# Questions tagged [mathematica]

Mathematica is a software package for symbolic mathematical computations.

45 questions
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### Why the ratio of (distance from expectation)^2 / expectation in a goodness fit test follow a chi-square distribution?

I know that the sum of square of normal random variables follow a chi-square distribution. But when I learn how to do a goodness-fit test I don't know why the ratio of (O-E)^2/E follows a chi-square. ...
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### How to derive the gradient for SSE cost function in Adaline?

I started learning machine learning and have some troubles in understanding derive rules for the gradient of cost function in particular I can't understand how sum(wjxj) transformed to -xj. I tried to ...
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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 ...
77 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 ...
155 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 ...
168 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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### 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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### 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 ...
67 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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### 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 ...
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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### 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. ...
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### 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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### 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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### 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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### 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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### Fitting one set of data with two functions

I have a set of data (42 points): ...
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### 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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### 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 ...
92 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, ...
692 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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### 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 ...
247 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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### 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)=-\...
746 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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### 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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### 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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### 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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### 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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### 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 ...
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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### 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 ...
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 ...
299 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 ...
311 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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### 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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### 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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### 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://...
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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### 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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### 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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### 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 ...