All Questions
Tagged with variance distributions
198 questions
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Bishop Gaussian Basis
In Pattern Recognition and Machine Learning by Christopher Bishop he says in Section 3.3.2 titled Predictive distribution
If we used localised basis functions such as Gaussians, then in regions away
...
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1
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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
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1
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64
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How would one describe such irregular data?
The situation is as follows (physics based): I have an array (7) of pixel sensors (imagine phone cameras) and a ton (millions) of particles crossing them (very large N). Each particle crossing a ...
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79
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Construct an estimator for the asymptotic variance of the MLE and and its asymptotic distribution
This is a question I have come across while learning about statistical inference and data analysis.
I think I have been able to solve question (a) and (b) already.
My solutions are:
$$
\hat{p}_{MLE} = ...
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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 ...
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30
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How to establish what distribution to compare my statistic to
Apologies for this poorly titled question, but I've been taking some statistics courses and sometimes when you try to learn too many things in too little time you want to take a step back to check if ...
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42
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Given two rvs $X$ and $Y$, if $X Y = Z$, is it possible to change the mean and sd of $X$ without changing the mean and sd of $Y$ and $Z$
I have two lognormal rvs $X$ and $Y$, and a third rv $Z$ which is the product of the former two. I know the mean and standard deviation of the three.
Is it possible to calculate an alternative pair of ...
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What is the distribution of a Poisson-Binomial variable where the probabilities of success are from another distribution?
If I have a Poisson-Binomial random variable $X$ built from $n$ trials where I draw each $p_i$ as either $a \in \left[0, 1 \right]$ or $b \in \left[0, 1 \right]$ with equal probability. How can I find ...
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186
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equal *population* variances in paired t test
I I want to perform a paired t-test to check if there's some effect, I have the distribution of "before" and the distribution of "after" the manipulation. Do I need to assume the ...
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47
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Why Does the Fisher Scoring Algorithm "Work"? [duplicate]
I was reading the following link (https://en.wikipedia.org/wiki/Scoring_algorithm) on the "Fisher Scoring Algorithm". As I understand, the Fisher Scoring Algorithm is similar to the Newton-...
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238
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Taking derivative of a function containing random variable wrt the variance of that variable [closed]
Say, I have a function containing a random variable such as $ f(X)$, where $X $ is the random variable that comes from a family of random variables that differ only in the first and second moments (e....
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88
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Is there a measure other than variance to know dispersion?
I have (x,y) values where x are integers that range from 0 to 843, and there is only one y value per x value.
And then I have a set S, which are (x,y) values. If an element of S is selected, it should ...
- 121
3
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2
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149
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Good teaching activities for variability and standardized distributions for undergrad stats
As the question states, I am looking for some warmup activities for teaching undergrads practical examples of variation and standardized distributions. I think the first part is relatively easy to ...
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65
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Compute Expectation and Variance of number of upper records
I should solve the following:
Let $X_i,...,X_n$ be independent random variables such that for any i, j, i$\neq$j: $P(X_i=X_j) = 0$. Then, $X_i$ is an upper record iff $X_i > \max$ {$X_1,X_2,...,X_{...
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Estimate Conditonal Moments from Conditonal Quantiles
In Chang et al. "The Higher Moments of Future Earnings" (2014), the authors say say that based on (predicted) conditonal quantiles of a variable $y$, one can derive the (predicted) ...
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468
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How to derive the short cut version of variance calculation for probability distribution
How to derive from formula 2 to 3?
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86
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When would the variance for a probability distribution give the same result as the standard equation?
Variance equation for a probability distribution:
$$
\sigma^2 = \sum_{i=1}^{N}(x_i-\mu)^2P(X=x_i)
$$
Standard variance equation:
$$
\sigma^2 = \frac{1}{N}\sum_{i=1}^{N}(x_i-\mu)^2
$$
I understand that ...
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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 ...
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1
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158
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More academic-sounding term for high-variance
The goal is to find a term to describe a distribution that fits with the other "lofty"-sounding words like:
Skewness: mode!=mean / symmetry
Kurtosis: How "fat" the tail is
???: ...
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3
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151
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Calculate the variance of a distribution analytically
I want to calculate the variance of a certain distribution.
I have a rectangle that is getting shifted to the right (i.e. shear transformation). To obtain the distribution I am computing the value of ...
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1
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27
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Estimation of mean, variance, proportion for cakes baking in 30 ± 2 minutes, or estimation of parameters of a law for a distribution: is it the same? [closed]
I'm a beginner in statistics and I'm trying to figure things to ensure that I can consider parameters the same manner in two cases :
I believe that if we have enlighten a distribution with the ...
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1
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111
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Mean variance relationship
I am working on a dataset on time devoted to domestic work by individuals I have grouped the data based on the day of the week the information has been collected. This was done to examine the relation ...
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151
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How to derive the determinant of the variance of a negative multinomial distribution?
The probability mass function of the negative multinomial distribution is:
\begin{align*}
\mathbb{P}(\boldsymbol{\rm{X}}=\boldsymbol{\rm{x}}|\mathbf{p})=\frac{\Gamma\left(x_0+\sum_{i=1}^{m}x_{i}\right)...
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711
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Why does "Hoeffding's bound greatly overestimates the probability of large deviations for distributions of small variance"?
I've read in a paper using Hoeffding's inequality to derive a bound on the probability of the difference of means of two samples being larger than a threshold that "Hoeffding's bound greatly ...
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1
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293
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covariance of lognormal random variables
I am trying to find the variance of b*log(x+y) - log(x), where x and y are independent and identically distributed lognormal random variables, the range for log(x) and log(y) is negative infinity to ...
