Questions tagged [mathematica]
Mathematica is a software package for symbolic mathematical computations.
61 questions
17
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2
answers
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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
16
votes
1
answer
1k
views
Why do Excel and WolframAlpha give different values for skewness
for the following 3 values 222,1122,45444
WolframAlpha gives 0.706
Excel, using =SKEW(222,1122,45444) gives 1.729
What explains the difference?
- 351
9
votes
3
answers
1k
views
Mathematica's random number generator deviating from binomial probability?
So, let's say you flip a coin 10 times, and call that 1 "event". If you run, 1,000,000 of these "events", what is the proportion of events that have heads between 0.4 and 0.6? Binomial probability ...
- 91
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
8
votes
1
answer
514
views
Symbolic computer algebra for statistics
What functionality should exist in a CAS that was specifically geared toward Statistics?
Symbolic algebra systems like Mathematica and Maple are often used for calculus, logic, and physics problems ...
6
votes
2
answers
1k
views
software library to compute KL divergence?
Are there any software libraries that compute KL divergences in closed form, that also give the derivatives of the KL divergence wrt the distributions' parameters? I'm using Julia, so it's ...
- 523
6
votes
1
answer
6k
views
Comparing two datasets with same variable
thanks in advance for anyone taking the time to read/answer this.
I am comparing a ground-sourced dataset versus a satellite-sourced dataset for weather conditions, such as temperature. Both sets are ...
- 175
5
votes
4
answers
6k
views
Wolfram Mathematica, MATLAB or something else?
I have only a little experience in math calculation tools. So please don't be strict if my question is not well defined :)
Which tool (Wolfram Mathematica, MATLAB or something else) is better to use ...
5
votes
1
answer
4k
views
Characterizing periodicity level of signal
What are some good ways of quantitatively characterizing the periodicity level of an approximately periodic $f(t), t \in \mathbb{R}$ signal?
I need this to tell if the output of some system is ...
- 1,408
4
votes
2
answers
305
views
Book recommendation for undergraduate stats with Mathematica
Having just completed my Bachelor with a major in math and physics, I am aware that due to my chosen specialisation, I lack a good training and exposure in statistics beyond the first year.
Could ...
4
votes
1
answer
687
views
Chi-square independence in political sciences
I've been assigned to do a cross-class project between political science and math about the behavior of voters in a democratic state. More specifically, I'm focusing on a party from a national ...
3
votes
1
answer
205
views
Visualizing a 3D dataset of proportions
I'm looking for visualization ideas for the following data:
I have a $10\times 12$ grid of points $(x_i,m_j)$, where the $x_i$ are a set of distances (e.g. 1,2,..., 10 m) and the $m_j$ are the ...
- 31
3
votes
1
answer
2k
views
How to calculate confidence and prediction bands for a linear regression using Mathematica?
I need to calculate confidence and prediction bands for a linear regression that is in the general form of $y=ax$, where $a$ is the multiplier and $x$ the variable.
I found a code in
http://...
- 505
3
votes
0
answers
532
views
How do I calculate the Bayes error of a multivariate normal Bayesian classifier?
I have a 4 dimensional feature and each of them are independent normal distributions. I want to calculate the bayesian error associated with this classifier. The covariance matrix and the mean have ...
- 131
2
votes
2
answers
289
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
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
1
answer
205
views
Prove E[Y|X] = f(X)
I have a model $Y = f(X) + \epsilon$
where $\epsilon$ is independent of $X$ and $\mathbb{E}[\epsilon]=0, \mathbb{E}\left[\epsilon^2\right]=\sigma^2$.
Show that
$$
f(X)=\mathbb{E}[Y \mid X]
$$
This is ...
- 25
2
votes
2
answers
2k
views
Choosing center of histogram bins for fitting
I have a bimodal distribution, and if plotted with Mathematica it looks like this:
Now, the lowest value from the actual data is 8196 and 690720, but as seen in the plot, Mathematica lets the data ...
user213095
2
votes
1
answer
14k
views
What is a good test for comparing frequency counts between two groups?
I am looking for statistical methods used to compare frequency of observations between two groups. I have two geographical locations with data on different soil types present.
for example, my data ...
- 21
2
votes
1
answer
4k
views
Best multivariate polynomial regression
I have a dataset (x,y) where x is a n-dimensional vector and y is an m-dimensional vector. (m=3, n>2) My goal is to find the best polynomial in x fitting the (x,y) dataset.
The dimension of x is ...
- 267
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
417
views
Linear Regression Coefficient Interpretation [closed]
I have a regression problem: regress y on x1 x2
y: Sales revenue, x1: is_holiday (dummy variable), x2: another continuous variable (note that this is just the ...
- 21
2
votes
1
answer
518
views
2
votes
0
answers
1k
views
How can I compute the lower and upper bounds of a confidence interval in a linear regression problem?
I am completing a university statistics assignment on the Mathematica program, and this is the initial question:
"The Medical Research Council wanted to evaluate the
effects of different dosages of a ...
- 21
2
votes
1
answer
295
views
Frequency of a wavelet filter
Assume that I have decomposed a data set using Symlet Wavelet with six levels. How can I estimate the approximate frequency interval of each level?
That would be great if you consider your answer in ...
- 505
1
vote
1
answer
5k
views
How can I calculate the autocorrelation of a signal in Mathematica environment?
I tried CorrelationFunction[Transpose[{data,data}]][[All,1,2]] but it doesn't work! I mean the results are identical with those if I run ...
