All Questions
11 questions with no upvoted or accepted answers
2
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234
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Calculate Variance from Dirichlet-like Distribution Empirically
I'm interested in the proportion of time that a sensor is in a particular state. The sensor tells me the amount of time that it's in each state, which I will denote by $X = \{ X_1, X_2, X_3\}$. I ...
- 737
1
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0
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86
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How to find $\mathbb{E} \left[\frac{\bar{\mu}}{\bar{\sigma}^2}\right]$?
I asked the same question on math stacks: MathStacks:, and some user suggest to ask it here for better insight. So this question has found interest in many research problems, but there have been no ...
- 11
1
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0
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32
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Finding variance from normal distribution
Suppose $Z_1$ and $Z2$ ~$N(0,1)$
Let $X_1=2Z_1$ and $X_2=X_1+\frac{\sqrt{3}}{2}Z_2$
Let $Y_1=\sqrt{3}Z_1+Y_2$ and $Y_2=Z_2$
I understand I have to show the mean and variance for $X_1$ and $X_2$ should ...
- 183
1
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0
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130
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Variance of a vector-valued random variable along a unit vector
Let $X$ be a vector-valued random variable with variance $\mathbb{V}[X] < \infty$. How is the variance of $X$ along a unit-vector $\hat{v}$ defined? Can we say that in general it is $\hat{v}^\top \...
- 2,286
1
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52
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Correlation Based Models vs Covariance Based Models
I am trying to better understand why some models are "covariance based" vs. why some other models are "correlation based".
1) For example, a Multivariate Normal Distribution ...
1
vote
0
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145
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Dirichlet distribution parameters from known variances
Let's assume, I know the variances of Dirichlet distribution parameters. Let these variances be:
$Var[X_1], ..., Var[X_n]$.
Is there a analytical solution to derive the parameter value alpha_i given ...
1
vote
0
answers
88
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What are meaningful ways to interpret Monte Carlo-simulated non-normal data?
My question relates to Confidence Interval (CI) calculation of Monte Carlo-simulated non-normal data
As answers and comments to that question show the confidence interval for the given distribution ...
- 113
0
votes
1
answer
101
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Variance of Multimodal Generalized von Mises Distribution?
How do you calculate the variance of a Multimodal Generalized von Mises (MGvM) distribution? Given its complexity with multiple modes and asymmetry, I'm looking for:
Any formula or method to calculate ...
- 113
0
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0
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178
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Calculating the Standard Deviation of Estimates from a Uniform Distribution
I was looking at this question on Sufficient Statistics and the Uniform Distribution: https://math.stackexchange.com/questions/1359183/why-should-we-care-about-sufficient-statistics
In this question, ...
0
votes
1
answer
181
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Variance of scalar function of 2 random variables
Suppose I have a scalar function $g(X,Y)$, where $X$ and $Y$ are jointly distributed with pdf $p(x,y)$. I think the expected value of $g$ is given by
$$ \mathbb{E}[g] = \int_{-\infty}^\infty \int_{-\...
- 1
0
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0
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1k
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MGF of sample variance
Let $$s^2=\sum\limits_{i=1}^n\frac{(X_i-\bar{X})^2}{n-1}$$ be the sample variance of a random sample of size $n$ from $N(\mu,\sigma^2)$. I am trying to derive the mgf of $s^2$ but have probably made a ...