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69
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Variance properties of transformed p-values using the standard normal distribution
I am searching for a reference or proof for the following situation:
Let t_df denote a t-test statistic for given degree of freedom df. The null hypothesis being tested is H_0: $\delta$ <= 0. ...
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54
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If variance of overlapping sums > variance of underlying?
Starting with a sample series $x_1, ..., x_n$, I generate overlapping sums $y_i = \sum(x_i,...,x_{i+9})$.
If $X$ ~ Normal then it appears that $Var(Y) \approx 10 \times Var(X)$.
But for samples from ...
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Under what conditions are there pairwise monotonic relationships between mean, variance, and (positive) skewness of a lower-bounded distribution?
I am dealing with empirical data, integer- and continuous-valued, with a lower bound (at zero) that are often positively skewed, and seem to be following either the Poisson, $\chi^2$, binomial, or ...
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63
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Why doesn't the t distribution depend on variance of the original normal distribution?
I just find it counter intuitive that, for an arbitrary normal distribution with 0 mean and unknown variance, the t statistic of $\frac{\bar{X}}{\hat{se}} $ is completely independent of the variance ...
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3
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71
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Distribution where the variance diverges for some parameter values but not others
I'm wondering whether there's a standard / nice / tractable family of distributions where the variance is defined for some parameter values but not others, while the mean stays finite.
I'm imagining a ...
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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 \...
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70
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what is the probability of sample variance when true variance and true mean is unknown?
Sample Variance by definition is $s^2 =\frac{1}{n-1} \sum{(x_i-\bar{x})^2}$
When the population distribution is normal and true variance $\sigma^2$ is known, Sample Variance follows the chisq ...
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Meaning of "Overdispersion" in Statistics
I am trying to understand what "overdispersion" means in statistics.
Based on the Wikipedia page, "overdispersion" is defined as follows : "In statistics, overdispersion is ...
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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 ...
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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, ...
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How $Var[e^{\frac{-1}{X+a}}]$ varies with $n$ where $X \sim Bin(n,p)$?
I have a binomial random variable $X \sim Bin(n,p)$. I am interested in the variance of a function $f(X)$ given by :
$f(X)=e^{\frac{-1}{X+a}}$. Here $a>0$.
Specifically, I would like to know how $...
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Does skewness decrease standard deviation ceteris paribus?
For a given probability distribution, probability mass must sum to 1, thus by increasing a parameter corresponding to skewness do you shift probability away from the second central moment (variance) ...
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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 ...
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Is it possible for a distribution to have infinite variance but finite covariance or vice versa?
Is it possible to have distributions s.t. one/both have infinite variance, but finite covariance? What about finite variance but infinite covariance?
If so, what are example distributions/what is the ...
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What is the distribution of cross-sectional volatility?
Assume we have a set of $N$ random variables with known multivariate distribution $\boldsymbol{X}\sim\mathcal{N}(\boldsymbol{\mu},\boldsymbol{\Sigma})$, and a series of realisations $\{\boldsymbol{X_t}...
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Intuition for hypergeometric variance?
I'm trying to learn the major facts about a bunch of probability distributions, hypergeometric included. I can use the commonalities between it and a binomial to my advantage for thinking through some ...
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what is the relationship between the two standard errors
I have two variables $X$ and $Y$.
Consider that there is one sample with 1000 observations, we can get the standard error of coefficient by this equation:
$se(\hat\beta) = \sqrt{\sigma^2(X^TX)^{-1}}$.
...
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109
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Distribution of $2X$
I’m fairly new to statistics
I’m confused if the distribution of a random variable $X$ and $2X$ are the same, since the variance of the latter is $\mathbb{V}(2X) = 4 \mathbb{V}(X)$. Is it exactly the ...
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2
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242
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Variance of a derived magnitude
I'm wondering about how to present results on a report (and how to interpret it).
Let $Y = f(\mathbf{X})$ be a random variable. Of course, if we derive its PDF $f_{Y}(y)$, we could present it on the ...
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72
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Variance of $\operatorname{tr}(W^2)$ with $W \sim \text{Wishart}(n, \Sigma)$
Suppose $W \sim \text{Wishart}(n, \Sigma)$, where $\Sigma \in \mathbb R^{p\times p}$, the expectation of $\operatorname{tr}(W^2)$ is
$$E[\operatorname{tr}(W^2)] =n(n+1)\operatorname{tr}(\Sigma^2) + n\...
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478
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Mean and variance of likelihood function wrt data
In my previous question I asked about the distribution of the likelihood function as a random function depending on the sample of data we have. It seems that this distribution depends on the ...
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3
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309
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Mean absolute difference for the gamma distribution
A wikipedia entry states that the mean absolute difference for the $\Gamma(k,\theta)$ distribution is $k\theta(4I_{0.5}(k+1,k)-2)$ where $I_z(x,y)$ is the regularized incomplete beta function, equal ...
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424
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Does sample variance has a Chi-square distribution?
Let $X_1, X_2, \ldots, X_n$ be a random sample from $N(\mu, \sigma^2)$. Does
$S^2=\frac{\sum^n_{i=1}(X_i-\bar X)^2}{n-1}$ has a Chi-square distribution?
I know that $\frac{(n-1)S^2}{\sigma^2}=\frac{\...
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136
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Bootstrapping variance in R gives weird shaped distribution- how to obtain confidence intervals?
this is the first time I've used bootstrapping so it's quite basic!
I'm trying to obtain confidence intervals for the standardised variance- defined as the variance over the square of the mean- across ...
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42
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What family of full support probability distributions satisfy that the density of any point in the domain vanishes as the variance goes to infinity?
Let $f(x,\sigma^2)$ be a representative element of a family of PDF's with full support over the reals that is indexed by their variance $\sigma^2$. Under what general conditions of the family of ...
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