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Questions tagged [mathematica]

Mathematica is a software package for symbolic mathematical computations.

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17 votes
2 answers
679 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)=-\...
corey979's user avatar
  • 1,244
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?
Scott Weinstein's user avatar
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 ...
Tim McKnight's user avatar
8 votes
2 answers
777 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 ...
corey979's user avatar
  • 1,244
8 votes
1 answer
511 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 ...
Jeff's user avatar
  • 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 ...
sanjayr's user avatar
  • 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 ...
Szabolcs's user avatar
  • 1,398
4 votes
2 answers
300 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
682 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 ...
Frederik Brinck Jensen's user avatar
3 votes
1 answer
203 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 ...
amet's user avatar
  • 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://...
K-1's user avatar
  • 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 ...
karthik A's user avatar
  • 131
2 votes
2 answers
286 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 ...
Alexey Popkov's user avatar
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 ...
Alexey Popkov's user avatar
2 votes
1 answer
173 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 ...
Cabbage Roll's user avatar
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 ...
user avatar
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 ...
Jia's user avatar
  • 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 ...
Flavian's user avatar
  • 267
2 votes
0 answers
89 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 ...
umesh's user avatar
  • 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 ...
Hyoceansun's user avatar
2 votes
1 answer
514 views

Fitting one set of data with two functions

I have a set of data (42 points): ...
fejsa's user avatar
  • 21
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 ...
Ana's user avatar
  • 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 ...
K-1's user avatar
  • 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 ...
K-1's user avatar
  • 505
1 vote
3 answers
245 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, ...
ani's user avatar
  • 13
1 vote
2 answers
64 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. ...
Userk1345's user avatar
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, ...
user406833's user avatar
1 vote
1 answer
241 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}_{...
Felipe Augusto de Figueiredo's user avatar
1 vote
1 answer
379 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 ...
Chen Sophie's user avatar
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., $$S_t = \tanh(U X_t + W S_{t-1} )$$ $$Y_k = \text{softmax}(V S_t)$$ ...
Mins's user avatar
  • 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 ...
score324's user avatar
  • 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 ...
Santhanam's user avatar
  • 111
1 vote
2 answers
495 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%:...
Adam Ryczkowski's user avatar
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. ...
K-1's user avatar
  • 505
1 vote
1 answer
98 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 ...
Elemento's user avatar
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
130 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 ...
Russel J's user avatar
1 vote
0 answers
101 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: ...
C.Ompiler's user avatar
1 vote
1 answer
401 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 ...
Brasol's user avatar
  • 13
1 vote
0 answers
51 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 ...
CFW's user avatar
  • 111
1 vote
0 answers
35 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 ...
user129412's user avatar
1 vote
0 answers
911 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 ...
spore234's user avatar
  • 1,771
0 votes
1 answer
173 views

mathematical proof that if the vectors 𝑞βƒ— and 𝑑𝑖 all are normalized unit vectors [closed]

In a vector space model when we are given a query as a vector π‘žβƒ— and documents 𝑑1 , 𝑑2 …, we usually rank the documents in relevance to the query vector using cosine similarity. Show by a ...
Eng.Anmar Sadiq's user avatar
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 ...
Léo Léopold Hertz μ€€μ˜'s user avatar
0 votes
2 answers
359 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 ...
Luxspes's user avatar
  • 301
0 votes
1 answer
865 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 ...
toddmo's user avatar
  • 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 ...
Sandipan Bhattacharyya's user avatar
0 votes
1 answer
56 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 ...
Houndbobsaw's user avatar