-1 autoregressive process with non-Gaussian innovation/residual error, which is capable of producing both skewed and non-skewed marginal distributions. I am ...
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### Converting Log-Likelihood to Chi-square

I'm using two different algorithms to get a periodogram. One outputs log-likelihood and the other outputs chi-squared test statistic, but I would like a way to convert from log-likelihood to $\chi^2$ ...
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### At chi squared qq plot, shouldn't normal samples be placed diagonally with chi-square?

I tried to draw a chi-square qq plot from sample following a bivariate normal distribution. This is my code: ...
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### What does "having excellent Likelihoods" mean ? (MCMC code) [closed]

I asked an astrophysicist about MontePython code (MCMC code). He told me that its team had excellent Likelihoods about a cosmological survey. What does "having excellent Likelihoods" mean ? ...
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### Non-centrality of likelihood ratio test statistic chi2 under alternate hypothesis

I am having trouble understanding how to determine the non-centrality parameter of the $\chi^2$ distribution symptotically followed by the likelihood ratio test statistic if the data follow the ...
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### How to rearrange a ratio of Gamma functions to code it

I have to evaluate the following ratio: $\frac{\Gamma(\frac{x}{2} - \frac{1}{2})}{\Gamma(\frac{x}{2})}$ I am coding in MATLAB and I have this equation inside a loop. $x$ takes values between 2 and 400....
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### Multiplying a chi-square distribution by a constant

If $X\sim\chi^{2}(3)$. What is the distribution of $2X$?
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### Can I use scipy.stats.chisquare and chi2_contigency interchangably?

The original question was here. Here is my extended question - If I use scipy.stats.chisquare, and set any one group as the "expected distribution" and the other group as "observed"...
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### Determine independence/dependence of random variables

Let $Z_1$ and $Z_2$ be independent standard normal random variables. Let $W = \frac{Z_1 + Z_2}{\sqrt{2}}$ so that $W \sim N(0,1)$. Let $U = Z_1^2 + Z_2^2$ so that $U \sim \chi_2^2$. How can I ...
I don't know how to find answer to this question. The answer is given as option (D). I know that total degrees of freedom is 18-1 = 17 and degrees of freedom for factor $\alpha$ and $\beta$ are 1 ...