- 505
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
2
answers
66
views
Comparing two crash rates and determine if they are statistically significant
Let's say I have two version of an App. Version A goes to 1000 users and Version B goes to 800 users.
A month into testing, I have all of my crash data and crash percentages for both of the versions. ...
- 11
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
251
views
Find $\mathbb{E} \bigg[ \frac{\textbf{h}^{H} \textbf{y}\textbf{y}^{H} \textbf{h}}{ \| \textbf{y} \|^{4} } \bigg]$ with Mathematica? [duplicate]
Considering the following complex random vectors (Complex Gaussian random variables):
\begin{align}
\textbf{h} &= [h_{1}, h_{2}, \ldots, h_{M}]^{T}\ \ \sim \mathcal{CN}(\textbf{0}_{M},d\textbf{I}_{...
1
vote
1
answer
524
views
Residuals not normal due to random effects structure
I am new to mixed-effect models and statistics, and I need to do a project for my thesis using mixed-effect modeling techniques.
My research aims to model how cardiovascular risk scores change over ...
- 11
1
vote
1
answer
2k
views
How do we update the parameters (weights) in recurrent neural networks?
In RNNs, how do we update the weights?
I have following understanding of RNNs:
Parameters are shared across all time-steps, i.e.,
$$S_t = \tanh(U X_t + W S_{t-1} )$$
$$Y_k = \text{softmax}(V S_t)$$
...
- 31
1
vote
1
answer
34
views
How to expand $\text{erf}\bigg(\frac{(ax-b)}{\sqrt{2}}\bigg) = \text{erf}\bigg(\frac{ax}{\sqrt{2}}\bigg) + \text{some_value}$?
The error function is defined as, $$\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
3k
views
On what basis we are evaluating variance is high or low? [closed]
I am having a below case where N = 300 , Mean = 67 and SD = 30. With the above data we can say the variance is high because of SD = 30. My question is how we are defining it as high on what basis we ...
- 111
1
vote
2
answers
496
views
Unkown 6-sided dice. After 600 rolls frequency for all sides exactly equal. What is the chance, that rolling "6" with this dice has frequency > 1/6?
Although it is unknown dice, the symmetry of the evidence tells us, that we can treat the dice as fair, so the chance should be exactly 50%.
But if we simulate it by hand, the result is less then 50%:...
- 2,200
1
vote
1
answer
1k
views
Normalizing error variance scale
Imagine we have two sets of data m1 and m2. m1 components have the dimension of [m^2/s] and m2 components are measured in [cm^2/s].
e.g.
...
- 505
1
vote
1
answer
107
views
How to simplify the understanding behind Hypothesis Testing? [duplicate]
Quote recently, I have trying to understand this confusing idea of Hypothesis testing. Although I am pretty much clear with the way it works, that is:
Choosing a test statistic
Then choosing a Null ...
- 11
1
vote
0
answers
84
views
What mathematical background do I need to do research in field of deep learning
I am familiar with few deep learning models and I understand how (little bit why) CNN/RNN works. But I still cannot make sense of new research papers. I want to dive deeper into field of deep learning ...
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
105
views
How can I incrementally calculate the 4 central moments in statistics (mean, standard deviation, skewness and curtosis) when a value is removed?
I'm incrementally calculating the 4 central moments. When a value x is added and n, M1, M2, M3 and M4 are some predefined values, I'm using the following algorithm:
...
- 11
1
vote
1
answer
435
views
Deriving parameters of an extreme value distribution from an initial distribution for finite n
Background:
For my research I've been trying to model brittle fracture mathematically. The basic concept is that a brittle materials fail because already existing small defects such as small cracks ...
- 13
1
vote
0
answers
53
views
Measuring Autocorrelation in Tail Events
I have a single time series of financial data (stock index returns) and would like to study the autocorrelation among (log-)returns that are classified as "extreme", for example via exceedance of a ...
- 111
1
vote
0
answers
36
views
Visualising n vectors of length n in a periodic fashion
I'm currently working on a specific problem in a periodic structure, for which I obtain a set of eigenvectors that I would like to plot. It is probably easiest if I give you an explicit example, then ...
- 211
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
1
answer
176
views
mathematical proof that if the vectors 𝑞⃗ and 𝑑𝑖 all are normalized unit vectors [closed]
In a vector space model when we are given a query as a vector 𝑞⃗ and documents 𝑑1
, 𝑑2 …, we usually rank
the documents in relevance to the query vector using cosine similarity. Show by a ...
0
votes
1
answer
2k
views
How to read/visualise this confusion matrix?
I was offered a confusion matrix, which is called Parametrised 5x5 confusion matrix by authors where I extracted the values and where the diagonal has the correct results (0 in all); the results are ...
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
0
votes
1
answer
868
views
Neural Network - Classification from Time series
I'm a .Net programmer who is fairly new to neural networks, but I know some of the concepts.
I have connected .Net to my copy of Mathematica 10
This is a classification
Our business problem is ...
- 103
0
votes
1
answer
99
views
Difference in output from mvtnorm and Mathematica/Java [closed]
Let $a \sim\mathcal{N}(6.532056,0.06532056)$,$b \sim\mathcal{N}(8.390961,0.08390961)$ and $c \sim\mathcal{N}(8.736566,0.08736566)$. We use $\mathcal{N}(\mu,\sigma^2)$ notation unless specified ...
0
votes
1
answer
59
views
How to produce synthetic (fake) data knowing the correct fit parameters?
For cross-checking purposes, if I want to check that a NonlinearModelFit performed in Mathematica is producing the correct standard errors, I would need to produce simulated data based on the fitted ...
- 25