All Questions
32 questions
0
votes
1
answer
101
views
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
1
vote
0
answers
86
views
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
0
votes
0
answers
47
views
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-...
1
vote
0
answers
239
views
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....
- 11
2
votes
1
answer
86
views
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 ...
- 123
1
vote
0
answers
32
views
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
vote
0
answers
130
views
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
14
votes
4
answers
6k
views
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 ...
1
vote
0
answers
52
views
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 ...
0
votes
0
answers
178
views
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, ...
4
votes
2
answers
72
views
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 $...
- 224
1
vote
0
answers
145
views
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 ...
0
votes
1
answer
466
views
Find variance of an estimator
Let X1,X2..,Xn a random sample from a population X having distribution function
$f(x;θ) = θx^{θ - 1}$ if 0 < x < 1
Where θ > 0 is a parameter. Is the estimator $θ = \frac{x̄}{1 - x̄}$ of θ ...
- 217
2
votes
1
answer
1k
views
Difference between Variance $\sigma^2$ and variance in binomial distribution
I am reviewing some basic statistic concepts. Now I am not sure what 's the difference between variance
$$\sigma^2=\frac{1}{N}\sum^N_{i=1}(x_i-\mu)^2.$$
and binomial distribution
$$\mathrm {Var}(X)=np(...
- 161
1
vote
1
answer
41
views
Question relating to joint PDFs
Here are my questions:
Let $X$ ~ Unif$(0, 1)$, and $0<a<b<1$. Also, let
\begin{cases}
Y = 1 & \text{if $0<X<b$} \\
...
- 25
3
votes
2
answers
95
views
$X$ has distribution function $F(x) = e^{-e^{-x}}$. Justify that such a probability measure on $\mathbb{R}$ exists
How can I prove a probability measure exists? If $F(x) \rightarrow 1$ as $n \rightarrow +\infty$, does that mean $F(x)$ does exist? And how should I calculate $\mathbb{E}(F(X))$ and $Var(F(X))$?
- 31
1
vote
0
answers
8k
views
How to calculate variance or standard deviation for product of two normal distributions? [duplicate]
For example if I have two multiplied distributions a * b:
...
- 111
0
votes
1
answer
181
views
Variance of scalar function of 2 random variables
Suppose I have a scalar function $g(X,Y)$, where $X$ and $Y$ are jointly distributed with pdf $p(x,y)$. I think the expected value of $g$ is given by
$$ \mathbb{E}[g] = \int_{-\infty}^\infty \int_{-\...
- 1
1
vote
1
answer
4k
views
Does the peak of a Normal Distribution mean anything? [closed]
What does the peak of a Normal distribution show? Let's say if I have a flat peak, does this mean I have a larger variance? What if I have a sharp peak?
For example,
Does the "blue distribution" ...
- 581
6
votes
3
answers
2k
views
Binomial distribution intituition for N
I am unable to convince myself intuitively as to why the variance of a binomial distribution increases with increase in n (number of trials). In general, I expect that as n increases, the distribution ...
- 113
2
votes
2
answers
196
views
Variance being negative
Let $X$ and $Y$ have joint pdf such that
$$f(x,y) = 3e^{-3x-y}, 0 < x< \infty, 0< y< \infty.$$
(a) Show that $X$ and $Y$ are independent.
(b) Calculuate $Var(X)$.
In ...
- 21
0
votes
1
answer
213
views
Do the location and scale parameters always control the mean/median/mode and variance, respectively?
Does a location parameter always control the mean/median/mode values of a PDF?
Does a scale parameter always control the variance of a PDF?
If the answer to any of the above questions is yes, then ...
- 115
2
votes
0
answers
234
views
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
5
votes
1
answer
3k
views
How do we derive that $S^2$ is chi-squared distributed (with $n-1$ df)?
The claim is that $$(n-1)S^2/\sigma^2$$ is chi squared distributed with degrees of freedom $n-1$.
$(n-1)S^2/\sigma^2$ can be written as $$\sum_i^n \left(\frac {x_i-\mu}{\sigma}\right)^2-\left(\frac {...
- 2,987
1
vote
0
answers
88
views
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
-2
votes
1
answer
97
views
Representing a distribution of probabilities
I'm running a simulation where, for every iteration $i$, I get a detection probabilities $P_i$. Because of the law of total expectation, I think the overall detection probability (i.e. marginalizing ...
- 167
6
votes
1
answer
458
views
How to estimate variance of sample variance?
Given an arbitrary sample, sample variance would be calculated. But how the variance of sample variance should be estimated? I tried to do some simulations using influence functions estimation methods....
- 211
5
votes
1
answer
541
views
Expected value and variance of moving a token on a cartesian plane based dice rolls
A fair four-sided die has its sides labeled U, D, L, and R, respectively. A token is placed at (0, 0) on the Cartesian plane and the die is then rolled repeatedly. After each roll, the token is moved ...
- 55
1
vote
1
answer
56
views
If $X=A-F/3$, how to calculate $E(X)$, $Var(X)$ and $P(X≥5)$?
The exercise
An examination of questions with multiple answers, has 20 questions, and each question consists of 4 alternatives, one of which is correct.
The student's score is a random variable $ X $...
- 169
6
votes
2
answers
1k
views
Variance of the modulus of a random variable
Let $X$ be a random variable with mean $\mu$ and variance $\sigma^2$. What is the upper-bound on the variance of $Y=\left|X\right|$?
My gut feeling says that $\operatorname{Var}(Y) \leq \operatorname{...
- 591
1
vote
1
answer
87
views
Confusing variance question
$E(x) = 4$ and $V(x) = 6$
What is the variance of $y=5x+2$?
$E(5x+2) = 5\times 4+2 = 22$
I don't get how the answer is 150
I thought it was $(x-\bar{x})^2$
$(4-22)^2 =324$
very confused
- 177
0
votes
0
answers
1k
views
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 ...
