All Questions
Tagged with mathematica distributions
12 questions
17
votes
2
answers
689
views
What's the distribution of $(a-d)^2+4bc$, where $a,b,c,d$ are uniform distributions?
I have four independent uniformly distributed variables $a,b,c,d$, each in
$[0,1]$. I want to calculate the distribution of $(a-d)^2+4bc$. I computed the distribution of $u_2=4bc$ to be $$f_2(u_2)=-\...
- 1,264
8
votes
2
answers
811
views
PDF of a sum of dependent variables
This is a direct continuation of my recent question. The thing that I actually want to get is the distribution of $a+d+\sqrt{(a-d)^2+4bc}$, where $a,b,c,d$ are uniform in $[0,1]$. Now, the ...
- 1,264
2
votes
1
answer
2k
views
How to estimate true value and 95% bands when distribution is asymmetrical?
I have a set of results of independent measurements of some physical quantity. As an example I give here real expermental data on methanol refractive index at 25 degrees Celsius published in ...
- 253
2
votes
0
answers
108
views
Maximum Uncertainty in Normal Distribution
While reading Goodfellow's Deep Learning Book, I came across the below fact about Normal Distribution. I am not sure I have understood what led to this conclusion, Can someone help with it?
"Out ...
- 51
2
votes
1
answer
518
views
1
vote
3
answers
271
views
Samples from a multivariate t distribution
Hi I have the following problem.
I draw a sample of a multivariate t-distribution with some fixed covariance matrix,
so that the realizations are correlated, and $\nu=4$. Now I repeat this $n$ times, ...
- 13
1
vote
1
answer
53
views
Number of simulated statistics more extreme than most extreme real data statistic
I have a distribution of $n_{obs}$ "real" data observations drawn from a normal distribution $X \sim N(\mu,\sigma^2)$, and a number $Q$ of simulated realizations of the same distribution, ...
- 13
1
vote
1
answer
34
views
How to expand $\text{erf}\bigg(\frac{(ax-b)}{\sqrt{2}}\bigg) = \text{erf}\bigg(\frac{ax}{\sqrt{2}}\bigg) + \text{some_value}$?
The error function is defined as, $$\text{erf}\bigg(\frac{(ax-b)}{\sqrt{2}}\bigg) = \frac{2}{\sqrt{\pi}}\int_{0}^{\frac{(ax-b)}{\sqrt{2}}} e^{-t^{2}/2}dt$$. My question is how to expand the above ...
- 335
1
vote
1
answer
132
views
Is there any relationship between two normalized gamma distributions?
Consider two normalized gamma distribution functions $\frac{\Gamma(x,y)}{\Gamma(x)}$ and $\frac{\Gamma(nx,ny)}{\Gamma(nx)}$ where $n$ is a positive integer value. Is there any relationship between the ...
- 11
1
vote
0
answers
915
views
Problem with multivariate lognormal distribution in R [closed]
I'm using the R package compositions for the multivariate lognormal distribution. This is the only package I found that supports it.
However I'm not sure how this ...
- 1,781
0
votes
2
answers
361
views
How to estimate storage needs using the PERT distribution for filesizes? How to aggregate them without falling into the flaw of extremes?
Lets say I know that I am going to store the information of 10,000 people each year for 4 years, that is 40,000 files. Now If I estimate that on the best case scenario the information from each ...
- 301
-2
votes
2
answers
1k
views
Uniform Density Function
As we know the uniform probability density function is
f(x)=1/(b-a)
if i find the density function and area of this uniform distribution between
(0, 1/2) then it would be
f(x)=1/(1/2-0)
f(x)=2
...
- 85