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Mathematica is a software package for symbolic mathematical computations.

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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 ...
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0answers
60 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 ...
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2answers
83 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 ...
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2answers
97 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 ...
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1answer
68 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}_{...
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2answers
108 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 ...
0
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1answer
56 views

$X_1, X_2$ are IID $N(0,1)$. Find Cov($X_1$, $X_1 X_2$).

Two variables $X_1, X_2$ are independent and identically distributed as $N(0,1)$. I need to find Cov($X_1$, $X_1 X_2$). Thanks!
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1answer
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 ...
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2answers
1k views

How to implement density-based clustering?

I’m looking to implement density-based clustering with R or Mathematica on a giant file (600,000 points on a 3 billion x 3 billion plane). Is DBSCAN the right method for data that is this sparse? I am ...
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2answers
49 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. ...
4
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1answer
3k 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 ...
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1answer
43 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 ...
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0answers
37 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 ...
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0answers
29 views

Why fitting does not find the true best point

I fitting an expression of the form: $s(t)=\frac{1}{1+\exp[a+\sum_k b_k x_k(t)]}$ Where $a$ and $b_k$ are fitting parameters and $x_k(t)$ an input time series. I have $k=1,...,N$ different types of ...
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1answer
110 views

Fitting one set of data with two functions

I have a set of data (42 points): ...
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1answer
7k 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 ...
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0answers
33 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 ...
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2answers
91 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, ...
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2answers
645 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 ...
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0answers
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 ...
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2answers
236 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 ...
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2answers
400 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)=-\...
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1answer
695 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 ...
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3answers
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 ...
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How can I fix a poor nonlinear curve fit?

I was trying calculating Fourier transform of some rings. as follow: By directly calculating of model as several rings, the result showed different from the the experimental ones. So I tried to get ...
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0answers
367 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 ...
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1answer
77 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 ...
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2answers
342 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%:...
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1answer
184 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 ...
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1answer
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 ...
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2answers
192 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 ...
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4answers
5k 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 ...
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0answers
255 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 ...
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2answers
305 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 ...
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1answer
3k 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 ...
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1answer
439 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 ...
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1answer
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://...
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1answer
2k 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 ...
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1answer
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. ...
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1answer
270 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 ...
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1answer
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 ...
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1answer
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?